GrayCode_StructuredLight

7/29/2019 GrayCode_StructuredLight

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3D Measurement Technology by Structured Light Using

Stripe-Edge-Based Gray Code

H B Wu, Y Chen, M Y Wu, C R Guan and X Y Yu

College of Measurement-Control Tech & Communications Engineering, Harbin

University of Science and Technology, Harbin, 150080, China

E-mail: [email protected]

Abstract. The key problem of 3D vision measurement using triangle method based onstructured light is to acquiring projecting angle of projecting light accurately. In order toacquire projecting angle thereby determine the corresponding relationship between samplingpoint and image point, method for encoding and decoding structured light based on stripe edgeof Gray code is presented. The method encoded with Gray code stripe and decoded with stripeedge acquired by sub-pixel technology instead of pixel centre, so latter one-bit decoding errorwas removed. Accuracy of image sampling point location and correspondence between imagesampling point and object sampling point achieved sub-pixel degree. In addition, measurement

error caused by dividing projecting angle irregularly by even-width encoding stripe wasanalysed and corrected. Encoding and decoding principle and decoding equations were

described. Finally, 3dsmax and Matlab software were used to simulate measurement systemand reconstruct measured surface. Indicated by experimental results, measurement error isabout 0.05%.

1. Introduction

Optical 3D measurement technology is one of the most effective methods to acquire object 3D

information. It belongs to non-contact measurement with advantages of non-contact to measured

surface and high sampling density. Among the methods, encoded structured light is to be used widely

in fields as 3D reconstruction and industrial measurement because of its advantages as high accuracy,

high measuring speed, low cost and so on.In the premise of acquiring system parameters by calibration, it is the key problem in encoded

structured light method that determining image sampling point and corresponding it with object

sampling point and encoding stripe region (namely projecting angle) in encoding patterns. Encoding

method can be sorted to time encoding, space encoding and direct encoding with their unique merits

and drawbacks.

Existing time encoding method divides projecting angle by binary code or Gray code, that

sometimes are combined with phase shift [1,2] or hierarchical [3] orthogonal to subdivide projecting

angle. Methods above adopt pixel as image sampling point that named pixel centre decoding.

Binary code may have several different bits between alternate code values. In course of decoding

some pixels may be situated at stripe edge several times in intensity images, so their code values could

be misjudged several times. If high bit is misjudged, the decoding error is larger. Gray code has only

one different bit between random alternate code valuesand each bit has same weight. In course of

Institute of Physics Publishing Journal of Physics: Conference Series 48 (2006) 537541doi:10.1088/1742-6596/48/1/101 International Symposium on Instrumentation Science and Technology

537 2006 IOP Publishing Ltd


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decoding, random pixel is situated at stripe edge at most once in intensity images, so its code value

could be misjudge at most one bit, and decoding error caused by random bit misjudged is only one bit.

However influence to acquiring projecting angle accurately caused by one-bit decoding error is hard tobe removed.

In order to remove one-bit decoding error of Gray code based on pixel centre, and increase

accuracy of image sampling point location and correspondence between image sampling point and

object sampling point, encoding and decoding method based on stripe edge of Gray code is presented.

2. Encoding and decoding method based on stripe edge of Gray code

The method adopts black-white Gray code encoding pattern. In course of decoding, it is different to

decoding by pixel centre that the method locates stripe edge in each intensity image (before

binarization) by sub-pixel location technology, then adopts points in edge as image sampling points

whose grey values (0 or 1) in intensity image (after binarization) are used to acquire Gray code. Gray

code value is used to determine the corresponding relationship between edge in intensity image and

encoding pattern, and acquire its projecting angle. The method includes two steps.

2.1. Acquiring stripe edge ordinal number in intensity image

The purpose of this step is to acquire edge ordinal number in encoding pattern corresponded by stripe

edge in intensity image. As is shown in figure 1, for example, four Gray code patterns are projected,

and there generate 24-1=15 edges. When acquiring edge ordinal number in the forth intensity image,

Gray code is determined by grey values (0 or 1) at position corresponded by the edge in former

(namely 1, 2, 3) intensity images (after binarization), then edge ordinal number is figured out by

equation (1).

11021210

22 ini

in GGGGk " (1)

Where k=1, 22n-1 is edge ordinal number; n is total number of intensity image; i=1, 2n is

ordinal number of intensity image; Gi is grey value in intensity image i, thereinto G0=0

151413121110

986 754321Ordinalnumber

4

3

1

Timesequenc

D1

D14

A

B

C

D

E

F

G

S

T

D13

D12

D11

D13

D11

D12

D14

D0

Figure 1. Stripe edge ordinal number. Figure 2. Even-width-stripe encoding.

2.2. Acquiring projecting angle corresponded by edge in encoding pattern

According to edge ordinal numberkfigured out by equation (1), projecting angle corresponded can be

acquired. Projecting angle range of projector is set 2D1 and angle between projecting centreline and

axisx is set D0. For example, three Gray code patterns are projected, thereby position of seven stripeedges in projecting angle is shown in figure 2. Where A, B, C, D, E, F, G is position of stripe edges

whose ordinal number is 1, 2, 3, 4, 5, 6, 7.

Encoding by even-width-stripe pattern has advantage that easy realization, while disadvantage that

dividing projecting angle irregularly, so projecting angle range corresponded by thinnest-stripe

deduces from centre to both sides. As is shown in figure 2, thinnest-stripe width SA=AB=BC=CD=

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DE=EF=FG=GT, while projecting angle D11!D12!D13!D14. If regions corresponded by thinnest-stripesare looked as even angel, projecting angle error that causes reconstructed surface bend in both sides

rises.Even-width-stripe projecting angle can be figured out by equation (2) that corrects the error above.

Putting edge ordinal numberkinto equation (2), projecting angle corresponded is acquired.

1

110

2

tan2arctan

n

n kD

DD (2)

Encoding and decoding method based on stripe edge of Gray code adopts Gray code value of point

in edge in former intensity image to correspond it with that in encoding pattern. As is shown in figure

1, edges marked by broken line are all situated at stripe inner not edge in former intensity images, so

their code values are hard to be misjudged. The method removes the one-bit decoding error in Gray

code based on pixel centre theoretically.

Decoding by pixel centre, one pixel is corresponded by many object sampling points, so its grey

value cant be determined accurately, while by stripe edge, corresponding accuracy between imagesampling point and object sampling point can achieve sub-pixel degree.

3. Stripe edge sub-pixel location

Sub-pixel location technology as fitting, grey square, resampling, space square, interpolation is widely

used this year [4]. This paper adopts fitting method to acquire stripe edge in intensity image. Because

stripes in encoding pattern are vertical and those in intensity image are the same, so they are detected

by horizontal scanning. Intensity image is filtered by equation (3), and grey valuef(j) is alternated by

g4(j).

21124 jfjfjfjfjg (3)

(a)

(b)

(c)

Particalmaximal value

Particalminimal value

Start

Input image

Filtering

Sub-pixel location byhorizontal scanning

Intensity image binarization

Detect Gray code, edge ordinalnumber and projecting angle

Figure out sampling point

space coordinate

Surface reconstruction

End

Figure 3. Sub-pixel location by horizontal scanning. Figure 4. Flow chart for reconstruction.

Where j is pixel row ordinal number. Figure 3(a) is intensity image whose line i is scanned, andgrey value of each pixel is shown in figure 3(b). Fitting change curve of grey value after filtering, as is

shown in figure 3(c), average of wave crest and wave hollow alternate to the edge is figured out.

Finally, its corresponded horizontal position in fitting curve is determined as sub-pixel location

position.

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4. Reconstruction experiments

Measurement system was composed of surface light source projector, camera and measured object

simulated by 3dmax software [5]. Thereinto, projecting angle range of black-white camera was 40q,and CCD resolution was 1024u1024; Projector projected continuous encoding pattern whoseprojecting angle range was 30q. System range was about 240u240mm. Matlab software was used toprocess image, calculate space point coordinate and reconstruct measured surface. Program flowchart

is shown in figure 4.

Flat with depth value z=508.499mm was reconstructed by Gray code based on pixel centre andreconstruction experimental result and error flat are shown in figure 5(a). Those by Gray code based

on stripe edge are shown in figure 5(b). Obviously, depth values of object sampling point with small

projecting angle in flat reconstructed by Gray code based on pixel centre diminished (close to camera),

while that by Gray code based on stripe edge augmented (apart from camera), because the irregular-

dividing error of projecting angle was not corrected. Depth values in flat reconstructed by Gray code

based on stripe edge did not deflect.

(a)

(b)

Figure 5. Plat reconstruction experimental results.

Specific reconstruction errors are shown in table 1.

Table 1. Reconstruction experimental findings.

Zmax(mm) Zmin(mm)Maximal

error (mm)

Relative

errorVariance

Gray code by

pixel centre509.770 507.103 1.271 0.25% 1.408

Gray code by

stripe edge508.753 508.345 0.254 0.05% 0.035

According to table 1, measurement accuracy by Gray code based on stripe edge are higher than thatby Gray code based on pixel centre.

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Complex 3D model was reconstructed by the method and system in this paper. Venus plaster model

and its reconstruction experimental results are shown in figure 6(a) is measured model, and (b), (c) and

(d) are reconstruction experimental results by multi-angle that can reflect measured surface truly.

(a) (b) (c) (d)

Figure 6. Reconstruction experimental results of Venus plaster model.

5. Conclusion

Method for encoding and decoding of Gray code based on stripe edge is presented. The method

adopted key technology as decoding by Gray code stripe edge, acquiring stripe edge by horizontal

scanning sup-pixel location, so one-bit decoding error of Gray code could be removed, as the same

time, advantage that high adaptability to steep part at measured surface was reserved; Object sampling

point and image sampling point corresponding point by point, quantization error caused by pixel-

centre decoding could be removed; Errors that reconstruction surface bending at both sides of

measured object caused by dividing projecting angle irregularly was corrected. According to

simulation reconstruction experiments, the method proved effective. Future plans include acquiring

higher sampling density by reducing encoding stripe width, and reducing influence to measurement

caused by shelter by multi-angle measuring and joint.

Acknowledgements

The support of National Natural Science Foundation of China under research grant 60572030,

Specialized Research Fund for the Doctoral Program of Higher Education under research grant

20050214006, Heilongjiang Province Education Department Overseas Scholars Science Research

Foundation under research grant 1055HZ027, The Key Science and Technology Research Project of

Harbin under research grant 2005AA1CG152 and Heilongjiang Province Graduate Student Innovation

Research Foundation under research grant YJSCX2005-238HLJ are gratefully acknowledged.

References

[1] Joaquim Salvi 2004 Pattern codification strategies in structured light systems PatternRecognition 37 827-849

[2] Jens Ghring 2001 Dense 3-D surface acquisition by structured light using off-the-shelf

componentsProceedings of SPIE - The International Society for Optical Engineering4309220-231

[3] Sukhan Lee 2004 An active 3D robot camera for home environmentProceedings of The IEEESensors 1 477-480

[4] Nelson l 2004 Creating interactive 3-D media with projector-camera systems Proceedings ofThe SPIE-The International Society for Optical Engineering5308 850-861

[5] Zhang Guangjun 2003 Elliptical-center locating of light stripe and its simulation for structured

light based 3D vision inspection Chinese Journal of Scientific Instrument24 589-593

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