lecture 06 binary image analysis lecture 06 binary image analysis mata kuliah: t0283 - computer...

Lecture 06Lecture 06 Binary Image AnalysisBinary Image Analysis

Mata kuliah : T0283 - Computer VisionTahun : 2010

January 20, 2010 T0283 - Computer Vision 3

Learning ObjectivesLearning Objectives

After carefullyAfter carefully listening this lecture, students will listening this lecture, students will be able to do the following :be able to do the following :

show how connected component labeling is show how connected component labeling is performed performed and its uses in shape classifierand its uses in shape classifier

demonstrate object area and perimeter demonstrate object area and perimeter calculation based calculation based on binary imageson binary images


From Processing to AnalysisFrom Processing to Analysis

Holistic perspective in binary image analysis

PHILHigh-level vision

Low-level vision

Localized perspective in binary image processing


ConnectivityConnectivity

X

Y

X’

Y’

X and Y are connected X’ and Y’ are NOT connected

a and b are connected if there exists a path from a to b

Notation: if a and b are connected, we write a ~ b


Connected Components in Digital Connected Components in Digital ImagesImages

A set S of pixels is a CC if there is at least one path A set S of pixels is a CC if there is at least one path that joins every pair {p,q} of pixels in S, and that joins every pair {p,q} of pixels in S, and contains exclusively of pixels in S.contains exclusively of pixels in S.

Two types of connectivity: 4 - (edge) connectivity Two types of connectivity: 4 - (edge) connectivity and 8- (vertex) connectivityand 8- (vertex) connectivity


Connected ComponentConnected Component

Two pixels are Two pixels are c-adjacentc-adjacent (c=4 or 8) if they share at (c=4 or 8) if they share at least an edge (c=4), or a vertex (c=8).least an edge (c=4), or a vertex (c=8).Two pixels are Two pixels are c-connectedc-connected (c=4 or 8) if it is possible (c=4 or 8) if it is possible to find a path between these two pixels through to find a path between these two pixels through pairs of c-adjacent (c=4,8) pixels.pairs of c-adjacent (c=4,8) pixels.A A c-connected componentc-connected component is a maximal connected is a maximal connected set where each pixel is c-connected to other pixels in set where each pixel is c-connected to other pixels in the set.the set.


ExampleExample

p

q

p ~ q no matter 4-neighbors p ~ q no matter 4-neighbors or 8-neighborsor 8-neighbors

p

q

p ~ q only when 8-neighborsp ~ q only when 8-neighborsis consideredis considered


Component LabelingComponent Labeling

If 4-neighbors,three connectedcomponents

If 8-neighbors,two connectedcomponents

originalbinaryimage


Connected Component LabelingConnected Component Labeling

1

2 3

4 5


MATLAB Function BWLABELMATLAB Function BWLABEL

>help bwlabel BWLABEL Label connected components in binary image.

L = BWLABEL(BW,N) returns a matrix L, of the same size as BW, containing labels for the connected components in BW. N can have a value of either 4 or 8, where 4 specifies 4-connected objects and 8 specifies 8-connected objects; if the argument is omitted, it defaults to 8. The elements of L are integer values greater than or equal to 0. The pixels labeled 0 are the background. The pixels labeled 1 make up one object, the pixels labeled 2 make up a second object, and so on. [L,NUM] = BWLABEL(BW,N) returns in NUM the number of connected objects

found in BW.

See also bwareaopen, bweuler, bwlabeln, bwselect, label2rgb.


Euler NumberEuler Number

Euler Number EN=number of connected components – number of holes

EN=-3

EN=0 EN=-1


CC AlgorithmCC Algorithm

Process the image row by rowProcess the image row by rowAssign a label to the first pixel of each CCAssign a label to the first pixel of each CCOtherwise assign its label by propagating from left or Otherwise assign its label by propagating from left or toptop

Clash! (equivalence)??111111

221111

2211

2211


One approachOne approach

Propagate the smaller label in case of clashPropagate the smaller label in case of clashRecord the equivalence in a tableRecord the equivalence in a tableAfter the entire image is processed, find the set After the entire image is processed, find the set of equivalence classesof equivalence classesSecond pass replaces each label with its Second pass replaces each label with its equivalent classequivalent class

Two passes!Two passes!


Boundary of Binary ObjectsBoundary of Binary Objects

XX

X=X-(X B)_ X=(X B) – B+or


Chain Codes Boundary RepresentationChain Codes Boundary Representation

4-directional chain code: 0033333323221211101101

8-directional chain code: 076666553321212


Two Problems with the Chain CodeTwo Problems with the Chain Code

Chain code representation is conceptually Chain code representation is conceptually appealing, yet has the following two appealing, yet has the following two problemsproblems

Dependent on the starting pointDependent on the starting point

Dependent on the orientationDependent on the orientation

To use boundary representation in object To use boundary representation in object recognition, we need to achieve invariance recognition, we need to achieve invariance to starting point and orientationto starting point and orientation

Normalized codesNormalized codes

Differential codesDifferential codes


Normalization StrategyNormalization Strategy

33001122

3300112230011223001122330112233011223300122330012233001123300112

Sortrows

0011223301122330112233001223300122330011233001123300112230011223

00112233

First row gives the normalized chain code


Differential StrategyDifferential Strategy

33001212 33010122

00121233 01012233

Differential coding:

dk=ck-ck-1 (mod 4) for 4-directional chain codes

dk=ck-ck-1 (mod 8) for 8-directional chain codes

normalize normalize

90o


Shape Numbers= Normalized Shape Numbers= Normalized Differential Chain CodesDifferential Chain Codes

Differential code: dk=ck-ck-1 (mod 4)

33001212

10101131

33010122

10113110

01011311 01011311

differentiate

normalize

differentiate

normalize

Note that the shape numbers of two objects related by 90o rotationare indeed identical


Examples : Chain Encoding

x

yEncoding

start point

1 unit pixel

2 unit pixel


P Direction 0

65

4

32

1

7

1 1 0 0 0 0 6 0 6 6 6 4 6 4 4 4 4 3 3 2

Start

Perimeter P = SE + V2 SO units

= 16 + 4 V2 = 21.66 units

Perimeter Calculation


Y

Direction 0Additive comp. = 1 x y

Y

Direction 5Subtractive comp = (1 x y) – 0.5

Y

Direction 1Subtrac. comp. = (1 x y) + 0.5

Direction 2 dan 6Zero component (neutral)

Area Calculation

Y


P 0

65

4

32

1

7

1 1 0 0 0 0 6 0 6 6 6 4 6 4 4 4 4 3 3 2

Start

AdditiveSubtractive

5

667

34

23

5

4

y-coordinate

Area = 5.5 + 6.5 + 7 + 7 + 7 + 7 + 0 + 6 + 0 + 0 + 0 – 3 + 0 – 2 – 2 – 2 – 2 – 2.5 – 3.5 + 0 = 29 square units

Area Calculation (cont’d)


MATLAB ImplementationMATLAB Implementation


Segmen citra biner

0 0 0 0 0 0 0 0

0 0 # # # 0 # 0

0 0 # # # # 0 0

0 0 # # # 0 # 0

0 0 0 0 0 # # 0

0 0 0 0 0 0 0 0

Run Length Encoding (RLE)

10(0), 3(1), 1(0), 1(1), 3(0), 4(1), 4(0), 3(1), 1(0), 1(1), 6(0), 2(1), 9(0)


Segmen citra biner

0 0 0 0 0 0 0 0

0 0 # # # 0 # 0

0 0 # # # # 0 0

0 0 # # # 0 # 0

0 0 0 0 0 # # 0

0 0 0 0 0 0 0 0

Chord Encoding

1 (2,4) (6,6); 2 (2,5); 3 (2,4) (6,6); 4 (5,6).

bariskolom


Matlab Implementation on Shapes Matlab Implementation on Shapes ClassifierClassifier

Step 1: Read image Step 1: Read image

Step 2: Convert image from rgb to grayStep 2: Convert image from rgb to gray

Step 3: Threshold the imageStep 3: Threshold the image

Step 4: Invert the Binary ImageStep 4: Invert the Binary Image

Step 5: Find the boundaries ConcentrateStep 5: Find the boundaries Concentrate

Step 6: Determine Shapes propertiesStep 6: Determine Shapes properties

Step 7: Classify Shapes according toStep 7: Classify Shapes according to


Step 1: Read image

RGB = imread('test.bmp');RGB = imread('test.bmp');figure, imshow(RGB), title('INPUT figure, imshow(RGB), title('INPUT IMAGE');IMAGE');


Step 2: Convert image from rgb to grayStep 2: Convert image from rgb to gray

GRAY = rgb2gray(RGB);figure,imshow(GRAY),title('GRAY IMAGE');


Step 3: Threshold the image. Step 3: Threshold the image.

threshold = graythresh(GRAY);threshold = graythresh(GRAY);BW = im2bw(GRAY, threshold);BW = im2bw(GRAY, threshold);figure, imshow(BW), title('BINARY IMAGE');figure, imshow(BW), title('BINARY IMAGE');


Step 4: Invert the Binary ImageStep 4: Invert the Binary Image

BW = ~ BW;figure,imshow(BW),title('INVERTED BINARY IMAGE');


Step 5: Find the boundaries

Concentrate only on the exterior boundaries.Option 'noholes' will accelerate the processing by preventing bwboundaries from searching for inner contours.

[B,L] = bwboundaries(BW, 'noholes');%[L, N] = bwlabel(BW,8);

Step 6: Determine objects propertiesSTATS = regionprops(L, 'all'); % we need 'BoundingBox' and 'Extent'


Step 7: Classify Shapes according to properties

% Square = 3 = (1 + 2) = (X=Y + Extent = 1)% Rectangular = 2 = (0 + 2) = (only Extent = 1)% Circle = 1 = (1 + 0) = (X=Y , Extent < 1)% UNKNOWN = 0

for i = 1 : length(STATS) W(i) = uint8(abs(STATS(i).BoundingBox(3) - STATS(i).BoundingBox(4)) < 0.1); W(i) = W(i) + 2 * uint8((STATS(i).Extent - 1) == 0 ); centroid = STATS(i).Centroid; switch W(i) case 1 plot(centroid(1),centroid(2),'wO'); case 2 plot(centroid(1),centroid(2),'wX'); case 3 plot(centroid(1),centroid(2),'wS'); endend


Step 7: Classify Shapes according to properties (cont’d)

figure, imshow(RGB), title('HASIL IDENTIFIKASI SQUARE, CIRCLE & RECTANGLE'); hold on

lecture 06 binary image analysis lecture 06 binary image analysis mata kuliah: t0283 - computer...

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