Introductie Beeldanalyse8 2013 [Compatibility Mode]

8/12/2019 Introductie Beeldanalyse8 2013 [Compatibility Mode]

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Introduction to QuantitativeImage Analysis

Karl-Heinz Wolf, Joost van Meel


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A course for MSc-students Geoscience & Engineering

Learn how to recognize and measure rock textures and

specific texture features.

Learn how to deal with pitfalls in image manipulation.

Basics for 2D 3D, i.e. slices to CT-scan volumes.

WHY?


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Content Day 1 Sources of images

Digitizing images Analysis of an image

Binary image

Processing of images

*Point Processing

*NeighborhoodProcessing

More terminology


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Content Day 2 Special Operations

*Logical Operators*Skeleton

*Pruning*Skiz

Content day 3: Excercises


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Sources of Images Image of a photocamera / a (digital) videocamera Microscopy Images (camera on microscope)

Electron Microscopy Images, CT-scans

Images (frames) from a video movie

Electronic information from sensors, arranged in a

2D matrix. These sensors may record electronic ormagnetic signals


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Sources & Example of SEM


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Core sample

Microphoto

Thin section

2-D //-nicols

Thin section2-D X-nicols

Sources & Example of Thin Sections


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Sources & Example of CT images of pores

& grains Bentheim sst core

X-Y CT scan and

X-Z reconstruction

x

y

z

CT-scan reconstruction of grains

Pore body reconstruction


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Sources & Example of CT images of Fracs

Orientation

Open fractures

Cemented

fractures


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Repeating Image Pattern


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Feret :

(breadth,

length)Roundnes,

aspect ratiodirection of an

object

This course is about obtaining quantitative data

from digitized images

1 2 3Counting Objects

Intergrowths


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Digitizing an Image-1 If an image is digitized, it becomes subdivided Picture

Elements (pixels)

Each pixel is valued in ones and zeros

The brightness of a pixel is subdivided in 8 ones and zeros;8 bits = 1 byte

This results in 256 grey values, varying from

00000000 (black) = 0 to 11111111 (white) = 255

With a green, blue and red component, represented by three256 grey values, the colour spectrum is represented with2563 = 18609625 colours.


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Digitizing an Image -2 A digitized image is a 2D matrix of pixels. In this matrix,

for every pixel a code is present which indicates the

greyvalue of the pixel

Image with 2 magnifications. In thelast one, one may see the pixels.


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Analysis of an ImageThe properties of an image may be recorded on two levels :

Grey / Colour Level

Measurements are conducted directly on the image, forinstance to determine the brightness distribution in an

image

Binary Level

Here a process is used that is termed detection, or

thresholding. Pixels matching a certain criterium arerecorded in a specific part of the memory of the computer :a binary image


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Binary image -1 Usingdetection, orthresholding it is investigated if a pixel

does or does not match a certain criterion (for instance a

specific grey value). Does the pixel match the criterion, then

the pixel is set on (1). If not, the pixel is not set (0).

The result is calledbinary, because the pixels in the resulting

image (present in another binary image) are either on (value

1) or off (value 0).

Therefore a binary image has NO grey levels !


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Binary image -2Detection

(criterion)

:

white

Binary Image


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Processing of Images -1For the processing of images there are generally

two different ways :

Point processing

Neighbourhood Processing


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Processing of Images -2Point Processing

In this type of processing, the value of a pixel is

changed without taking into account the value of

neighboring pixels.

Examples of this are:

- operations wherebrightness orcontrast are

changed, or,

- an operation calleddetection (thresholding).


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Point Processing-1+10

+10

Brightness

Brightness

0

0

255

0

10

255

10

10

255

10

20

255

Note: 00000000 (black) = 0 to 11111111 (white) = 255

Grey Image Grey Image


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Point Processing-2x10

x10

0

0

255

0

0

255

0

10

255

0

100

255

Contrast

Contrast

Grey Image Grey Image


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Point Processing-3Threshold

> 250

50255 Detection or

Thresholding

0

1

Grey Image Binary Image


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Neighbourhood Processing-1This can be subdivided into :

Mathematical Morphology

Examples : Erosion, Dilation, Sharpen, Smoothing,

Edge Detection

Convolution

Examples : Gauss Filters, Sobel Filters


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Neighbourhood Processing-2Structuring Element :

also called the operator. It is a square matrix of pixels

moving over the object.

The Structuring Element defines the behaviour of erosion

and dilation

To erode an object, every pixel must be compared with its

neighbours.


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Neighborhood Processing-3

In abinary image every pixel can be turnedon (1) oroff

(0). The structuring element moves over the object. Thevalue of the central pixelp becomes dependent on theneighboring pixels

If a pixel in abinary image coincides with the boundary ofthe object,at least one of the neighboring pixels will have thevalue zero (0). In the erosion process,the central pixel is set tozero (0) too.

p

Structuring element


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Neighbourhood Processing - 4 Erosion :

this proces erodes a layer of pixels around an object. Only

those pixels are removed, which have a boundary with thebackground.

It leads to a different result if one takes into account onlythe sides of the pixels (4-connected erosion) orsides andcorners (8-connected erosion).

After erosion of a pixel, theoriginal image is taken as sourcefor the next erosion step (non- iterative process).


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Neighbourhood Processing-Erosion

Red = unset, Green = set

Note: The pixel matching thecentral

pixel will be marked, and later be unset

Erosion : If at least one pixel in thestructuring elementcoincides with a

pixel which is unset, the pixel matching

the central one will be unset too. If the

central pixel doesnot coincide with apixel of the object,nothing happens

P


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Neighbourhood Processing-ErosionPixels marked will be unset,when all pixels of object

have been investigated

P


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Neighbourhood Processing-ErosionP


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And so on......

Neighbourhood Processing-Erosion


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Neighborhood Processing-ErosionAfter a while .....

P


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Neighbourhood Processing-ErosionAfter another while .....

Orange pixels will be eroded in

8-connection erosion, butnot in

4-connection erosion


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Neighbourhood Processing-ErosionFinal state of

4-connected erosion

Marked pixels will be deleted


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Neighbourhood Processing-ErosionFinal state of8-connected erosion

Marked pixels will be deleted

This final state is also used in

Edge Detection (contouring)


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Neighbourhood Processing - 5 Dilation : this is exactly the opposite of erosion:a layer of

pixels is added to the object.

N.B. : In general dilation after erosion will ONLY

give the original object when it is a circle!!


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Neighbourhood Processing - 6 Open:an erosion followed by a dilation

Close:a dilation followed by a erosion


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Neighbourhood Processing - 7 In agrey level image the central pixelp will be set to the

minimum value of the neighbouring pixels.

Edge detection in binary image : if one of the neighbouring

pixels has the value zero, the central pixel coincides with apixel on the boundary of the object. If the central pixels

matching this criterion are recorded, this results in another

binary image containing only the edge (contour) of theobject.


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Erosion DilationExercise8-connected processes1. Erosion of the objects2. Dilation of the remainingshapes


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More Terminology


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More Terminology-1 Feature Count Point (FCP): the coordinates of aspecific pixel, recorded by the program as being

the location of the object. In the software used inthe course this is the lowest rightmost pixel of theobject. Other software packages may use anotherpixel for this .

Image Frame: the frame indicating which part ofthe image should be processed (red frame)

Measure Frame: the frame indicating which part of

the image should be measured (blue frame).

N. B. : Objects with their FCP outside the measure

frame are ignored in measurement !!!!


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More Terminology-2Feret : measure of length in a certain direction

the length of the object is the longest feret,

de breadth theshortest feretFeret : think of Calliper

embayments are not takeninto account

BreadthLength

and

orientation


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More Terminology-3Convex perimeter: The length of thepolygon fitting to the object

Think of a rubber band around the object.

Convex area: the area of the mentioned

polygon.

Area:area of the object

Orientation:orientation of the longest feret

Aspect ratio:ratio of shortest and longest feret


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More Terminology-4 Perimeter: real perimeter, or the total length of the

boundary of the detected object

Roundness: a shape factor defined as

064.1***4

2

area

perimeterroundness


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More Terminology-5In the roundness equation, what is the factor 1.064 for?

The perimeter is nothing more but the sum of all such pixels.

This is different from the true length of a curve.

The factor 1.064 is an empirical correction factor for this effect.


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Program: Leica QWIN

Image files:

Group (G: ) : .AES0101

File names probably without extension !


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DAY 2More Operations


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Logical Operators-1Because binary images consist of pixels with value 1 or 0, it ispossible to use Boolean logical rules for adding and

subtracting the images .

The logical condition NOT must be interpreted as

INVERTED : every pixel which is set becomes unset, and

vice versa

Logical Operators-2


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Skeleton Skeletonizing is a special kind of erosion, creating a

conditional thinning of the features in an image.

Exhaustive Skeletonizing reduces features to a single pixel

width, thus thinning the feature to its central framework


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Pruning-1 Very often skeltonized features contain many branches or

dendrites, or they may be caused by the digital nature of thepixel grid.

To reduce these effects, the skeleton can be prunedby

iteratively removing the end points. Pruning is a conditional erosion, in which only those pixels are

removed, that have only one side connected to their neighbour.

Pruning can also be exhaustive, in which no branches are left,only loops


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Pruning-2Image

Skeleton

Pruned skeleton

(non-exhaustive)


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Skiz-2A group of features and the

boundary lines formed by

the Skiz operation

The dark spots are theoriginal features, the lines

represent the boundaries of

equal distance.


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Introductie Beeldanalyse8 2013 [Compatibility Mode]

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