University of Nigeria Research Publications

CHARLES, M.C Ichoku

Aut

hor

PG/M.Sc/83/2170

Title

Evaluation of the Zeiss C-8 Precision Coordinatograph for Use as a Monocomparator

Facu

lty

Environmental Studies

D

epar

tmen

t

Surveying, Geodesy and Photogrammetry

Dat

e January, 1987

Sign

atur

e

EVALUATION OF THE ZEISS C-8 PRECISION

COORDINATOGRAPH FOR USE AS A

MONOCOMPARATOR

ICHOKU, CHARLES MBADUGHA CLIFFORD

B. Sc (Hon s) Surveying, Geodesy and

Photogrammetry

January 1987

EVALUATION OF THE ZEISS C-8 PRECISION COORDINATOGRAPH FOR USE AS A

MONOCOMPARATOR

This research report has been approved for the Department of Surveying, Geodesy and Photogrammetry University of Nigeria, Nsukka.

. .

Supervisor

.................... External Examiner Dean of Faculty

EVALUATION OF THE ZEISS C-8 PRECISION

COORDINATOGRAPH FOR USE AS A

MONOCOMPARATOR

Dissertation submitted in partial fulfilment of the requirements for the award of Master of Science (M.Sc) Degree in Photogrammetry and Remote Sensing of the Department. of suheying, Geodesy and Photogramme,try, University of Nigeria, Nsukka

ICHOKU, CHARLES MBADUGHA CLIFFORD

(PGfM.Sc/83/2170)

January 1987

SUPERVISOR: DR. N. K. NDUKWE

DEDICATION

To my parents:

. .

Mr. Fabian 0. Ichoku

and

Mrs. Grace 0. Ichoku

ABF TRACT

At times it becomes necessary to use non-

conventional instruments or devices for measurements,

especially when the conventional ones are either not

available or very expensive. In this research the

capability of the Zeiss C-8 coordinatograph as a photo

coordinate measuring instrument has been investigated.

Image coordinates of a number of selected test points

were measured on the instrument. They were refined *

and used to derive their equivalent ground coordinates.

These photogrammetrically derived coordinates were

compared with the ground survey values of the test

points and discrepancies were generated. Statistical

evaluation of results show that the procedure and

principles presented can be used for providing control

for mapping at medium and small scales, mosaic

construction, and remnnaissance surveys.

ACKNOWLEDGEMENT

The successful completion of this research has

not been achieved single-handedly. Help was

obtained from other quarters when necessary. The

persons involved are numerous and I appreciate their

individual roles; although it may be difficult to

mention all names here.

My most sincere appreciation goes to

Dr. N. K. Ndukwe - my supervisor - who actually suggestegthis topic and saw to its progress till the

end. In addition, he travelled with me when I was

having instrumentation problems initially and also

provided most of the books and other materials including

the computer programmes used.

Messrs E. I. Ulasi, J. K. Okae, V.E.N. Nwokoro,

K. C. Moemenam, A. Otu - all senior Technical staff of the Department - were involved in the field work for this research. I am very grateful fo them for their

invaluable help. I am also grateful to all the junior

technical staff who participated in the field work too.

They are Messrs D. Agu, F. Fubara, C. Ike,

A.A. Ikpeamagheze, E. Ugwu. Worth mentioning also are

Messrs M.A. Mong and John Quarshie-Doku who are in

charge of Practical Photogrammetry in the Department and

who were very helpful in various ways. Messrs E.C. Moka,

U.G.O. Okafor and O.C. Ojinnaka offered very meaningful

contributions to most of my structural and computational

problems. To all of them I express my sincere

gratitude.

I gratefully acknowledge the cooperation of the

Surveyor-General and all the staff of-the Survey Division

in the Anambra State Ministry of Works, Lands and L

Transport for allowing the use of their instrument; The

Head and staff of the Statistics Section of the Anarnbra

State Ministry of Finance and Economic Development, whose

keypunch machines were used; and the Director and staff

of the computing Centre of the University of Nigeria,

Nsukka who dutifully ran my computer programmes.

Dr. S.I. Agajelu, Mr. R. N. Asoegwu, Dr. K. Sawicki,

who at uarious times were either Head of Department or

Dean of Faculty had on many occasions provided

transport for my numerous journeys to Nsukka for running

the computer programmes.

My gratitude also go to Mr. and Mrs. R.N. Iloanya

(M.O.N.) and family; with whom I have lived all these

iii

years and who have acted more like loving parents to

me than distant relations. They have always shown a

lot of interest in my progress and given me immense

encouragement during my formative years and, especially,

at the time of this research.

One person that cannot escape mention is

Mr. C. K. Chidi. He typed this work. It was an

indispensable contribution. I am very grateful to him.

Finally, I wish to thank all those who offered

one help ,or another on account of this research,

including staff and students of the Department, and

other people. My appologies to them that I cannot

mention their names owing to shortage of space.

TABLE OF CONTENTS

Page

Abstract

Acknowledgement

~ i s t of Figures

List of Tables

i

ii

viii

ix

CHAPTER

1 INTRODUCTION . . . . . . 1

1 .10 General . . . . . . 1

1.20 Justification of Research . . 3

1.30 Objective and scope of Research 6

3 THEORETICAL CONSIDERATIONS AND PROCEDURE 15

3.10 Theoretical considerations . . 15

3.11 Measurement principles of the coordinatorgraph . . 15

3.12 Transformation of image coordinates . . . . 16

3.13 Photocoordinate refinement 23

3.14 Space Resection .. . . 33

3.15 Space Intersection . . 4 3

3.20 Procedure . .. . . . . 49

4 EQUIPMENT AND FIELD DATA ACQUISITION 54

4.10 Materials and Equipment used .. 54

4.20 Establishment of Ground Control and Test Points . . . . 60

5 PHOTOGRAMMETRIC DATA ACQUISITION . . 76

5.10 Point Marking and Transfer . . 76

5.20 Main Instrument - The Zeiss C-8 Precision Coordinatorgraph . . 77

5.30 Image Coordinate measurement .. 81

v

6 DATA REDUCTION

6.10 Coordinate Reduction and Refinement

6.11 Transformation of instrumental coordinates to photo coordinates

. 6.12 Principal Point Offset Correction

6.13 Film Deformation correction

6.14 Lens Distortion correction

6.15 Atmospheric Refraction correction . . . . . .

6.16 Earth curvature correction .. 6.20 Space Resection . . . . . . 6.30 Space intersection

6.40 Documentation of Computer Programmes " used . . . . . .

. .

7 RESULT ANALYSIS

7.10 Measurement Accuracy of the coordinatograph . . . . . .

7.20 Comparison of Test Points . . . . 7.30 Statistical Evaluation of Results ..

7.31 Achieved Accuracy . . . . 7.32 Accuracy Requirement for Mapping

8 CONCLUSIONS AND RECOMMENDATIONS

8.20 Recommendations for future research Work . . . . . .

BIBLIOGRAPHY . . . . . . APPENDIX . . . . . .

APPENDIX

1 Point Description . . . . . . 129

2 Camera calibration certificate . . 171

3 Measured Image Coordinates .. . . 176

4A . Computer programme for parametric Adjustment . . . . . . 187

4B Computer programme "TRAN 2B" .. . . 191

4C Computer programme "RESINT" 214

vii

LIST OF FIGURES

Figure Page

3.1 Layout of an A e r i a l Photograph 1 7

3 . 2 Rela t ion between coo rd ina t e systems

of photograph and measuring ins t rument . . . . 23

3.3 Components of Radia l D i s t o r t i o n 27

3 . 4 Atmospherical Re f r ac t ion i n V e r t i c a l A e r i a l Photography 29

3.5 Displacement of p o i n t due t o * E a r t h ' s Curvature .. . . 3 2

3.6 Elements of E x t e r i o r O r i e n t a t i o n 3 4

3 . 7 Flowchart of Procedure . . 53

4.1 T rave r se s . . . . 6 6

6.1 Flowchart f o r Adjustment by Paramet r ic Method . . 9 1

6.2 Flowchart f o r Photocoordinate Refinement . . I 92

6.3A Flowchart f o r "RESINT" (Space I n t e r s e c t i o n ) . . 93

6 . 3 B Flowchart f o r Subrout ine "RESECT" (Space ~ e s e c t i o n )

v i i i

LIST OF TABLES

Table Page

3.1 Computation of Fiducial coordinates of Fiducial Marks Using Distances Between Fiducial Marks ....... 1 8

3.2 Correction for Principal Point offset to Photocoordinates of Fiducial Marks ....... 1 9

4.1 Coordinates of Existing Control .... 7 0

4.2 Coordinates of Basic Control ....... 71

4.3 Coordinates of Photo Control ....... 73

7.1 ,Measurement Accuracy Determination . 96

7.2 Comparison of Test Points ....... 1 0 1

7.3 Achieved Accuracy ....... 107

7.4 Confidence Coefficients for Two-Dimensional Normal Distribution 1 1 2

7.5 Confidence Coefficients for One- Dimensional Normal Distribution .... 112

7 .6 Accuracy Requirements for Mapping (Based on Photo Scale 1/6 ,000 and flying height 1 ,100m) ....... 117

8.1 Rate of Observation . . . . . . . 1 2 0

C!HAPTER ONE

1.00 INTRODUCTION

1.10 General

Photogrammetry has, over the years, been

found to have very useful applications in the

fields of Engineering, Archeology, Astronomy,

Natural Resources Exploration, Urban and Regional

Planning, Space Exploration, etc.[3, 281. But

its greatest application to date is in the field

of Land Surveying; mainly for the production of

topographic maps as well as other allied products

such as photomosaics, orthophotos, orthophoto maps

etc.

Like in Land Surveying, most practical photo-

grammetric activities require the use of suitable

control points whose accurate positions or

coordinates are known. A certain degree .of density

and distribution is required of the control points

before they can be used for photogrammetric

purposes. Because of the tedium involved in using

ground survey methods to achieve this control

requirement, a photogramnetric method has been

developed for the provision of additional control

to supplement the sparse ground control. This

method is known as aerotriangulation.

Aerotriangulation has undergone a series

of changes and modifications during several years

of its applications. It started with the radial

line triangulation whereby aerotriangulation is

executed graphically or by the use of slotted

templets. Later, analogue (instrumental) and semi-

analytfcal aerotriangulation came into existence

only to be joined a little while after by the much

preferred analytical method whose numerous

advantages are far reaching[l7]. This latest

method owes its popularity to the plausibility of

the use of computer for the solution of its problems.

Although the earlier methods are still in use,

depending on the purpose and accuracy specifications,

the analytical method is the most accurate of all

aerotriangulation methods[l, 171.

The major problem of analytical photogrammetry

is that the main instrument used - the comparator - is very expensive and its use is limited to the

measurement of photocoordinates. The enormous

capital investment required for the acquisition of

the comparator is therefore hardly justifiable. But

then there are other instruments such as the stereo-

plotters used for analogue and semi-analytical

aerotriangulation and map compilation which could be

adapted to perform the function of the comparators[l3,

27, 391. The results of the researches done in that

regard have been yielding good results in many photo-

grammetrtc organisations. Thus, to further

encourage the practice of analytical photogrammetry,

it is deemed necessary to research on the use of some

other photogrammetric instruments as comparators. The

coordinatograph which is hitherto used in such duties

as drawing of maps, plotting of grid, and enlargement

and reduction of maps, comes uppermost to mind.

Hence the choice of this research is on the

"Evaluation of the Zeiss C-8 precision coordinatograph

for use as a monocomparator."

1.20 Justification of Research

Control extension by photogrammetric means

(Aerotriangulation) is a very important aspect

in the photogrammetric mapping process. In recent

years the analytical method of control extension

has grown very popular because of its numerous

advantages over the conventional analogue method[l51.

The instrument requirement in analytical aero-

triangulation is limited to that used for measurement

of image coordinates; the rest of the work is done

by computation. Thus instrumental errors which are

inherent in the analogue methods are almost

eliminated. Again, instrument operators are spared

long periods of strenuous work. Furthermore, there

is the possibility of using all types of photographs

regardless of angular coverage, size of photo format,

tilt, and whether they are aerial or terrestrial,

frame, strip or panoramic photography. Moreover,

the applications of analytical photogrammetry have,

in general, become more diverse in recent times

such as in the tracking of ballistic missiles,

satellites, etc. Above all, there is the possibility

of incorporating auxilliary data in the solution of

photogrammetric problems which will definitely

reduce some other requirements and enhance accuracy.

A turning point in Analytical photogrammetry

has been reached with the introduction of the use of

fast speed computers in the solution of its

problems. Most photogrammetric activities which had

previously been carried out by the analogue methods

have become fully analytical and a lot of computer

softwares have been developed for them. Thus, an

increased need has arisen for image coordinate 4

measuring instruments. Although the comparator is

known to have been in existence since AD 1901 when

Carl Pulfrich of the Zeiss Group of Jena announced

the development of the first. stereocomparator, it has

never been as idolised as it has become in recent

times. As a result the scarcity of the instrument

has become aggravated.

In the circumstances, many organisations (both

private and government) which had invested in other

instruments such as the stereoplotters and coordinato-

graphs have felt that their instruments have become

obsolete not long after spending a lot for their

purchase. Worse still, smaller organisations which

cannot afford the huge capital outlay required for

the acquisition of the comparator and computer have

become resentful of undertaking analytically'oriented

jobs, especially the aerotriangulation[l5, 171.

In the face of the prevalent

situation, researchers saw the need to make the

existing analogue instruments more useful in the

area of Analytical Photogrammetry. Many stereo-

plotters (especially the universal and precision

types) Qave been investigated for use as both mono

and stereo-comparators.and found to be dependable[5,

13, 27, 391.

Based on the successes of the foregoing

researches, one gets the inspiration that some other

analogue photogrammetric instruments might also have

potentialities in analytical photogrammetry. The

coordinatograph is one such instrument and, since it

works in the monoscopic mode, it can only be evaluated

for use as a monocomparator.

1.30 Objectives and Scope of Research

The Zeiss C-8 precision coordinatograph,

although an integral plotting table to the Zeiss

Stereoplanigraph C-8 stereoplotter, is detachable

and can be used as a separate unit. Like other

precision coordinatographs of its type, it is

designed to carry out such duties as plotting of

grid, plotting of maps, and enlargement and reduct-

ion of maps.

The main objective of this research is to

evaluate the use of the coordinatograph as a mono-

comparator in terms of measurement accuracy and the

accuracy" of the final product - ground coordinates of selected points appearing on photographs. The

coordinatograph to be used is that attached to the

Zeiss Stereoplanigraph C-8 belonging to the Survey

Division of the Anambra State Ministry of Works,

Lands, and Transport Enugu.

It is hoped that a successful completion of this

research will open up avenues for further work in

Analytical Photogrammetry which has been seriously

hampered by the inavailability of the comparator any-

where in Anambra and other neighbouring States (up to

the time of this research). In particular the

Ministry staff and other close associates will be

availed of the opportunity of measuring photo-

coordinates for use in both aerotriangulation and

other analytical work.

The generation of data for this research will.

be restricted to a few models of two strips and is

considered sufficient for the desired investigation.

CHAPTER TWO

2.00 LITERATURE REVIEW

Photogrammetric researchers have made some

inroads into the adaptation of analogue stereoplott-

ing instruments for use as comparators. Thus the

industry has been exploiting the achievements so far

made to appreciable advantages. Perhaps a review of

some of the publications encountered in the course

of the library search for this research will serve ,. better to enunciate the . . state of affairs.

Levy1271 made a description of a general

method of analytical aerotriangulation using analogue

instruments. But no indepth study was made of any

one particular instrument. Since each stereoplotting

instrument is unique in its own way, the method is

far from being applicable to any one instrument unless

the study is carried out again with an instrument

specifically considered. Again, no mention was made

of the accuracy of the method in the said study,

although it was stated that the object of the study

was to develop a method whereby analogue instruments

could be used for analytical aerotriangulation.

Hence when considered within the framework of the

scope of the research, it was successful.

In their own research, Wolf and Pearsall[39]

dealt with the use of the Kern PG-2 as a mono-

comparator. But then the experimental design

involved the use of terrestrial photographs alone.

The accuracy of the method in this study was

determined by comparing the photocoordinates of

points obtained using the Kern PG-2 as a mono-

compard'tor with those of the same points obtained

with a conventional monocomparator. In other words,

coordinates were measured in the instrument and

transformed into photocoordinates and, without

coordinate refinement, they were compared with those

obtained with a monocomparator. Then a third degree

polynomial was used to generate error models using

the descripancies. Finally these error models were

used to refine the coordinates. Thus it is evident

that the comparator was used as a standard for

accuracy determination. It was however highlighted

that although the comparator was apt to introduce

some errors in the photocoordinates, the results were

adequate for the comparisons desired. The outcome

of this research was very impressive and was summed

up in the following words. "The PG-2 when used as

a monocomparator is accurate, fast, and very

convenient, especially for small-format photos which

fit within the model area on the plate carrier." 1

It is certain here that there is a restriction

to the use of small format photographs which must fit

into the model area of the plate carrier. In other

words, the photograph must occupy less than 60% of

the width of the plate carrier. This condition is

applicable to most other mechanical projection

plotters (except the universal instruments with the

base-in base-out capability). As a result a stand-

ard format (23cm. x 23cm) photography cannot be used,

since the instruments cannot measure through the

entire breadth of the photograph at once. But coord-

inates are required across the photo format to enable

a true analytical solution. The entire photo format

may however be measured using one of the following

three procedures:

(i) One half of.the photograph is measured

1 . Wolf, P.R. and Pearsall, R.A. "The Kern PG-2 as a Monocomparator," Photogrammetric Engineering & Remote Sensing, vol. 42, No. 10, October 1976, p. 1259.

on one projector and the other half is

measured on the other projector.

(ii) The photograph is measured on one half

and then rotated on the same projector to

complete measurement on the other half.

(iii) The photograph is cut into two and measured

one after the other and, of course, a

reseau photography (which is not always

available) is required for this.

A.

It is evident here that to engage in any of these

processes would be cumbersome. Hence the coordinato-

graph which normally has a very large table surface

would be used to great advantage if the measuring

scales are properly and accurately graduated; since

it can accommodate any size of photograph.

Exintavelonis, et a1.[131 investigated the use

of the Zeiss Stereoplanigraph C-8 as a comparator.

The work entailed the use of C-8 both as a mono-

comparator and as a stereocomparator. The procedure

for coordinate refinement was elucidated. The

reseau grid plate was used as the standard basic

framework for comparison. The known grid

intersection coordinates were compared with their

measured coordinates to arrive at the presented

accuracy of the method. After obtaining several

measurements and making statistical analysis, the

results showed that a standard error of measurement

of 4.5pm, on the average, was obtainable in both

the mono and stereo modes. The accuracy level was

therefore very encouraging.

This last described method has been applied for

product5on purposes, but with a different instrument - the Kern PG-2[5]. The'instrument was used as a

stereocomparator though. The results showed that

the absolute mean square error placed side by side

with that obtained using a Hilger and Watts stereo-

comparator was appreciably satisfactory; although

most of the points were fixed in plan only. It was

also reported that the average time of observation

of one model containing 10 to 12 points was 40

minutes. But there was no time information in

respect of the use of the stereocomparator. Thus no

comparative analysis could be made of the time

factor. In another development, it was revealed that

the photogrammetric Department of the Durban City

Corporation of South Africa employed the same

method on their Wild A-8 stereoplotter but

observed no superiority in accuracy over the

analogue method done in the same instrument.

An investigation into the use of the coordinato-

graph as a monocomparator would certainly be an

added dimension to the quest for the applicability

of analogue instruments to analytical photogrammetry.

If the measurement accuracy in this research is

satisfwtory then there is no doubt that the

coordinatograph will, otherwise, be more adaptable

to the method than any stereoplotter. To the best

knowledge of the author, this is the first time this

investigation is contemplated upon.

CHAPTER THREE

THEORETICAL CONSIDERATIONS AND PROCEDURE

3.10 Theoretical Considerations

The theories involved in this research

include :

if

ii,

iii,

iv,

v,

3 .11

Measurement principles of the coordinatograph

Reduction of measured image coordinates

to photo coordinates

Refinement of photocoordinates

Photogrammetric space Resection

Photogrammetric space Intersection. Ir

Measurement Principles of the Coordinatograph

The Zeiss C-8 precision coordinatograph, like

many other coordinatographs, operates as an

orthogonal axes leadscrew system. The two axes

are graduated uniformly, and they represent the

x and y axes. A system of lenses in a housing

constitutes the observation system. This observat-

ion system has a black annular measuring mark.

There are two read-out units from which image

coordinates (x and y) could be read out and

manually recorded.

The foregoing qualities of the coordinatograph

are almost the same as the basic qualities of

some mono-comparators that operate on the leadscrew

principle. It was therefore probable that the

coordinatograph could be used as a monocomparator

for the measurement of image coordinates on

photographs.

3.12 Transformation of Imaqe Coordinates

Image coordinates measured in the coordina-

tograph have their origin somewhere outside the

photograph. For use in analytical photogrammetry,

coordinates in the photographic coordinate system;

with origin at the principal point of symmetry of

the photograph; are required[29]. There was the

need, therefore, to transform the image coordinates

measured in the coordinatograph coordinate system to

photocoordinates using a two-dimensional trans-

formation equation.

Figure 3 . 1 shows a schematic diagram of the

layout of an aerial photograph.

*

1 - 4 Fiducial Marks

FC Fiducial Centre

PPA Principal point of Autocollimation

S Principal point of symmetry

(Origin of Photocoordinate system)

Fig. 3.1 Layout of an Aerial Photograph

In the calibration certificate (Appendix 2)

the distances between fiducial marks (numbered

1 to 4 in fig. 3.1) are given. Also coordinates

of the principal point of autocollimation (PPA)

and the principal point of symmetry (S ) with

respect to the fiducial centre (FC) are given. If

'i j represents distance between fiducial marks

i and j, the coordinates of the fiducial marks

with respect to the fiducial centre (FC) were

computed as shown in Table 3 . 1 .

Table 3 . 1 : Computation of Fiducial Coordinates of Fiducial Marks Usinq Distances Between Fiducial Marks

, Point

Fiducial Marks 1 .

The algebraic signs on the coordinates in

table 3 . 1 are assigned to them in accordance with

the location of the points with respect to the

positive and negative directions of the x and y

axes. The coordinates are, however, not the

required photo coordinates of the fiducial marks

since their origin is not in the principal point

of symmetry. To obtain the photocoordinates, the

coordinates of the principal point of symmetry ( S )

with respect to the fiducial centre (FC) designated

X 0' Yo (also called principal point offset) were

applied to each of the fiducial coordinates to

obtain the calibrated photocoordinates of the

fiducial marks as shown in table 3.2.

Table 3.2': Correction for Principal Point Offset in the Photocoordinates of the Fiducial Marks

Having obtained the calibrated photocoordinates

of the fiducial marks (as in table 3.2). the

transformation of all measured coordinates to

photocoordinates was carried out using the Two-

Dimensional Affine Transformation whose equations

are given by

1 x = x1 + a + blx + cly 1 1 ... 13.la)

where

XtY = photocoordinates

x1 tyl = observed image coordinates J,

a's to c's = transformation coefficients

To determine the numerical values of the

coefficients, the calibrated photocoordinates of

the fiducial marks were substituted for x,y and

the measured coordinates of the fiducial marks were

1 substituted for x , y1 in equations (3.1atb). A

pair of equations of the 13.latb) type was generated

in respect of each fiducial mark; thus making for

a total of eight equations with six unknowns (a's to

c's). Solution was by the method of least squares,

as follows:

The observation equation resulting from

equations (3.1atb) are

Equations (3.2a,b) can be written in matrix

notations as

V = AX-L . . . ( 3 . 3 )

where

The matrix of unknowns, X, (which is also the

matrix of corrections to the matrix of approximated

values, assumed to be a zero matrix) is obtained

from the least squares solution

-1 T x = (A~A) (A L) ... (3.4)

The numerical values of the unknowns thus

obtained were put back into equations (3.1afb).

Subsequently, the pair of coordinates (x ,y I)

of each measured point were put into the equations

which kielded the transformed photocoordinates of

the point (x,y) . The Two-Dimensional Affine (as apposed to

Two-Dimensional Conformal) Transformation was

employed here because, in addition to transforming

coordinates, it corrects for systematic errors

arising from film shrinkage and deformation, and

non-perpendicularity of the axes of the measuring

instrument. The coefficients (a ,a2) achieve the 1

translations from the origin of the coordinato-

graph coordinate system to that of the photo-

coordinate system (see fig. 3.2) ; and (bl , b2, c ) accomplish rotations, corrections for C 1 f 2

non-perpendicularity of axes, correction for

scale changes, as well as for linear film

deformations in x and y [ 1 5 , 291.

Fig. 3.2 Relation between coordinate systems of the photograph and measuring instrument.

3.13 Photocoordinate Refinement

The refinement of photocoordinates involves

the elimination of systematic errors which affect

the geometry of photographs. The include the

principal point displacement, film deformation,

lens distortion, Atmospheric refraction, and

Earth's curvature effect[291.

3.131 The Principal Point Offset Correction

The principal point offset correction to all

points was effected by the application of x ~ ~ Y ~

(coordinates of the principal point of symmetry)

to the fiducial coordinates of the fiducial

marks, to transform them to the photocoordinates

of the fiducial marks (see table 3.2) .

3.132 Film Deformation Correction

FiTm deformation can occur in various forms.

They include:

i. The uniform systematic distortion which

is a unifonn distortion in all directions and is often

considered radial from the fiducial centre.

ii. The differential systematic distortion which

entails a uniform distortion along the x

direction and a different but uniform

distortion along the y direction.

iii. The irregular distortion which can result

from varying elastic properties of the film

material, non-flatness of the emulsion

surface, localized emulsion creep, etc.

Distortions of the types in (i) and (ii)

are automatically corrected to varying degrees

by the two-dimensional affine transformation

equations (3.latb) [15]. Thus they were deerred to have been

corrected simultaneously during the transformation

of coordinates achieved with equations (3.la,b).

Distortions of the type in (iii) do not follow

any systematic distribution pattern and as such do

not offer themselves to straightforward solutions

115, 361: However, the correction achieved during

the coordinate transforination is considered

sufficient for this work and for most others except

those which require exceptionally high accuracies.

3.233 Lens Distortion Correction

Lens distortion generally exists in three

forms - symmetric radial distortion, assymmetric radial distortion, and tangential distortion[29].

A great part of the assymmetric radial distortion

is absorbed during camera calibration; in the process

of determining the principal point offset referred

to in section 3.13'1. The remaining part is complex,

2 6

and, since it is usually very small, it is

considered insignificant and therefore not corrected

for. Tangential (or decentering) distortion is

also negligible (seldom more than one-seventh of

the radial distortion at the same point) and, so,

no attempt is made to correct for it in practice

[ 15 , 381.

Correction to symmetric radial distortion is

considered sufficient for all but the most precise

photogfammetric work. Different methods exist for

the determination of this correction. The method

used in this work is one most adaptable to analytical

procedures and it is given by the equation:

9 Ar = k,r t klr3 + k2r5 + k r7 t k4r ... ( 3 . 5 ) 3

where

Ar = the radial distortion (positive in the

direction away from the principal point)

r = the radial distance of any point from the

principal point

k's = distortion coefficients

The coefficients, k's, are determined first

by the least squares methods. In the calibration

certificate, values of distortion are tabulated

against some radial distances. These were

substituted in equation (3.5) to generate a system

of equations with the k's as the unknowns. The k's

were therefore determined and put back in the

equation for subsequent use in the lens distortion

correction to any point.

For application to photocoordinates, radial

distortion, A r t is considered in two components

Ax and 2y; corresponding to radial distortions

along the x and y axes' respectively. The mutual

relationship between distortion and distance in

the various directions is given by (see fig . 3. 3j

, Fig. 3.3 Components of Radial Distortion

Based on the relationships in equation (3.6)

the corrected photo coordinates become:

- nr 2 4 y = y-ny = y(1- -) = yll-ko-k r -k r -k3r6-k4r8. . ) (3.7b) r 1 2

In equations (3.7a,b) five or six terms in

the series should be used to achieve very good results

1151. All six terms in the equations were, however,

used in this work.

.+

3.134 Atmospheric Refraction Correction

Owing to variation in the refractive indices

of the different levels of the atmosphere - caused

by variation in temperature, pressure, and composition

(humidity, carbon dioxide, dust, etc.) of the levels -

light rays travelling from the ground to the aerial

camera bend in their paths. As a result, images are

displaced in t.he image plane. Image displacement due

to atmospheric refraction is considered radial about

the principal point of the photograph (see fig. 3.4)

Fig. 3.4 Atmospheric Refraction in Vertical Aerial Photography

The radial displacement of image points due

to atmospheric refraction is given by [ 2 9 ] :

where

H = the flying height in kilometers

h = the ground elevation in kilometers

r = the radial distance of an image from

the principal point

f = focal length of taking camera

*

Equations (3.8) and (3.9) are based on the

atmospheric models adopted by the ARDC (Air Research

and Development Command of the United States Air

Force) and reported in [ I 5 1 as having the same

effect as any of the models adopted by other

organi-sations (like the U.S. Committee on Extension

to the Standard Atmosphere, and the International

Civil Aviation Organization, ICAO) up to a flying

height of 20km.

It is evident from equations (3.8) and (3.9)

that error due to atmospheric refraction is dependent

on flying height and ground elevation. A table of

atmospheric refraction errors based on the ICAO

model shows that the error increases with flying

height and decreases with ground elevation [IS].

However, for ground elevation at sea level and

flying height of 3000m the error occuring at a

point Illmrn from the principal point was 5.9pm.

Also Wolf[38] noted that from a series of

experiments a nomograph was plotted which showed

that for a flying height of 10,000ft (3,000m)

and an average elevation of 1,500ft (500m) the

refraction distortion Tor a point 100m from the

principal point was 4pm.

The photographs used for this research were

taken at an average flying height of 1,100m and all

ground elevations were in the neighbourhood of 200m

above mean sea level. Hence, errors due to refract-

ion were considered insignificant and, thus were

not corrected for.

3.135 Earth's Curvature Correction

Image displacements in vertical photographs

also result from the curvature of the earth

(see Fig. 3.5)

negative

plane

Fig. 3.5 Displacement of point due to Earth's curvature

Image distortion due to earth's curvature

is radial from the principal point of a vertical

photograph. It is given by1291 :

where

H' = flying height above ground nadir point

R = radius of the earth

r = radial distance of image point from

the principal point

f = focal length of taking camera

Ghoshll5J made a table based on equation (3.10)

which shows that, for a focal length of 150m and

a flying height of IUOOm, an image point 100mm

from the principal point is displaced by 3.5pm.

Also a nomograph in Wolf[38] gives the error as

6pm for a flying height of 6,000ft (2000m) and an

image point 100m from the principal point.

The degree of occurence of earth's

curvature errors is considered negligible in

respect of this research. There was, therefore,

no correction for errors due to earth's curvature.

3.14 Space Resection

Space resection in photogrammetry is the

determination of the parameters expressing the

position and attitude of a camera at the instant

of exposure. These parameters normally called

exterior orientation parameters of the photograph

are: ( 1 ) X,, Yo, Z, which are the coordinates

of the perspective centre determined in the object

space coordinate system, and

( 2 ) either W(omega) , 4 (phi) , and k (kappa) , or t (tilt) , S (swing) , and cr (azimuth) (depending on

the adopted system) which express the spatial

angular relationship between the object coordinate

system ( X , Y, Z) and photo coordinate system

( x , y , z ) [ 2 9 ] (see also fig. 3 .6 ) .

\

Fig. 3.6 Elements of Exterior Orientation

One of the methods of space resection which

employs the well known collinearity condition

equations has been used in this work. Without

derivation the collinearity condition equations

can be stated as follows[3, 29, 31, 381:

where

X I Y = refined photocoordinates

f = focal length (calibrated)

XI Y, Z = object space coordinates of a

control point

Xo,Yo,Zo = object space coordinates of the

photograph.,exposed station

m ij = elements of orientation matrix, M,

and

The elements of orientation matrix, M, are

the direction cosines of the spatial angles between

individual axes of the object space (X, Y, Z)

coordinate system and those of the photographic

(x,y,z) coordinate system. The orientation

elements w, $, k (or t, s, a; as the case may be)*

are therefore implicit in the orientation matrix, M.

Thus

r cos xx cos XY cos xz (r 1

M = / cos yx COS yY cos yz

LCOS zx cos zY cos zzj

cos $ cos k cos w sin k sin w sin k +sin w sin 4 cos k -cos w sin4cos k

= I -cos Q sin k cos w cos k sin w cos k -sin w sin $ sin k +cos w sin$ sin k

sin $ -sin w cos $ cos w cos 4

... (3.13)

I The collinearity condition equations (3.11a1b)

are employed in different forms for the solution of

*Although w, $ , k are not equal to t, st a, either set can be used in any situation where orientation angles are required.

various analytical problems in photogrammetry.

As far as Space Resection is concerned, there are

six unknowns (X,,Y,,Z,,w,~,k). A unique solution

can be achieved with three pairs of equations of

the (3.11atb) type. Thus three control points

with known ground (X,Y,Z) coordinates are essential.

Four control points were however used in all cases

to achieve redundancy and to enable least squares

solutions. The collinearity condition equations

are no%-linear and are linearized by the Taylor

series e::pansion . The collinearity condition equations (3.11a,b)

can be written in matrix notations as:

F~ = ~ ~ 2 . x + ~ ~ 2 . f = o ... (3.14a) -

F =M3?.y +M2X.f = 0 ... (3.14b) Y

where

M~ = [ml m~ 2 m~ 3'

Higher order terms of the Taylor series expansion are

ignored and the linearized equations became

The partial derivatives are given by the following

expressions [ 151 :

a Fx - X + ~Xcos@+ ~Y(sin w sin + ) + AZ(-sin 4 cos w) - a @ - -=[ M3X . . 1 f

cos k) + ~Y(sin w cos @ cos k)

+ AZ ( m s w cos 4 cos k)]

aF = L[aXcos @ + dY(sin w sin @ ) + AZ(-cos w sin $ 1

a @ . M ~ B 3 + +px(sin @ sin k) + AY (-sin w cos sin k)

M P

The subscripts (0) in equations (3 .l5a,b) (with the

exception of Xo,Yo,Z,) indicate that the partial

derivatives are evaluated using the approximate

values of the parameters Xo,Yo,Zo,w~@~k.

An iterative procedure is entered into to achieve

the least squares solution.

The adopted approximate values of the

parameters were as follows:

w, = +, = 0

h he angle kappa (k) is usually taken as the

angle measured counterclockwise from the photo-

graphic position of the ground X-axis to the photo-

graphic x-axis. It assumes the value +90°, -90°, 0°,

or 180, if the flight line is due North, South,

East, or West respectively[29].

Thus kobis given by

k, = X - A G P

where

-1 h~

= tan

h = tan -1 P

A and B are any two ground control points with

corresponding photographic images a and b. However,

the computed value of k, was rounded to the nearest

degree before use.

The approximate values of X, and Y o (which

are' X,, and Yo,) were obtained from the visual

interpolation of the coordinates of the fiducial

center from known ground coordinates.

Z o o was computed as follows:

where

ground distance between ground points

A and B computed from their ground

coordinates

photo distance between photo points a

and b computed from their photo

coordinates . .

focal length

mean of ground elevations of A and B.

The value of Z o o was rounded to the nearest 100m

before use.

The observation equations obtained from

equations (3.15) are given by:

&pations (3.18a,b) can be expressed in a matrix form

as follows:

v = A X - L

where

The number of columns of the matrices V I A I and

depend on the number of control points used. The

matrix of corrections, X, was computed from the

least squares solution:

T -1 T X = (A A) (A L)

If weighted observations were used, the correspond-

ing least squares solution would be given by:

x = (A~PA)-' (A~PL) ... (3.20b)

However, the updated values of the parameters

become

If the corrections are large the adjusted values

in equation (3.21) are used as approximate values

and the exercise is repeated until the corrections

become small in accordance with given limits of

convergence.

3.15 Space Intersection

Photogrammetric space intersection affords the

possib'ility of analytical computation of object

space (in this case, ground) coordinates from photo-

coordinates of points which appear in more than

one photograph. The inputs in this exercise are

focal lengths, refined photocoordinates, and

exterior orientation parameters of the photographs

involved.

Space intersection can be performed in

different ways, depending on the mathematical model

adopted for use. In this research the collinearity

condition equations (3.11atb) were again used. The

unknown3 were the X,Y,Z, ground coordinates of each

required point. Since' the equations are non linear,

linearization was effected by Taylor series

expansion. Observation equations were formed from

the linearized equations as follows:

The partial derivatives are given by [15]:

All elements have the same meaning as in section

3 .14 .

As indicated by subscript (o), the partial

derivatives should be evaluated with approximate

values of the parameters. As such initial values

were determined for the ground (X,Y,Z) coordinates

based on empirical procedures (vector solution) as

follows :

If subscript 1 is used to denote elements of

the left hand photograph and subscript 2 is used to

denote those of the right hand: and if ui,v.,wi 1

denote unit vectors in the x,y,z directions of

the photographic coordinate system, then

Also, if MI and M2 are the orientation matrices of

the left and right photographs respectively,

let

The approximate values then became

where

X , Y o , (Z), = approximate coordinates of an .r

intersection point.

Now given that aij are the partial derivatives

evaluated with the approximate parameters the

observation equations (3.22) become:

v = a dX + a22dY + a23dZ + L Y 2 1 Y ... (3.23)

v' = a dX + aj2dY + a dZ + L I X 3 1 33 X

v 1 = a dX + a dY + a$dZ + L I Y 4 1 42 Y

where

Lx = [F (x), -XI and L = [F(Y)~ -y] Y

The primes ( I ) in equation (3.23) are used to

distinguish equations of the right hand photographs

from those of the left.

Equations (3 .23 ) are solved separately for

each intersected point. Since there are four

equat'ions and three unknowns, solution is by the

least squares method. Written in matrix notations,

however, equation (3 .23 ) can take the form of

equation (3 .19 ) written as follows:

V = AX-L ... ( 3 . 1 9 )

where

The matrix of corrections, X, was determined from

equation ( 3 . 2 0 ) . It was added to the matrix of

approximate values of the unknowns to obtain the

coordinates of each ground point.

3.2 0 Procedure

In this research the selection of ground

points was based on the principle of postmarking.

Well defined points which appeared on the photo-

graphs were chosen to serve as control points,

test points, and pass points. They include such

points as corners of buildings, concrete slabs, I.

lawn tennis courts, etc. The ground control points

and test points were coordinated by field survey

methods (discussed in chapter 4). Traversing was

used to determine the X- and Y- coordinates, while

spirit levelling was used to determine the Z-coord-

inates (i.e. the heights) . Each of the diapositives was measured on the

coordinatograph. Image coordinates of the fiducial

marks, control points, test points, and pass points

were read and recorded. These coordinates were

transformed to photocoordinates and subsequently

refined in order to eliminate systematic errors

usually inherent in photographies and image

coordinate measurements. The steps in the

coordinate refinement included corrections for

principal point offset, film deformation, and

lens distortion. The corrections for atmospheric

refraction and earth's curvature which would have

been part of the package were not effected. This

is based on the consideration that, owing to the

relatively low precision of the measured

coordinates and the low flying height of the photo-

graphy; the two systematic errors would be of no

effectll51.

All the coordinate refinement processes were

accomplished with the use of a computer programme

named "TRAN 2B." Before this, the photographic

coordinates of the fiducial marks referred to the

fiducial centre were computed from the distances

between fiducial marks obtained from the calibration

certificate (see Appendix 2). The correction for

the principal point offset was applied to the

fiducial coordinates of the fiducial marks to obtain

their calibrated photocoordinates. These calibrated

photocoordinates of the fiducial marks together

with the measured coordinates of all points

(including the fiducial marks) were fed into

the computer programme. The programme made use

of the two-dimensional affine transformation

equations to perform coordinate transf ormation

from coordinatograph coordinates to photo-

coordinates and also to apply the film deformation

correction. The lens distortion correction was

performed with the use of lens distortion equation

which contains distortion coefficients k o t klt kit

k3? kqA(see section 3.133) determined from

calibration values obtained from the calibration

certificate. The distortion coefficients were

first computed with a computer programme which does

adjustment by the parametric method. The programme

"TRAN 2B" also contained an option for correcting

atmospheric refraction and earth's curvature; but

that aspect of it was not used.

The determination of the exterior orientation

parameters was accomplished by space resection using

collinearity condition equations. Ground coordinates

of the test points and pass points were subsequently

determined by the process of space intersection,

also using the collinearity condition equations.

Both processes of space resection and space

intersection were executed with a computer programme

named "RESINT". The programme performed space

resection in a subroutine whose output was

utilized in the main programme, together with the

refined photocoordinates, to achieve space inter-

section.

The result of the space intersection was the

ground*(^, Y, Z ) coordinates of all the points

(control points, test points, and pass points)

whose image coordinates were measured originally.

The ground coordinates of the test points were

compared with their corresponding values determined

by the field survey methods. The residuals

generated were then used to compute the root mean

square error (r.m.s.e.) of the X, Y, and Z

coordinates. The coordinates were also tested for

use as control for mapping.

The flowchart in figure 3.7 summarizes the

steps taken in the methodology of the research.

Acquisition of / materials

1

Reconnaisance point selection and planning

L

I -

1 and test points I Image coordinate measurement

Image coordinate reduction and

I Establishment of ground control I

photocoordinate refinement

Space resection of left and right photos

Space Intersection

Ground coordinates of Test points X Y Z !

Fig. 3.7 Flow chart of Procedure

CHAPTER FOUR

4.00 EQUIPMENT AND FIELD DATA ACQUISITION

4.10 Materials and Equipment Used

In accordance with the composite nature of

this research, the material and information

requirements were varied and so were their sources.

The materials and equipment used included:

(1) Aerial photographs and camera calibration

certificate

(2) Theodolite '

(3) Electronic Distance Measuring (EDM)

Instrument and Accessories

(4) Level and staff

(5) Zeiss Snap Marker

(6) Zeiss C-8 precision coordinatograph.

4.11 Aerial Photoqraphs and Takinq Camera

Aerial photographs contain images of terrain

features and they form basic sources of data for

application in aerial photogrammetry[3].

The photographs used for this research

cover the entire premises' of the

University of Nigeria, Enugu Campus and environs

which include Anambra State University of Technology

ASUTECH) Enugu, Institute of Management and

Technology (Campus 3) Enugu, Women Training College

(WTC) Enugu, Queens College Enugu, The Nigerian

Television Authority (NTA) Enugu, some parts of

Uwani, Maryland, Ogui-New Layouts. There are six

photographs in all - three in each of two everlapping strips. The photographs in the first strip are

ENG 03/129, ENG 03/130, ENG 03/131, and those in the

second one are ENG 03/173, ENG 03/174, ENG 03/175.

The photographs are vertical photographs with format

sizes of 23cm by 23cm. They were taken in 1977 with

a wide angle aerial camera of serial number 15 UAgII

3057, having a nominal focal length of 153.14mm.

Like all other measuring instruments, the

aerial metric camera (being the camera used to obtain

photographs for photogrammetric work as opposed to

photo interpretation) is calibrated periodically in

order to assign values to some of its parameters[l9].

Usually, the output of each calibration exercise is

properly documented for use in correcting systematic

errors which do occur in measurements made on photo-

graphs. The document containing the calibration

values of a photogrammetric camera is called the

calibration certificate (see Appendix 2).

Some of the information contained in the

calibration certificate include the focal length,

coordinates of the principal points of auto-

collimation and symmetry with respect to the fiducial

centre,+tabulated values of radial distortion against

radial distances, distortion curve, distances

between fiducial marks, resolution values etc. Most

of these are used in photocoordinate refinement

(discussed in section 3.23).

The calibration certificate used for this

research contains values based on the calibration

exercise carried out on the 27th of June 1977; which

is the year of photography. It was issued by the

Federal Surveys Lagos on request.

4.12 The Theodolite

A theodolite is a ground based instrument with

which horizontal and vertical angles are determined.

The theodolite was employed in traversing, for the

determination of the planimetric (X,Y) coordinates

of the ground control and test points used in this

research.

The theodolite used here was a Kern DKM 2AE

which has a least angular reading of one second (1")

of arc in both the horizontal and vertical circles[8].

The instrument was taken on loan from the Federal

Surveys 'Field Headquarters in Makurdi, Benue State.

4.13 Electronic Distance Measuring (EDM) Instrument and Accessories

Distance measurement was accomplished with Kern

DM502 Electronic Distance Measuring (EDM) Instrument

during the field work for this research. The

instrument is mounted on the Kern DKM 2AE theodolite

at one end of a traverse line, while a glass optical

reflector is at the other end. When the EDM is

operated, the slope distance between the Instrument

and reflector stations is measured. The vertical

angle determined from the theodolite measurement is

used to reduce the measured distance to its horizontal

equivalent which is needed in the computation of

coordinates.

The instrument and its reflectors as well as the

battery that activates the instrument are available

in the stores of the Department of Surveying of the

University of Nigeria.

4.14 Level and Staff

The+vertical ( Z ) coordinates of the control and

test points were determined in the field by spirit

levelling. The instrument used was the Zeiss Ni2

automatic level and a levelling staff. They are both

available at the stores of the Department of Surveying.

4.15 Zeiss Snap Marker

A pair of Zeiss snap marker was borrowed from

the Survey Division of the Anambra State Ministry of

Works, Lands and Transport with a view to having the

points on the diapositives marked before image

coordinate measurement. They could not mark the

diapositives because the impact of their hammers were

dissipated owing to the elastic nature of the film

material of the diapositive[l5]. It would have been

of great use if the diapositives were on glass plates.

4.16 The Zeiss C-8 Precision Coordinatograph

The main instrument whose performance in image

coordinate measurement is investigated is the Zeiss

C-8 precision coordinatograph. Like any other

coordinatograph, this instrument has hitherto been

employed in such functions as plotting of grid,

digitizing and plotting of maps, and enlargement and

reduction of maps.

The Zeiss C-8 Precision Coordinatograph serves

as a plotting table to the Zeiss stereoplanigraph C-8

Stereoplotter. It is detachable from the stereo-

plotter. The stereoplotter, together with the

coordinatograph are located at the Photogrammetric

Laboratory of the Survey Division of the Anambra State

Ministry of Works, Lands and Transport Enugu.

Access to the instrument was gained sequel to

official correspondences entered into between the

Head of the Department of Surveying of the University

of Nigeria and the Surveyor-General who is the

Head of the Survey Division of the Ministry.

4.20 Establishment of Ground Control and Test Points

Usually known ground points are required to

control the photographs in most photogrammetric work.

The control is usually in the form of ground points

with known planimetric (X,Y) and/or vertical ( Z )

coordinates, established either by field survey 2.

methods or by a previous, but more accurate, photo-

grammetric method. All control involved in this

research were established by field survey methods and

each point is a combination horizontal and vertical

control point. The same is applicable to the test

points. As such all references made to control points

in this section should be deemed to include test

points.

Ground control establishment in photogrammetry

is usually carried out in two phases. The first

phase referred to as basic control involves the

coordination by either triangulation, trilateration,

traversing, intersection or resection, and levelling

of such permanent marks as beacons, monuments,

benchmarks, etc. which are not necessarily

identifiable on photographs. The second phase

known as photo control is established with respect

to the basic control by any survey method. The

photo control points must be identified on the

photographs as well as on the ground (although they

need not be permanent ground points) because they

are the, actual control used in the photogrammetric

process [291 . The 'horizontal (X, Y) coordinates of the control

were determined by the method of traversing (see

section 4.23), while the vertical coordinates were

determined by spirit levelling (see section 4.24).

4.21 Basic Control

In the premises of the University of Nigeria

Enugu Campus there are a series of survey control

points established on a previous survey operation.

The control is made up of a series of survey beacons;

each measuring 20cm x 20cm on the cross section with

a nail at the centre to define the point of interest

precisely. The serial numbers of the control

points are prefixed by NK. The horizontal (X,Y)

coordinates of the points are based on the Enugu

Local Coordinate System with origin at a Secondary

National Control Station - the TB20 -, and the vertical (Z) coordinates are based on the National

Zero Datum.

During the reconnaissance preceeding the

establishment of the basic control for this research,

it was evident that the NK series of control was

insufficient for use as basic control. A new set

of control points was therefore established (mainly

along the roads in the campus). The points were

marked with concrete beacons, each measuring about

18cm x 18cm on the cross section and 75cm in length

out of which about 68cm was submerged below ground

surface. The specific point of interest is identified

with the top of a nail that features at the centre

of the cross section, and the identifying serial

numbers of the points were written with prefix UNEC.

This new series of control together with another

series identified with UNP...E and whose coordinate

system had been obliterated were coordinated with

respect to the former series (the NK).

The entire network of control which include the

NK, UNEC, and UNP.. . E series constituted the basic control for this research. The coordinates of the

photo control (section 4.22) were determined with

respect to those of the basic control to the same

precision.

4.22 Photo Control

The identification of photo control on the

ground is achieved by either premarking or post-

marking; depending on the prevalent circumstances[29,

3 8 1 . In premarking, points are selected and targets

are placed on them before photography to enable easy

identification on the photographs after flying. In

postmarking, points are marked after photography by

first selecting distinct points on the photographs

and subsequently identifying them on the ground. - the latter procedure (i.e. postmarking) was adopted

in this research since the photographs used were not

premarked.

Owing to the nature of the terrain photographed

and the need for multiplicity of points (such that

sufficient points would be available for use as

contro'l and test points) the selection of the photo

control points did not follow any systematic pattern

in terms of density and distribution. It was a

random selection of descrete points on each of the

photographs involved. The selected points included

corners of concrete slabs, lawn tennis courts,

buildings, and concrete pavement. Each selected point

was ericircled with a chinagraph on each of the paper

positives where it appeared. Numbers were assigned to

them.

Each photo control point was identified on the

ground by using a red paint to make a dot which

defines the point. It is then encircled and the

identification number is written beside it with the

red paint. Descriptions of all photo control points

are given in Appendix 1.

4.23 Traversinq

The horizontal (X,Y) coordinates of the basic

and photo control were determined by the process of

traversing (for a detailed understanding of

traversing see [€!I ) .

4.231 Field Work in Traversing

The practical process of traversing was under-

taken by a field party comprising of at least five

persons, out of whom, there was one instrument man,

one booker, one umbrella man, two or more target men

(one at the back station, another at the forward

station: and one at each of a nearby photo control

point). The author was always the team leader who

coordinated all field activities.

Traversing of the basic control was done in loops

starting from a pair of NK stations and closing on

the same or another pair of NK series of control;

thereby constituting a closed traverse or a closed

loop traverse, both of which afforded checks[€!]

(see fig. 4.1). In the case of the latter, the loop

was traversed in the clockwise direction and exterior

angles were measured. Angle and distance measurements

were done simultaneously. Both horizontal and

vertical angles as well as distances were measured in

both the back and forward directions. Each photo

Closed traverse (b) Closed loop traverse

A = known stations

o = new stations

Fig. 4.1 Traverses

control was coordinated by observing a ray comprising

of angle and distance measurements from one or two

basic control stations.

4.232 Traverse Computations

The results of field observations in traversing

are angles and distances. The final output of a

traversing job is the horizontal (X,Y) coordinates

of traverse stations, which are obtained through

traverse computations and adjustment. Adjustment of

traverse in this research was done using Bowditch

method [8 1 . Relative accuracy ratios were computed for

each of the traverse loops. They ranged between

1/5,496 and 1/58,495. Although third order traverse

specifications were adopted during the field work,

the values of the relative accuracy ratios showed an

inclination towards both third order (1/5,000 to

1 /10,000) and second order (1 /20,000 to 1/50,000)

work[8]: However, second and third order traverses,

among other surveys, afe recommended for controlling

most photogrammetric jobs[291.

Moreover, the computed Eastings were adopted

as X-coordinates while the Northings were adopted as

the Y-coordinates.

4.24 Spirit Levellinq

The method of spirit levelling was used in the

determination of the vertical ( Z ) coordinates of the

control points (both basic and photo control points).

The field work was undertaken by a field party of,

at least, three persons. The author was the

instrument man most of the time and personally

supervised the work at other times.

Levelling of all control was carried out in

loops; starting from a point of known elevation and

closing at the same point or another point of

known elevation. Also, since the interest was only

the elevations of the control points, there was no

distance measurement during levelling. The work

was, therefore, not a profile levelling but a

differential levelling[8].

During levelling, attempt was made as much as

possible to equalize the distances between the

instrument and staff stations in order to preclude

refraction and earth's curvature errors[4]. The

method adopted in computing the elevations of the

control in this research was the 'rise and fall'

method[8].

At the end of each loop the level was adjusted by

a fair distribution of the misclosure. All

computations were done in the field book.

4.25 Summary

All control used in this research possess

both the planimetric (X,Y) and vertical ( Z )

coordinates.

The values of all coordinates of the existing

control (i.e. the NK series) are given in table 4.1.

The values of all coordinates of the basic

control (i.e. the UNEC and the UNP...E series) are

given in table 4.2.

The values of the coordinates of the photo

control (i.e. the pp series) are given in table 4.3.

Table 4.1: Coordinates of Existing Control

POINT NO.

NK 1

NK2

NK 3

NK4

NK 5 4

NK6

NK7

Nk 8

NK9

NKlO

NKl 1

NK12

NK13

NK14

NK15

NK16

NK 2

-- - -

(All values in meters)

X (EASTINGS)

2251.246

2479.695

2672.577

2947.368

2778 .O24

2692.811

2614.431

2695.669

2606.405

2351.479

2201.646

21 80.970

2028.470

1603.952

1968.036

2552.851

2241.287

Y (NORTHINGS)

-1 205.256

- 873.459 - 959.972 -1052 .O46

-1242.035

-1495.707

-1435.338

-1557.212

-1773.686

-1 756.221

-1 770.242

-1442.259

-1 205.204

- 908.837 -1 026.227

-1 378.998

-1 300.649

NATIONAL COORDINATES OF ORIGIN, TB20

EASTINGS NORTHINGS

+1831369.23ft +883801.63ft

Z (HEIGHTS)

214.4447

203.2060

203.0593

195.0722

207.2712

212.9675

220.0324

211.1752

195.0409

198.5552

196.5891

208.5403

216.5690

207.8336

219.9752

219.3327

217.5124

T a b l e 4 . 2 : C o o r d i n a t e s of B a s i c C o n t r o l

P O I N T NO.

UNEC 1

UNEC 2

UNEC 3

UNEC 4

UNEC 5

UNEC 6 +

UNEC 7

UNEC 8

UNEC 9

UNEC 1 0

UNEC 1 1

UNEC 1 2

UNEC 1 3

UNEC 1 4

UNEC 1 5

UNEC 1 6

UNEC 1 7

UNEC 1 8

UNEC 1 9

UNEC 2 0

( ~ l l va lues i n m e t e r s )

Z (HEIGHTS)

Z (HEIGHTS)

196.952

199.428

196.364

- 190.864

220 .030

198.051

210.774

201 .I38

210.788

209.080

Y (NORTHINGS)

-1770.165

-1757.518

-1 764.565

-1977.171

-1936.716

-1229.264

-1620.664

-1557.411

-1688.776

-1451.443

-1434.875

POINT NO.

UNEC 21

UNEC .22

UNEC 23

UNEC 24

UNEC 25

DS7

UNP5E

UNP8E

UNPI 7E *

UNP20E

UNP4E

X (EASTINGS

2194.905

2335. 196

2545.989

2438.909

2331.353

2700.063

2184.164

2616.044

2646.936

2493.162 -

2195.309

Table 4.3: Coordinates of Photo Cont ro l ( A l l v a l u e s i n meters)

POINT NO.

PP 1

PP 2

PP 3

PP 4

PP 5 '

PP 6

PP 7

PP 8

PP 9

PPlO

PPl 1

PP12

PP13

PP14

PP15

PP16

PP17

PP18

X (EASTINGS) - 301 7.235

2881 -074

2753.794

2638 -090

2543.155

2272.250

2448.844

2573.51 2

Z (HEIGHTS)

194.554

198.322

202.525

206.979

207.340

21 0.789

212.520

210.078

210.893

198.282

202.602

-

206.399

21 1.831

218.685

215.341

216.947

206.140

POINT NO.

PP19

PP20

PP2 1 (UNEC18)

PP22 (UNECI 7)

PP23

PP24

PP25

PP26 "

PP27

PP28

PP29

PP30

PP3 1

PP32

PP33

PP34

PP4 0

PP4 1

PP42

PP43

X (EASTINGS)

2468.164

74

Z (HEIGHTS)

218.600

219.762

211 .O7O

206.357

199.414

19'9.700

204.940

202.100

197.408

197.150

199.292

197.709

190.841

189.633

191.735

207.877

192.632

201.206

219.864

223.919

POINT NO.

PP44

PP4 5

X (EASTINGS)

3 5 8 7 . 1 5 3

3 4 8 8 . 5 3 5

-

2696 .625

1 7 3 8 . 5 0 0

1 4 7 4 . 2 7 9

Y (NORTHINGS)

- 321 .780

- 8 3 9 . 5 7 5

- -2402 .585

-2837 .413

-2265.704

Z (HEIGHTS)

2 2 4 . 7 9 9

200.254

-

186.676

194 .686

1 9 1 . 3 7 0

CHAPTER 5

5.00 PHOTOGRAMMETRIC DATA ACQUISITION

5.10' Point Markinq and Transfer

Since natural discrete points were chosen in

the photographs to serve as control, test, and

pass points, there was no need for point marking

and point transfer from one photograph to another.

It was achieved by a mere visual identification of

identical points in any number.of photographs where

they featured.

It has however been proved that point marking

and transfer with the use of point marking devices

may not, afterall, be superior to well defined

discrete points. Hempeniusl201 carried out a

research involving points marked with the WILD PUG

and the ZIESS SNAP MARKER as well as pre-signalised

points. One of the conclusions of the research was

that points marked by the evaluated point marking

devices are not as ideal as pre-signalised points.

Also Amer F., et al.121 in their own paper stated

that the accuracy of aerotriangulation after

independent model adjustment is 8-12pm for pre-

signalised points and 15-30ym for both natural

points and pricked points.

Natural points at good locations possess almost

the same physical characteristics as presignalised

points. They also yield the same accuracy as marked

points after measurement and adjustment. As such the

use of natural points in this research was considered

adequate as far as photo point identification and

transfer are concerned.

JI

5.20 The Main Instrument - Zeiss C-8 Precision Coordinatoara~h

The Zeiss Precision Coordinatograph of the C-8

Stereoplanigraph consists of the following main

design elementsE71.

Tracing table with tracing surface and

transillumination system.

Rectangular cross slide system

Drive system, transmission gears, and

coordinate counters.

Tracing device and viewing device.

5.21 The Tracing Table

The tracing table is a rectangular table

standing on four legs, three of which are adjustable

by setscrews. The adjustment enables the table to

be set and levelled on an uneven floor. The table

measures about 1.5m x 1.5m and is standing about Im

above the floor.

The tracing surface is made of glass. It is

capable of illumination from underneat by switching

on an eiectric bulb contained in a metal housing

called the light table. The light table can be

moved to any part of the undersurface of the tracing

table to illuminate any area of interest.

5.22 Rectangular Cross Slide System

The coordinatograph is equipped' with a

rectangular cross slide system. It is this system

that makes the necessary movements that enable the

performance of the functions of the coordinatograph.

The cross slide moves in two perpendicular directions;

representing the x and y axes.

Both x and y axes feature coordinate shafts

with metal scales divided in millimeters. Coordinates

can be read from these scales to O.lmm with the

aid of a vernier attached to the coordinate

carriages.

5.23 Drive System Transmission Gears and Coordinate Counters

The coordinate carriages on the coordinatograph

are driven by two hand wheels (for x and y) which are

attached to the gear box on the coordinatograph.

Movements on the coordinatograph can be transmitted to

the ster;oplotter and vice versa through a system of

gears in the gear box and a mechanical link. The

movements can however be localized on the coordinato-

graph by disconnecting the mechanical link between it

and the stereoplotter.

Notwithstanding the availability of the

coordinate scales on the coordinate shafts, counters

are provided at convenient locations to record x and y

coordinates. The coordinates can thus be read out

from the sitting position of the operator. Coordinates

on the counters are graduated to read to O.lmm.

Estimation to 0.Olmm can be made very conveniently.

The readings on the counters are, however, not

necessarily synchronised with those on the

coordinate scales. Hence it is advisable to use

one system for any particular work. In this

research coordinates were read out from the counters.

5.24 Tracinq and Viewinq Devices

The tracing devices comprises of a tracing

head and a lifting magnet. The tracing head holds

the pencil lead holder which is manually introduced

in the"bore of the guide sleeve of the lifting

magnet. The movement-of the tracing head is

normally done back and forth along the x-coordinate

shaft which in turn moves along guide rails in the

y direction.

A spotting microscope is provided for viewing.

This microscope can be slid in place instead of the

pencil lead holder. The microscope contains a

black annular mark of O.5mm diameter. The images

together with the mark is magnified seven times by

the microscope when viewing.

It is this annular mark that was used in

tracking image points on the diapositive during

image coordinate measurements.

5.30 Image Coordinate Measurement

Measurement of image coordinates on the

coordinatograph was preceeded by necessary checks.

The horizontality of the tracing surface was tested

with a small spirit level. The level was placed on

different parts of the table in both the x and y and

a few other arbitrary directions. In all cases, the

level revealed that the tracing surface was horizontal.

If however, it was found that the surface was not

horizontal, adjustment would be done by the use of

setscrews on the three.adjustable legs of the tracing

table (see section 5.21). The measuring stability

of the coordinatograph was tested with a calibrated

Wild grid plate.

All photographs were measured on one section

of the surface of the tracing surface marked out by

the author. They were illuminated from above with

a table lamp because the light table could not

provide adequate illumination from under the tracing

surface. Regardless of the situation of the light

source, however, viewing was greatly hindered at

first. This was because there was no adequate image

contrast on the photographs owing to the dull nature

of both the diapositives and the tracing surface

of the coordinatograph. Several attempts were made

at improving the situation. Viewing was eventually

enhanced by introducing a white cardboard paper

under each diapositive during measurement.

In order to measure a point, the annular

measuring mark was used in bisecting the point. The

coordinates of the point would then be read out and

recorded. For each of the photographs all the

four fiducial marks were measured before the rest of

the marks. In order to ensure the shortest tracking

path, all point numbers were written down before the

commencement of measurement on each diapositive. The

points were measured in the order in which their

numbers were written.

Each measured point was bisected four times

and x and y readings taken in each case. The adopted

image coordinates were the means of the four sets of

measurements. From test measurements conducted by

the author, four readings offered optimum accuracy.

Any increase in the number of measurements would not

improve the accuracy significantly. It is also

n o t i c e a b l e t h a t some p o i n t s were measured j u s t

once ( s e e Appendix 3 ) . These a r e p o i n t s which

a r e obscured by e i t h e r f e a t u r e s w i th h ighe r

e l e v a t i o n s o r t h e i r shadows. A s such t h e i r

p o s i t i o n s w e r e on ly e s t i m a t e d , and t h e r ead ings

taken once.

CHAPTER SIX

6.00 DATA REDUCTION

In this research data reduction includes the

reduction of measured image coordinates to photo-

coordinates, the refinement of photocoordinates, and

the use of the refined photocoordinates and the

ground coordinates of the control points for the

computation of ground coordinates of the test points 4

and pass points. The theoretical background to all

the foregoing operations have been discussed in

chapter 3.

Coordinate Reduction and Refinement

Based on the distances between fiducial marks

(given in the calibration certificate), photocoordinates

of the fiducial marks were determined. These were

subsequently utilized in the determination of the

photccoordinates of the other photo points from

their measured image coordinates.

The distances between fiducial marks, as given I

in the calibration certificate, (see also Fig. 3.2)

are :

1 - 2 = 211.998mm

2 - 3 = 212.001mm

3 - 4 = 212.012mm

4 - 1 = 212.006mm

Using these distances, fiducial coordinates

computed for the fiducial marks, based on the

procedures given in table 3.1, are as follows:

Point x (mm) y (mm)

1 105.999 -106.003

2 -'105.999 -106.001

3 -1 06.006 106.001

4 106.006 106.003

The coordinates of the principal point of

symmetry with respect to the fiducial centre

(see fig. 3.1) are:

xo = -O.O06mm, yo = 0.Ollmm

These are called the principal point offset. They

are applied to (subtracted from) the fiducial

coordinates of the fiducial marks to compute their

photocoordinates as given in table 3.2. The photo-

coordinates of the fiducial marks are therefore:

Point x (mm) Y (mm)

1 106.005 -106.014

2 -105.993 -106.012

3 -1 06 .OOO 105.990

4 106.012 105.992

These were used to compute the transformation

parameters for the affine transformation equations Z

(3.1) used in reducing the measured image coordinates

of the rest of the photo points to their equivalent

photocoordinates (see section 3.1 2) .

6.11 Transformation of Instrumental Coordinates - to Photoco-ordinates

The measured (image) coordinates were reduced

to photocoordinates using the computer programme

"TRAN 2B" based on the Two-Dimensional Affine

Transformation (discussed in section 3.12).

6.12 Principal Point Offset Correction

The principal point offset correction applied

to the fiducial coordinates takes care of principal

point offset correction to all measured coord-

inates.

6.13 Film Deformation Correction

Film deformation correction was not carried

out independently. The reader is referred to

section 3.132 for a detail information on this.

6.14 Lens Distortion Correction

Lens distortion correction was also accomplished

with the use of the programme "TRAN 2BW, based on

equation (3.5). The distortion coefficients, k's,

were first computed with a programme which does

adjustment by parametric method. The theoretical

background to the process is given in section

3.133. The computed values of k's are given in

table 6 -3

TABLE 6.3 Distortion Coefficients

Coefficients

k0

kl

k2

k3

k4

Computer qenerated values

-0.7297148 x

0.3887852 x lo-' -0.5960596 x 10-I

0.3326968 x

-0.6078753 x

These were the values of the distortion

coefficients used in the progr~mme, "TRAN 2BW, for

lens distortion correction.

6.15 Atmospheric Refraction Correction

It was possible to apply atmospheric refraction

correction in the programme, "TRAN 2Bn, but this

was not done. See section 3.134 for details.

\

6.16 Earth Curvature Correction

Earth's curvature correction was also not

applied. See section 3.1 35 for details.

6.20 Space Resection

The exterior orientation parameters of the

photographs were determined by the method of space

Resection (see section 3.14). This was the

function of subroutine "RESECT" in the programme

"RESINT." See Ap1)endix IVU for input data and results.

6.30 Space Intersection

Ground coordinates of the test points pass

points and even the qontrol points were computed by

Space Intersection (see section 3.15). The main

programme "RESINT" was used in doing this.

See Appendix IVB for input data and results.

6.40 Documentation of Computer Programmes Used

The computer programmes used in this research

include :

(1) Programme for adjustment by parametric

method - This programme was used in the computation of distortion coefficients (k's)

use8 in the correction for lens distortion

(see Appendix 4A) .' ( 2 ) Programme for Coordinate Transformation and

Refinement (TRAN 2B) - This programme was used in the transformation of measured (image)

coordinates to photo coordinates. It also

incorporates procesures for refinement of

photocoordinates. (See Appendix 4B).

13) Programme for Space Resection and Space

Intersection (RESINT) - This programme was used in executing both the space Resection and

space Intersection (see Appendix 4C).

All the programmes were written by Dr. N.K.

Ndukwe and tested on the UNIVAC 1110 Computer at

the University of Wisconsin Madison, Wisconsin,

U.S.A. The adaptation of the programmes for use in

the IBM 370 computer was done by the author.

Begin 0 I

Read NO = Number of observations NU= Number of unknowns

I

11 N = APA

t Write computed values

-1 N I U, X I V I 00

t END

Fig. 6.1: Flowchart for Adjustment By Parametric Method

Begin 0

YES

Compute Transformation coefficients I Compute Transformed coordinates I for systematic errors

Print refined coordinates

t END 'I

Fig. 6.2: Flowchart for Photocoordinate Refinement

Begin

I Read

f l f £2

I 1 Perform space Resection I for left and right I photos (Subroutine RESECT)

I 1

/ Read I

/ Number of photos NC Number of points NP

1

t Read xi yi for left and right Photos (i='i12)

J Compute ~p~roximate Ground Coords ( X ) 0 1 (Y) 0 1 (Z) 0

Update the ground coord by least squares f Print Ground Coords / (X,Y,Z). Std. Errors

Fig. 6.3A: Flowchart for "RESINT" ( space Intersection)

( End

ENTER

\ :::Number wor$or kor of Xoor cok YOO, Z"0 (Approx

Ext. orient. paramete

Read xi,yi,Xi,Yi,Zi

#

I

Compute corrections Update Approx. to approximate values- values

I

Compute orientation c' i Parameters

( Return J Fig . 6 . 3 8 : Subroutine "RESECT" (Space Resection)

CHAPTER SEVEN

7.00 RESULT ANALYSIS

7.10. - Measurement Accuracy of the C-8 Coordinatograph

The handbook of the Zeiss C-8 coordinato-

graph quotes the plotting accuracy of the coord-

inatograph as O.lmm. Since it was never meant for

image coordinate measurement, there was no

indication of the measurement accuracy for the 4

coordinatograph. It is possible to determine the

precision of measurements if at least two independ-

ent observations are available[9]. Such a

precision determined for measurements made by the

C-8 coordinatograph could then be used to

approximate its measurement accuracy.

In an attempt to achieve the foregoing, a grid

intersection was chosen arbitrarily from a

calibrated Wild grid plate. This point was measured

12 times arbitrarily and x and y image coordinates

recorded (see table 7.1). Based on the readings,

standard deviations were computed for both x and y.

TABLE 7.1

Measurement Accuracy Determination

Standard deviations u = +0.0119mm, u = k0.0083mm X Y

48.12 1-0.008 1 60.25

This yields a positional accuracy of:

0.008

Mean 48.112 1 60.258 1

It is evident that the standard deviations

in x and y are each approximately equal to 0.Olmm.

It can therefore be said that the measurement

accuracy of the zeiss C-8 precision coordinatograph

is 0 . 0 1 ~ (low) in x and y.

7.20 Comparison of Test Points

As a necessary step,in the analysis of results

in this research, the ground coordinates of the test

points dktermined photogrammetrically (XI, YI, ZI)

were compared with those determined by ground survey

methods (XG, y ~ , ZG). The discrepancies were derived

as follows:

Ax, = - (XG) i

AZi = (ZI) - (ZG) i

The values of coordinates of control and test

points and their corresponding discrepancies are listed

in table 7.2. A statistical rejection test was

carried out with a view to isolating points where

systematic errors may have occured. First, the

discrepancies which for the purposes of the test are regarded as

residuals were assumed to be normally distributed

since there were almost as many negative residuals

as positive ones. A root mean square error (r.m.s.e.)

was computed for each of the coordinates (x,Y,z),

using all the residuals as follows:

where

e = the root mean square error (r.m.s.e.)

A = difference between the photogra~nmetrically

determined and given ground coordinates

n = number of check points used.

The computed values are ex = 1.043mt e = 1.074mt Y

e = 1.948m. These r.m.s.e. values were regarded Z

as standard deviations and used as such in the

statistical test. The test involved the use of the

standardized variable a/e, (mean, 0 and standard

deviation 1) which is equivalent to the z score given

by z = (S-p)/u (in which s is the variable, P is the

man, and u is the standard deviation) 1341. A one-tailed

test was conducted at 90% confidence level. The use

of this (90%) confidence level in statistical decision

theories is, in practice, customary although other

confidence levels can be used especially 95% and 99%.

The critical value chosen at 0.10 level of significance

is given as z = +1 .28 [34 ] . It was the intention to

isolate all standardized variables which would not obey

the condition given by

The test was conducted differently for X, Y and Z

coordinates. However, even if one of the coordinates

of a point was significant, the point was isolated

entirely. Out of the total of 52 points involved, 15 h

were significant at a 0.10 level of significance. Such

points did therefore not meet the level of tolerance

required of test points in this research.

The affected points are shown asterisked(*) in

table 7.2. The residuals of most of these points

are very large. Almost all the points with these

residuals are p0int.s which are located at or near

the foot of the corners of buildings or vertical

walls. During observation, each of such points was

visible in one member of the stereopair where it

featul-ed but its conjugate was obscured in the other

member of the stereopair owing to relief displacement

which caused the building or wall to tilt in the

direction of the point. As a result, the position

of the conjugate points were always estimated during

obsertration (see section 5.30). In particular, the location of

points 21 and 22 were not well defined as natural

points. They were just estimations of survey

pillar locations which were close to prominent

features but were in themselves not visible on the

photographs. Table 7.2 could be compared with the

stationhdescriptions (Appendix 1) in order to

appreciate these phenomena. All such points are,

however, included for experimental purposes. It was

aimed at determining the applicability of such

points as natural points. The result has thus far

exposed the danger of such an exercise, especially

when measurement is made monoscopically.

Points which fall into the groups described in

the foregoing paragraph were regarded as having

been afflicted by systematic errors; which were

manifested mostly in their Z coordinate residuals.

They are, therefore, for the purposes of this research

classified as bad points, while the rest are classified

as good.

SPACE INTERSECTIOIG

SPACE INTERSECT1 ON .- .

VALUES 21

195.572

GROUND I r PGINT humm SURVEY RESID.

.- . PAUIES i :I VALUES

XG VALUES YI

POINT , NUM3ER

SP.4CE INTERSECTION

VALUES XI

205 1.720

GROUND SUWEY RZS T D . . VALUES

YG XI-XG

2351~823 -0.103

2&48,844 0.095

2515~918 -101~2

YI-YG

SPACE

7.30 Statistical Evaluation of Results

The evaluation of the performance of the

Zeiss C-8 precision coordinatograph as a mono-

comparator can be achieved by the determination of

the accuracy of the computed coordinates. There are

various ways of expressing the accuracy of computed

coordinates[9]. The techniques that would be of

significance as far as this research is concerned

are based on the determination of the achieved

accurac? and the accuracy requirement for mapping.

'7.31 Achieved Accuracy

In this type of study the achieved accuracy (e),

is evaluated in terms of the root mean square error

(r.m.s.e.1 computed from the residuals generated by

the differences between the photogrammetrically

determined ground coordinates of the test points and

their equivalent ground survey values. They are

determined by equation (7.2).

Achieved accuracies are determined independently

for X,Y, and Z coordinates. The values for X and Y

are subsequently combined to determine one value which

represents the achieved accuracy in planimetry

(positional accuracy) given by the expression:

While the value for Z is left alone and it represents

the achieved accuracy in elevation.

It is noteworthy here that even the so called

control points coordinates were involved in the

computation of achieved accuracy because:

(1) They were merely used in space resection

for the determination of exterior

* orientation parameters and not actually

used in the adjustment of ground coordinates.

(2) Their residuals were in the same order of

magnitude as the rest of the

test points.

The achieved accuracies as computed from the

results of this work are tabulated as follows

(Table 7.3) :

Table 7.3: Achieved Accuracy

Category of points I 9[ I e~ I eXY 1 e~

All points

Good points

1.043rn

0.524m

1.074111

0.557m

1.497m

0.765m

1.948rn

0.863m

In table 7.3 accuracy values have been presented

for all the points and also for the good points alone.

,An alternative method to the determination of

accuracy is the computation of standard errors of

computed coordinates. They are the diagonal

elements of the variance - covariance matrices of the adjusted unknowns

Variance - covariance

with --

where

(ground coordinates).

matrix is given by:

IX = variance - covariance matrix a, = standard error of unit weight

V = weighted residuals

n = number of observations

- 1 N = inverse of the normal equation

matrix

The variance - covariance matrices are separate for individual points owing to the nature of the

mathematical model used in the computation. The

standard errors have, however, been printed side

by side with the coordinates of the intersected

points in the computer programme "RESINT"

(see Appendix IVC), With the exception of a few

points believed to have been affected by systematic

errors, the standard errors of the coordinates

( X I Y and Z) ranged between 0.000m and 3.000m;

with the majority (more than 90%) being less than

1.000m.

Ir

7.32 - Accuracy Requirement for Mapping

The accuracy of a set of photogrammetrically

determined points can also be evaluated by investigat-

ing their plausibility as control for mapping at a

certain scaleL91. Accuracy in mapping is usually

subdivided into accuracy in planimetry and accuracy

in elevation.

It is a general concept in cartography that

with a very sharp hard pencil and extreme care,

points can only be plotted to within 0.3mm in

planimetry[8]. Notwithstanding, however, in respect

of planimetric accuracy, it is required that for

maps on scales of 1/20,000 or larger, not more

than 10 percent of well-defined points tested

shall be in error by more than O.8mm at the map

scale; for maps at scales of 1/20,000 and smaller,

the tolerance is O.5mm at the map scale. In

respect of vertical accuracy, not more than 10 per-

cent of the well defined points tested shall be in

error by more than one half the contour interval.

Furthermore, contour intervals and scales of maps

are related to the extent that the smaller the scale,

the larger the contour,interval[8]. For any range

of map scales there is a corresponding range of

contour intervals can be chosen for any given

scale, by proportion.

The above conditions are normally referred to

as "National (USA) Map Accuracy Standardsn[8].

They are functions of the limiting (maximum allowable)

standard deviations in planimetry and elevation. It

is evident that the limiting standard deviation for

planimetry combines the standard deviation in X,(ox),

and that in Y , ( a 1 , to realise what is known as Y

circular standard deviation (oC) related by the

expression [8, 281 .

u - 4 ( u x + u ... (7.5) C Y

Equation (7.5) is valid especially for o

0.5 - < '/u < 1.0 (when o x > o ) . Thus the X - Y

specification for planimetry in the National Map

Accuracy standards is referred to as the circular

Map Accuracy Standard (CMAS) which can be loosely

interpreted as the estimated deviation with 90%

probability; whereas that for elevation, which is

the estimated deviation in elevation with 90%

is referred to as the vertical Map

Accuracy Standard (VMAS) [ 8 ] . In other words, the

CMAS and VMAS correspond to the limiting standard

deviations in planimetry and elevations, respectively,

at 90% confidence level.

CMAS and VMAS are a product of the limiting

standard errors in planimetry and elevation by

confidence coefficients for two-dimensional and

one-dimensional normal distributions respectively.

Table 7.4 lists the scale multipliers

(confidence coefficients), k t for the two-dimensional

normal distribution at various confidence levels.

The scale multipliers are factors that relate the

size of the error ellipse at a given probability

(or confidence level) to the size of the standard

ell.ispe which occurs at 39.4% confidence leve2.1281.

Table 7.4: Confidence coefficients for two-dimensional normal distribution

Confidence level (p) 1 39.4% 1 50% 1 90% 1 95% 1 99%

Confidence I I

Coefficient (k) I 1.000 ! 1.177 12.146 i2.447 , 3.035

SimiJarly, Table 7.5 lists the confidence

coefficients, zc, for the one-dimensional normal

distribution at various confidence levels[34].

Table 7.5: Confidence coefficients for one dimensional normal distribution

It is desirable to compute the limiting

standard deviations for planimetry and elevation

% and aZ) based on the national Map Accuracy standards as follows[8].

Confidence level

Confidence Coefficient zc ) 0.6745

50% 68.27% ! 9081 95%

5.000

99% 99.73%

1.645

I - '

1.96 2.58 3.000 I

For planimetry:

CMAS = 2.1460~ . .. (7.6)

If it is assumed that ax = CJ for a circle, it Y

follows from equation (7.6) that

= a = C X

CMAS = 0.466CMAS . . . (7.7) y 2.146

For elevations :

VMAS = 1.6450~ ... (7.8)

whence

- az A- I VMAS = 0.608VMAS 1.645 ... (7.9)

The standard deviation for any specific map would

then depend on the scale of the map. For instance,

for a map of scale 1:5,000 and contour interval 2m

CMAS = 0.8 x 5,000 = 4000mm = 4m

VMAS = 4 x 2 = Im

The limiting standard errors for planimetry and

elevation for that map can be computed respectively

from equations (7.7) and (7.9) . Thus

a = 0 . 4 6 6 x 4 = 1.864m C

Oz = 0.608 x 1 = 0.608m

It is therefore required that the standard

deviations of points in the map in planimetry (m ) P

and elevation (mZ) shall satisfy the following

conditions:

1.86m and mZ - < 0.6m

The total error in planimetry for a map

produced photogrammetrically generally originate

from three main sources[9] :

(1) Identification and pointing error at the

time of observation.

(2) Errors in relative and absolute

* orientation of the stereomodel

(3) Errors in the coordinates of the control

points used for absolute orientation.

Assuming all three errors are uncorrelated, then

the standard error of map points in planimetry

becomes [ 9 1 :

where

m = standard error of identification and i

pointing

m, = standard error of the orientation of

the model

m = standard error of planimetric control pt

Based on equation (7 .10 ) the limiting standard

deviation of planimetric control becomes

The error in elevation for a map produced

photogrammetrically comes from[91:

where

Errors in elevation of the control

points used for absolute orientation

Errors in the plotting of contour lines.

= standard error of height control

= standard error of contour elevations

The limiting standard error of elevation for a

height control point should therefore be deduced

from equation (7 .11 ) as:

It

quality

has however been decided that for good

photography, well identifiable points, and

u s i n g a p r e c i s i o n s t e r e o p l o t t e r f o r map c o m p i l a t i o n ,

a c o m f o r t a b l e assumpt ion would be

m = +20m a t image scale i

m, =. +20m a t image s c a l e

mc = f 1 5 % , o f t h e f l y i n g h e i g h t (H)

Thus, t h e l i m i t i n g s t a n d a r d e r r o r s f o r v a r i o u s map

scales and v a r i o u s p h o t o s c a l e s c a n be de te rmined .

Tab le 7.6 g i v e s t h e v a l u e s computed f o r some s e l e c t e d

map s c a l e s ; g i v e n a pho to s c a l e o f 1 /6 ,000 and f l y i n g

h e i g h t o f ~ 1 , 1 0 0 m (which i s t h e a v e r a g e s c a l e and f l y i n g

h e i g h t f o r photography used i n t h i s r e s e a r c h ) .

The a c c u r a c y o f t h e computed ground c o o r d i n a t e s a s

f a r as map a c c u r a c y s t a n d a r d s a r e concerned c a n be

e v a l u a t e d by comparing t h e v a l u e s o f eXy and eZ ( r o o t

mean s q u a r e e r r o r s i n p l a n i m e t r y and e l e v a t i o n ) de te rmined

i n s e c t i o n 7.31 t o t h e v a l u e s i n columns 10 and 11,

r e s p e c t i v e l y , o f t a b l e 7.6.

S i n c e eXy = 1.497m and eZ = 1.948m it is , t h e r e f o r e ,

e v i d e n t t h a t t h e c o o r d i n a t e s de te rmined i n t h i s r e s e a r c h

c a n be used f o r t h e c o n t r o l o f mapping a t s c a l e s o f

1/13,000 and smaller. But i f t h e good p o i n t s are

c o n s i d e r e d a l o n e t h e n t h i s work c a n be used t o c o n t r o l

mapping a t 1/6,000 and s m a l l e r . I f , however, t h e c o n t r o l

r e q u i r e m e n t i s i n p l a n i m e t r y a l o n e , t h e n t h i s work can

Table 7.6: Accuracy Requrements for Mapping Based on 1/6,000 photo scale and 1,lCOm flying height ,

I

1 2 3 4 5 6' 7 8 9

Op- ~QP contour m (0 1 mZ(uZ) rn m o m P C i c Scale interval CMAS VMAS

1 :1,000 1 .Om 0.8m 0.50m 0.373m 0.304m 0.12111 0.12111 0.165m

1 :2,000 1.5m 1.h 0.75m 0.746m 0.456m 0.12111 ,0.12m 0.165m

1 :5,000 2.5m 4.h 1.25m 1.864m 0.760m 0.12111 0.12111 0.165~1

1 :6,000 3. Om 4.8m 1.50m 2.237m 0.912.m ,0.12m 0.12111 0.165m

be used in controlling maps of larger scales (up to

1/5,000) as can be seen from table 7.6. However, since

achievable accuracy in coordinates determined photo-

grammetrically depend to a great extent on scale of photo-

graphy, it follows that if larger scale photos are used

the overall results would improve and could, therefore,

be used in controlling mapping at scales larger than the

stated ones.

The results of this research can also be used in b

controlling some other photogrammetric activities such

as mosaicing, reconnaissance work and some engineering work

such as:

( 1 ) Some highway engineering projects

( 2 ) Agricultural and Irrigation projects where

height determination is essential.

CHAPTER EIGHT

8.00 CONCLUSIONS AND RECOMMENDATIONS

8.10 Conclusions

Many revelations have been made in this

research which, perhaps, can best be appreciated if

outlined in the form of conclusions as follows:

(1) It is possible to measure image coordinates

from diapositives on the Zeiss C-8 precision

coordinatograph and many other coordinatographs

wikh good read-out facilities using the

methodology stated i n this text. Even

coordinatographs with opaque table surfaces can

be used, since illumination can be made from

above the table.

Measurement of image coordinates on the Zeiss

C-8 precision coordinatograph can be made to

an accuracy of O.Olmrn in x and y.

( 2 ) Photo points measured monoscopically must be

well-defined in all the photographs where they

are expected to feature. They must be on

relatively smooth surfaces which do not have

any sudden change in elevation close to the

location of the point. Points that do not

conform with these stipulations are prone to

misidentification during measurements.

Coordinates computed from image coordinates of

misidentified points are highly probable

to be wrong.

(3) With regard to the time of observation, table

(8.1) lists the time of observation of each

photograph used in this research, based on which

the, rate of observation is calculated. It is

pertinent to note that each point was measured

four times (see section 5.30). As such the time

may reduce or increase depending on whether the

number of measurements is reduced or increased;

other factors being constant.

Table 8.1

Rate of Observation

Photo Number

ENG/03/129

ENG/03/130

ENG/03/131

ENG/03/173

' No. of points ( n )

23

34

18

26

Time(t)

2 hours 20 min

3 " 05 " 1 " 50 " 2 " 20 "

Points/ Hour

-

9.857

11.027

9.818

11.143

Since the photographs were observed in

the order in which they have been listed in

table 8.1, it follows that there was an

'improvement in the rate of observation of the

observer as more experience was acquired with

time. However, it has been shown that when

four independent measurements are taken on each

point, between 10 and 15 points can be measured

in 1 hour with the Zeiss C-8 precision

cwrdinatograph.

(4) Using image coordinates measured in the Zeiss

C-8 precision coordinatograph from photography

of scale 1/6,000, ground coordinates can be

determined to an accuracy (r .m. s. e. ) of 1 .497,m

and 1.948m in planimetry and elevation respectively.

This accuracy can be higher when the photography is

of a larger scale and when the photo points are good.

(5) Based on the analysis of results made in

section 7.32, it is certain that points whose

ground coordinates have been determined from

image coordinates measured in the Zeiss C-8

precision coordinatograph, when the photographic

scale is 1/6,000 can be used to control

mapping at a scale of 1/13,000 and smaller.

Maps of larger scales (up to 1/5,000) can be

controlled if the requirement is only in planimetry.

(6) The aforesaid control points can also be used

in controlling some other photogrammetric

activities such as mosaicing, reconnaissance

work, and some engineering projects.

8.20 Recommendations for Future Research Work

Naturally, some need has arisen for futher

investigations to be made on the outcome of some

aspects of this research. The most imperative areas

include the following:

(1) It is known that the movement of the tracking

device of the C-8 coordinatograph can also be

transmitted to the coordinate counters of the

stereoplanigraph C-8 stereoplotter when the two

are connected. An attempt should be made to

read out measurements made on the coordinato-

graph through the coordinate readout system of

the stereoplotter. These should be used in the

computation of ground coordinates such that

it may be determined whether or not they would

have a higher accuracy in accordance with the

higher reading precision of the stereoplotter.

(2) The tracking miscroscope with annular measuring

mark should be replaced with one having a

cross or dot as measuring mark and the effect

monitored.

(3) Other coordinatographs can be investigated to

debermine their reliability as image coordinate

measuring equipment, using the methodology

established in this research.

(4) Instead of a sequential solution, image

coordinates measured in the C-8 coordinatograph

may also be subjected to a simultaneous solution

to explore a possibility of improvement in

accuracy. This could not be carried out in this

research owing to time limitation.

BIBLIOGRAPHY

Ackerman, F. "Results of Recent Tests in ~erial Triangulation. " Photogrammetric Engineerinq and Remote Sensi3, Vol. XLI, No. 1, January 1975, p. 91.

Arner, F. et al. "Aerial Triangulation with Emphasis on Equipment, Methods, and Application," ITC Journal, 1977-1, p.4.

American Society of Photogrammetry. Manual of Photoqrammetry. 4th edition. Menasha, Wisconsin: George Banta Co., 1980.

Bomford, G. Geodesy. New York: Oxford University Press, 1980.

oni if ace, P.R.J. "Results of Analytical Triangulation,Using the Kern PG-2 Stereo- plotter." Paper presented at the XIth International Congress for Photogrammetry in Laussanne, 1968.

Brock (Jr.) , Robert H. "Methods for Studying Film Deformation," Photoqrammetric Enqineerinq, Vol. XXXVIII, No. 4, April 1972, p. 399.

Carl Zeiss, Handbook of the Precision Coordinatograph of the C-8 Stereoplanigraph.

Davis, Raymond E. et al. Surveyinq: Theory and Practice. New York: McGraw-hill Inc., 1981.

Derenyi, Eugene E. and Maarek, Ahmed M. "Evaluation of Aerial Triangulation Techniques" Department of Surveying, University of New Brunswick Technical Report No. 17, August 1972.

[lo] Eden, J.A. "Point Transfer from one Photo- graph to another," The Photogrammetric Record, Vol. VII, No. 41, April 1973, p.531.

[I 1 ] Elassal, Alef A. "Generalised Adjustment by Least Squares," Photogrammetric Engineering and Remote Sensinq, Vol. XLIX, No.2, February 1983, p. 201.

[I21 Erio, George W. "Plotter Orientation from Aerotriangulation O ~ t p u t , ~ ~ Photoqrarnmetric Engineering, Vol. XL, No. 12, December 1974, p. 1403.

[I31 Exintavelonis, John, et al. "Image coordinate Measurement on a Stereoplanigraph C-8," - -

Photoqrammetria, Vol. 36, No. 3, April 1981, p. 101.

r.

[I41 Forster, Bruce C. "Aerotriangulation Accuracy," Photogrammetric Engineering and Remote Sensing, Vol. XLI, No. 4, April 1975, p.533.

[I51 Ghosh, Sanjib K. Analytical Photogrammetry. New York: Pergamon Press Inc., 1979.

[I61 Goudswaard, F. "Compensation for Earth Curvature Influence in the Kern PG.2." Paper presented at the Xth International Congress for Photogrammetry, 1964.

[I71 Goudswaard, F. "New Kern Equipment for Analytical Aerotriangulation." Paper presented at the XIth International Congress for Photogrammetry in Lausanne, 1968.

[ 181 Hardy, R.L. "Least Squares Prediction, " Photogrammetric Enqineering and Remote Sensinq, Vol. XLIII, No. 4, April 1977, p. 475.

Hallert, Bertil P. "Basic Quality Control and Tolerances in Photogrammetry," World Cartography. Vol. XII, 1972. p. 21.

Hempenius, S.A. "Physical Investigation on Pricked Points Used in Aerial Triangulation," Photogrammetria, Vol. XIX, No. 7, 1962/64 p. 301.

Karara, H.M. "Theoretical Determination of the Minimum Density of Ground Control in Aerotriangulation Projects," Photogrammetria, Vol. XIX, No. 7, 1962/64, p. 386.

Kenefick, J.F., et al. "Analytical Self Calibration," Photogrammetric Engineering, Vol. XXXVIII, No. 11, November 1972, p. 1117.

~ii~el'a', E. "Compensation of Systematic Errors of Image and Model Coordinates," Photogramrnetrfa, Vol. 37, No. 1 , November 1981, p. 15.

Kratky, V. and El-Hakim, S. F. "Quality Control for NRC On-Line Triangulation," Photoqrammetric Engineering and Remote Sensing, Vol. XLIX, No. 6, June 1983, p. 763.

Kraus, Karl "Film Deformation Correction with east Squares " Photoqrammetric Engineerinq , Vol. XXXVIII, No. 5, May 1972, p. 487.

Leberl, Franz "Photogrammetric Interpolation," ITC Journal, - 1975-2, p.205.

Levy, N.I. "Analytical Aerial Triangulation with ~nalo~ue~nstruments," ~hoto~rammetria, Vol. XIX, No. 7, 1962/64, p. 279.

Mikhail Edward M. Observations and Least Squares. New York: IEP-A Dun-Donnelley Publisher, 1976.

[29] Moffit, F.H. and Mikhail, E.M. Photogrammetry, 3rd Edition. New York: Harper and Row - Publishers, 1980.

[30] O'connor, Desmond "Some Factors Affecting the Precision of Coordinate Measurements on Photographic Plates," Photogrammetria, Vol. 22, No. 3, March 1967, p. 77.

[31] Rampal, Kunwar K. "A closed Solution for -

Space Resection," Photogrammetric Enqineering and Remote Sensing, Vol. XLV, No. 9, September 1979, p. 1255.

1321 Rampal, Hunwar K. "Least Squares Collocation in Photogrammetry," Photoyrammetric Engineering and Remote Sensing, Vol. XLII, No. 5, May 1976, p. 659.

[33] Scherz, James P. "Errors in Photogrammetry," Photogrammetric Enqineering, Vol. XL, No. 4, April 1974, p. 493.

1341 Spiegel, Murray R. Theory and Problems of Statistics (Schawm's Outline Series) New York: McGraw-Hill Book Company, 1972.

[35] Stefanovic, P. "Pitfalls in Blunder Detection Techniques," ITC Journal, 1981-1, p.81.

[36] Tewinkel, G. C. "Film Distortion Compensation for Photogrammetric Use." Coast and Geodetic Survey Technical Bulletin, No. 14, September 1960.

[37] Thompson, L.G. "Determination of the Point Transfer Error," Photoqrammetric Engineerinq and Remote Sensing, Vol. XLV, No. 4, April 1979, p. 535.

1381 Wolf, Paul R. Elements of Photoqrammetry. New York: McGraw-Hill Inc., 1974.

[ 3 9 ] Wolf, P.R. and Pearsall, R.A. "The Kern PG-2 as a Monocomparator," Photoqrammetric Engineering and Remote Sensing, Vol. 42, No. 10, October 1976, p. 1253.

[40] Wong, Kan W. "Propagation of Variance and Covariance," Photoqrammetric Engineerinq and Remote Sensing, Vol. XLI, No. 1, January 1975, p. 75.

APPENDIX I

STATION DESCRIPTION

! STATION DESCRIPTIBN I

lEPAF4EO BY:

- ----- STATION NO: PP 1 - -----

ETHOD OF FIXATION: STATION NAME

MAP SHEET NO:

MAP SHEET NAME:

ORDER OF PRECISION

SKETCH AND DFW ?TION

HARACTEH OF MARK :

I RECOVERV NOTE:

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>ATE: MAP SHEET NAME:

ORDER OF PRECISION O \tbTo Po141 14 G

SKETCH AND MXRIPTK)FI

APPROXIMATE -: V I L I r l l T Y S U h T W HARACTCR OF MARK .

. J

(+) $ Ldk m d id, + * %- & & lc(b5) or,%. en-& ,&a p i c : u.r4L,t 4f-rr vn k- vf&k+Js&. ,kN,p~ & Mi. DN YU 0-4 dab

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1 3 1 LOCALITY:

LINE: MAD 5HSET NO:

- - . - -. - . )ATE :

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IETHOD OF FIXATION: STATION NAME ORDER OF PRECISION.

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SKETCH AND DESCRIPTION I

HAAACTEII OF MARK : -'

MAP SnEET NO:

MAP SnEET NAME.

ITHOD OF FIXATION: OHOER OF PRECISION

+or0 P O I ~ T I N G 1 SKETCH AND DEXRlrYlON

LOCALITY:

u .d .EL.

--

-- lECOVERV NOTE:

STATKW DESCRIPTION

I REPARED BY: LINE' MAP SMEET NO.

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SKETCH AND MSCRIPTOfd

1

RECOVERY NOTE:

-7 LOCALITY:

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f I . ' . . _ . . , . . z . . . . , . . . . . . . . . . . . . . . . . . . . .

3ECOVERY NOTE --

1 I PREPARED BY: LINE:

ICHQUU C.N. C. MAP SHEETNO:

--- - STATION NO: MAY SHEET NAME:

METHOD OF FIXATION: STATION NAME - --I---

OROFH OF PRFClSlnm

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APPROXIMATE -: \ I I C I A \ ~ ~ SKETCH I CI

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-- I I LOCALITY:

I I

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I C H O K ~ C.M. C. I STATION NO

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WETCH AND DESCRIPT tON

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-. -. - . -- - - ETHOD OF FIXATION' STATION NAME

STATION DESCG.. L I O N

SKETCH AND D E X R I P T W

q ,h\ . E .C.

PREPAREDBY: ICHOUU C. M. C,.

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STATKM DESCRIPTION

I . SKETCH AND DESCRIPTION

LOCALITY:

u. r\l. E , C.

HARACTER OF bl,.l<U :

I 1

LINE: MAP SHEET NO:

DATE: STATION NO: PP 13 MAP SHEET NAME:

iuLY 19% METHOD OF FIXATION: I STATION NAME

I SKETCH'AND DESCRIPTION

- --

HAHACTEA OF MARK

PREPARED BY: MAP SHEET NO' r ~ t i o ~ u C. M.L. .--

STATION NO: HAP S U i E T NAME:

UETHOO OF FIXATION: STATION NAME

STATtON DESCRIPTKW

SKETCH AND DEXRIPTtON ---

L O C A L I T Y

u . 4. E . C.

HARACTBR OF hl I K .

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JhLY I 81p STATION NO:

ITHOD OF FIXATION: STATION NAME

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l o rn PoIHTIFLG I SKETCH AND DESCRIPTION

LOCALITY:

MAP SHEET NO:

MAP SHEET NAME:

- - - ORDER OF PRECISION

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LOCALIIY:

STATKW DESCRIPTION u .d, 6C.

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SKETCH AND M X R l P T l O N I

- -- IECOVERY NOTE:

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PAo7W ~ I N T I A G

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I STATION DESCRIPTION d . d . E . C .

PAEPARED BY: LIIIE: MAP SHEET NO: --

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1 I

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--

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ATE:^^^^ 19sb ETHOD OF FIXATION:

H O D porr l~ i r4G

CHAR4CTER OF MARK :

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LINE:

STATION NO: PP 95 -- STATION NAME

MAP SHEET NO:

MAP SHEET NAME:

OHOEH OF PREClSlOf

PREPARED BY: LINE: - ICHOKY C. N. C- ----. - DATE: STATION NO:

TuLV 19%(5 --- METHOO OF FIXATION: STATION NAME

I SKETCH AND WXRIPTW

CHARACTER OF MAIIK :

DATE: TLt LLl , QQ L? STATION NO: - ---IuIIIIILI*yI PP 27

I SKETCH AND MXRIPTtON

7 . - , . ,-.- 1 , . - - , METHOD OF FIXATION: S A T I O N NAME ORDER OF P)IECISlON

P W o P O ~ H T I ~ G ---I

STATKIN DESCRIPTION

LOCALITY:

U. r J . e . c-

MAP SblE6T NO:

MAY SHEET NAME.

---- ORDt'R OF PREClSlOll

SKETCH AND DESCRIPTION ---

I ( STATION DESCRIPTION U, .E = , I

I SKETCH AND DESCRIPTION

-- -- PREPARED BY: ICHOItU C. M . C . DATE:

~L (L \ ( 19Bd METHOD OF FIXATION:

m o T o P O INTIAG

LINE:-

STATION NO: PP 29 -

-ATION NAME

MAP SHEET NO:

MAP SHEET NAME:

ORDER OF PREclSlOh

SKETCH AND DESCRIPTION

LEPARED BY:

.HOKU C. M, C. ATE: 3uLY \98b ETHOD OF FIXATION;

~ O T O P O I H T I ~ G

-- IECOVERV NOTE:

LINE:

STATION NO: P? 30 FTATION NAME

MAP SHEETNO:

MAPSHEETNAME:

OHOER OF PRECISlOh

SKETCH AND DESCRIPTKHJ -.---

r- STATION DESCRIPTION

L D C A L I T Y .

u. , E. C.

IEPARED BY: LINE: MAP SHEET NO:

1HOKU C . PA. C.. - ATE: STATION NO: P P 31

MAP SHEET NAME:

TULY 198b ETHOD OF FIXATION: STATION NAME ORDER OF PRECISION

tOT0 POvJ7 \F\G

SKETCH AND M X R I P T W N

*EGOVERY NOTE:

4TE: J ULY 1 9 % ~ 1 No'

SP 33 MAP S I I T L T N A M E :

!THO0 OF FIXATION: STATION NAME

SKETCH AND DESCRIPTION --

STATION MXR1PTK)N

+oTo P O I ~ T I ~ G 1 - SKETCH AND DESCRIPTION

LOCALITY

cil. ,.J . E .

IEPAREO BY: , C . H Q K ~ C. M , C

ATE: JULY 1986 ETHOO OF FIXATION:

- LCIMPW/ GATE --

LINE:

STATION NO: ?P 3y- STATION NAME

MAP SIIEET NO:

MAP StIEET NAME.

ORDER OF PRECISION

STATION D€SCRIPTK))J

I SEPARED BY: LINE: IcHoUL( C. M . C .

'ATE' JULY. ( ~ E L STATION NO.

ETHOD OF FIXATION. STATIOV NAME

P+tOTO ? 0 1 ~ 1 l r C C

SKETCH AND DEXRIPTDN

LOCALITY:

&bELAbu 5i&5~r

LOdkp'I I

MAP SHEET NO:

M A P SHEET NAME:

-. ORDER OF PRECISION

HARACTER OF MARK .

I- I I LOCALITY:

DATE: .;ru L-r , 98b STATION NO' MAP SHEET NAME:

-- STATION NAME

-- METHODOF FIXATION: Oi{OEu OF PRECISION

P M T O D n ~ d T \ r l C *

. I SKETCH AND DESCRIPTION

I APPROXIMATE .LIZXPXPVlLI H IT\( S KkTCH I HARACTEH OF MARK :

f i ~ k tcde h d 0.k Y Q . ~ parnt on

P-

1 6 4

' H o ~ o P O I F I T I A G I -I SKETCH AND DEXRlPTlON

--

REPARED BY, I C H O K ~ c.MA. )ATE: TLII LY , gsL tETHOD OF FIXATION:

HARACTEH OF MARK

STATION DESCR1PTK)N

LINE:

- STATION NO:

_EL_---.

LOCALITY:

&L( EE& COUELG E ENUGU

MAP SHEETNO:

- MAP SHCET NAME:

- STATION NAME 1 OHOEH OF PHECISION

I

iz$IpJ$ C. M. C . I LINE:

)ATE: ,986

STATION NO: PP 43 MAP SHEET N A M E

TU LY ETHODOF F IXATION: STATION NAME

~HDTO P V I N T I ~ C

SKETCH AND DESCRIPTION

RECOVERY NOTE T

I I LOCALITY:

I STATION DESCRIPTM d.7: A. Ep4UCU

EPARED BY: LINE: MAP SliEET NO: :FiolCu c. M. c... 4TE: STATION N O :

Q Q 4-4 MAPSHEET N A M E : TULY 19gb

I T H O D OP F I X A T I O N : STATION N A M E O R o t H OF PFIECISION:

STATION DESCRIPTION

M T C H AND D E X R I P T W

LOCALITY:

I f+,T C k M ? u 3

REPARED Y : 1 c ~ o 2 a C. M . C

DATE: ,gs(O IETHOD OF FIXATION:

P H O P PDI~\TIF\L

HMACTER DF MARK

LINE:

STATION NO. ,?P 45 STATION NAME

MAP SHEET NO:

MAP SHEET NAME

ORDER OF PRECISION

DATE:

METHOD OF FIXATION:

STATION DLSCRlPTlON

LINE:

-- STATION NO:

PP 47 STATION NAME

LOCALITY:

MAKY LAUD LAY0U-r

E ~ I U GIA

MAY SilCETNO:

- MAP SHEET NAME.

-~.-- ORDER OF PRECIS101

SKETCH AND DESCRIPTION

I LINE:

r ATE:

JL( , S(o STATIONNO: MAP S I I C E T NAME.

- ETHOD OF FIXATION: STATION NAME OPOER UF PRECISION:

'WT" P O \ l . r ~ l d G

STATION DESCRIPTION

SKETCH AND DESCRIPTION

LOCALITY:

A ~ t l - w A u y o u l -

RELOVEHY NOTE

LOCALITY

Actt44A ~kymSur Er3\IGU

MAP S n C t T N O

- M h P SHEET NAME

- OPDER OF PRECISION

-

PREPARED BY . IceoKa C fl.

OAT' Tw-t t99 b METHOOOF FIXATION

pttoro POIATIAG

SKETCH AND DESCRIPTION - ----- -

STATION DESCRIPTION

-- LlNC

STATION NO

P P _ B _ _ - STATION NAME

APPENDIX I1

CAMERA CALIBRATION CERTIFICATE +

CAM ERA CALIBRATI0 N CERTl FICATE

!

WILD LENS CONE

Ir )

1 NO. 15 UAg 11 W57

FI..TER TYPE : NONE FI'lliLl; I Serial No. : -

C. . iG IN OF MEASUREMENTS 0: The point of Syri-irnetry

I I

S I i N CONVENTION : Distort~on IS positive if away from origin I

C \LIt.RATED AT A TEMPERATURE OF 200C I

C LI: RATION PERFORMED B Y : D.PHILFOT

I

c *LII,RHTED PRINCIPAL DISTANCE: 153.13 mrn I , -

4 i C IOEDINATES OF POINT OF .SYMtvlcTRY

LADIAL DISTORTION IN I ILLIMETRES.:

-

mi dialonal (1) -

: C ~ I I diagonal (2) - . c m ~ d~agonal (3) -

>,ern1 d~ayonal (4 ) I - Mean -

Back of Canicra

,EFORk CALIBRATION THE OPTICAL jE I V A SERVICEABLE CONDITION.

I

I

i i

LENS : 15 UAG I1 KO.: 3 0 5 7

POINT X MM

CALIBRATION DATE 27/OF! 77

. DI' TANCES BETWEEN FlDUClAL MARKS IN MM.

4 S : OlNT OF BEST SnrlMETRY

PPA RlNClPAL POINT OF AUTOCOUlMATlON

(SEEN ON IMAGE PLANE FRAME) - I RECORDING INSTRUMENTS

LENS : 15 UAG II NO.: 3 0 5 7 CALIBRATIOK DATE 27 /06 / 77 I 1

I

POINT X MM

4 S : OlNT OF BEST SYMMETRY

PPA RlNClPAL POINT OF AUTOCOLLIMATIDN

- (SEEN ON IMAGE PLANE FRAME)

RECORDING INSTRUMENTS

CALIURATION ' ~ o . H L c / ~ ~ UAg 11 )057/3 DATE O F CALILKATIC,, -77. , I

1 RESOLUTION

LENS TYPE : W I L D UKiWXSAL AVlWO I1 SERIAL N ~ . : 15 likg 11 ~ ; 5 7 1 I I

F O C A L LENGTH : 153.13 ma

I I

' A P E R T U q E f .4 / I I

F l L M T Y P E : A(SAPA& 25 PROFESSlONAL

I

HIGH CONTRAST T E S T CHART

RESOLUTION DEGREES O F F

i T A ngent ia l

APPENDIX 111

Z

IMAGE COORDINATE MEASUREMENTS

i'OllM 1

1 7 7 I M A G E COL'RDINATE MEASLJRICMENT - - ~- -. -

Z€iSS C-B .- . . -. - . - o t > - ~ - r v a l - : ICHOKU C - M ( ~ n s t r u m e n t ~o_~pb. ~ t , ~ c : 2 0 , / 2 / 8 &

* r e n l p c r o t , , l 2b*Loc ; . I , : s t a r t l ! 9 s t o p : 1.20pm

- -. ______II._.._ -- - . -- ----- P ~ n t N s .

M E A S U R E D C 0 0 1 < 0 1 N A T S S

- - .- - -. .

23

- - -- -- - - -- - -- - -- RESEALCI~ 514 USE OF 2ClS.S U d 6 L A m

dC)u c-8 C O O A D I ~ ~ T O ~ P A D LO^-allty E . * ~ ~ , R o & I J ~ U ~ O ~ o . ~ d ~ / 0 3 / 1 3 0

- -- - -.-..--.-_-....----__.̂ ._I _ - - - - - 7--- ---

MCA.SUl7ED C O O R D I N A T E S :-IP&N :.X.~!'iliil;ll COORDS.

i' (rr") RcrnJrks

- 13i

--

- - ..

30.:. .

31; ax-

F O R M 1

- -- - .- - ~ - - . ~ E S E A R C ~ ~ grl U S . ~ OF ~ C I S ~ U . N . E . C . M.rD

J O B : 5-8 C O ~ D I ~ ~ T ~ , G W + I Locality : W~KOIJS ? i , c t u t;o . . € ~ J ~ / ~ 3 / 1 7 4 --

-_ _ - ..__ .- . - - ._--.- _ . -- ..

' o iaL No.] MEASURED COORUINATES . :AN t.XA . ::D COORDS.

I M A G L C O O R D I N A T E MEASURLlq'.N'I' 186

- - -- - .- - - . - -~ .. - . f c , - -- -- - U.hl,E.L. W9

J O B : ~ o D I ~ A T o G ~ ? ~ , ? ~ L o c n l ~ t y : N V J R D ~ U ;.i>uto N O . W G , / O ~ ] ~ ~ ~ Z E l S S c-g

O b s e r v e r : .uoKu C'fl'C, I n s t r u m e n t ~rnm 11;ite : 28/2 /gb

- -- -- - -- -- - __ - -- M E A S U R E D C O O R D l N A r C S

- I... _. .-+I___

APPENDIX IVA

COMPUTER PROGRAMME FOR PARAMETRIC ADJUSTMENT

c F R I b T I h F t T L F L l E S F F l K ' T 5 ;

r

F F l h T 5 1 C C 2C . I = l - h C T E I ( C ( I , J ) , J = I , h L )

12 F C F P E T ( ' ' , ' C i C . l C ) i C C C h T I h U E

F P I h l 5 1 h f ( I T E ( ? g 1 4 ) ( E L ( 1 , 1 1 9 I = ] ,R[.)

1 4 F C F P C t i l C X , F l C * f ) FRIKT- C l c 2 I = I , b C h F I T E ( Z , I F ) I F l l r J I r J = l r h C )

1 5 F C R P l 7 ( ' ' , ? F I C . L 1 2 4 ( C h T I L L E

5 C F C F P C T ( I C X , / / / I

I

n n n A nnn I

APPENDIX IVB

COMPUTER PROGRAMME FOR

PHOTOCOORDINATE REFINEMENT 's

S T C P E r\ C

F I C L C I P L C t K K S

F'C I h T X

P H O T O cOORC Th,ATE R F F I N t M E b . 1 f109 IJHOIDCRAFH F . r \ \ ~ / ~ 3 / 1 7 3

F C I h T X Y

C I S T C R T I C h C i E F F I C 1FhT.S

C I Z T C R T I C h C L E F F IC I E i ' s T 5

C I S T C R T I C h C L E F F IC J t : h T S

APPENDIX IVC

COMPUTER PROGRAMME FOR SPACE b

RESECTION AND SPACE INTERSECTION

PE'ECIICh PhC I A T E R 5 E C 1 I C h R k $ L L T $ 224

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l V ! W l U 3 w 1 ' 1 1.1 1 - 1 I., LW