Digital Image Processing. Lecture # 15 Image Segmentation & Texture

Transcription

1 Digital Image Processing Lecture # 15 Image Segmentation & Texture 1

2 Image Segmentation

3 Image Segmentation Group similar components (such as, pixels in an image, image frames in a video) Applications: Finding tumors, veins, etc. in medical images, finding targets in satellite/aerial images, finding people in surveillance images, summarizing video, etc. 5/26/2015 Image Segmentation 3

4 Image Segmentation Segmentation algorithms are based on one of two basic properties of gray-scale values: Discontinuity Partition an image based on abrupt changes in gray-scale levels. Detection of isolated points, lines, and edges in an image. Similarity Thresholding, region growing, and region splitting/merging. 5/26/2015 Image Segmentation 4

5 Thresholding Segmentation into two classes/groups Foreground (Objects) Background 5/26/2015 Image Segmentation 5

6 Thresholding g( x, y) 1 if f ( x, y) 0 if f ( x, y) T T Objects & Background Global Thresholding Local/Adaptive Thresholding 5/26/2015 Image Segmentation 6

7 Global Thresholding Single threshold value for entire image Fixed? Automatic Intensity histogram 5/26/2015 Image Segmentation 7

8 Global Thresholding Single threshold value for entire image Fixed? Automatic Intensity histogram 5/26/2015 Image Segmentation 8

9 Global Thresholding Estimate an initial T Segment Image using T: Two groups of pixels G1 and G2 Compute average gray values m1 and m2 of two groups Compute new threshold value T=1/2(m1+m2) Repeat steps 2 to 4 until: abs(t i T i-1 )<epsilon 5/26/2015 Image Segmentation 9

10 Global Thresholding Multilevel thresholding 5/26/2015 Image Segmentation 10

11 Thresholding Non-uniform illumination: 5/26/2015 Image Segmentation 11

12 Global Thresholding 5/26/2015 Image Segmentation 12

13 Adaptive Thresholding 5/26/2015 Image Segmentation 13

14 Adaptive Thresholding Threshold: function of neighboring pixels T T mean median T max 2 min 5/26/2015 Image Segmentation 14

15 Adaptive Thresholding Original Image Global Thresholding 5/26/2015 Image Segmentation 15

16 Adaptive Thresholding T=mean, neighborhood=7x7 T=mean-Const., neighborhood=7x7 5/26/2015 Image Segmentation 16

17 Adaptive Thresholding Niblack Algorithm T m k s m mean s standard deviations k Niblack constant Neighborhood size??? 5/26/2015 Image Segmentation 17

18 Document Binarization Local Thresholding Examples Original Niblack Sauvola Wolf Feng NICK 18

19 Color Segmentation

20 K-Means Clustering 1. Chose the number (K) of clusters and randomly select the centroids of each cluster. 2. For each data point: Calculate the distance from the data point to each cluster. Assign the data point to the closest cluster. 3. Recompute the centroid of each cluster. 4. Repeat steps 2 and 3 until there is no further change in the assignment of data points (or in the centroids). 5/26/2015 Image Segmentation 20

21 K-Means Clustering 5/26/2015 Image Segmentation 21

22 K-Means Clustering 5/26/2015 Image Segmentation 22

23 K-Means Clustering 5/26/2015 Image Segmentation 23

24 K-Means Clustering 5/26/2015 Image Segmentation 24

25 K-Means Clustering 5/26/2015 Image Segmentation 25

26 K-Means Clustering 5/26/2015 Image Segmentation 26

27 K-Means Clustering 5/26/2015 Image Segmentation 27

28 K-Means Clustering 5/26/2015 Image Segmentation 28

29 K-Means Clustering 5/26/2015 Image Segmentation 29

30 Clustering Example 5/26/2015 Image Segmentation 30

31 Clustering Example 5/26/2015 Image Segmentation 31

32 Clustering Example 5/26/2015 Image Segmentation 32

33 Clustering Example 5/26/2015 Image Segmentation 33

34 Clustering Example D. Comaniciu and P. Meer, Robust Analysis of Feature Spaces: Color Image Segmentation, /26/2015 Image Segmentation 34

35 K-Means Clustering Example Original K=5 K=11 5/26/2015 Image Segmentation 35

36 Texture Based Descriptors

37 Texture Organized patterns of quite regular subelements called textons. Texture is a property of sufficiently large regions Applications: Texture based segmentation Texture synthesis Texture analysis and texture based matching Shape (surface orientation) from texture 37

38 Texture Examples (a,b): Artificial textures (c,d,e): Naturally occurring textures 38

39 Statistical Representing textures yields characterization of textures as smooth, coarse grainy, etc. Spectral are based on Fourier spectrum and are primarily used to detect the global periodicity in an image by identifying high energy narrow peaks in the spectrum. 39

40 Statistical approaches Based on the histogram measures of image Based on the Grey Level Co-occurrence Matrix (GLCM) and related measurement Histogram based texture description Using statistical moments of grey level histogram of the image or region Let p(z i ) is the histogram of the grey levels z i of an image The nth moment about the mean is given by: Where mean is ( n m L z) 1 ( zi i 0 L 1 zi p( z i i 0 The variance is the second moment and is given by m) ) n p( z i ) 2 ( z) ( z) 2 L 1 i 0 ( z m) p( 2 i z i ) 40

41 Histogram based texture description For texture description the following parameters are useful Variance and related measures: descriptor of relative smoothness, use normalized variance 1 R ( z ) Skewness of histogram ( z) Relative flatness of histogram ( z) Uniformity U Average Entropy L 1 i 0 p 2 ( e z i ) L 1 i 0 p( z L ( zi m) p( z i ) i 0 L ( zi m) p( z i ) i 0 i )log 2 p( z i ) 41

42 Histogram based texture description (example) 42

43 GLCMs For texture description the following parameters of GLCM are measured and analyzed Maximum probability Contrast i j ( ) max( c i, j 2 i j cij ij ) Uniformity Entropy i j i j c 2 ij c log c ij 2 ij 43

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49 Spectral Texture Analysis

50 Spectral techniques: Fourier transform Suitable to detect directionality of periodic and almost periodic 2- D patterns in an image Periodic texture patterns are easily detectable by concentration of high energy burst in the spectrum Features of Fourier spectrum for texture representation are: Prominent peaks in the spectrum give the principal direction of texture patterns The location of peaks give the frequency and thus the scale of repetition of a pattern Eliminating any periodic components via filtering leaves nonperiodic image elements which can be described by statistical techniques 50

51 Spectral techniques: Fourier transform Simplified by expressing the spectrum in polar coordinates to yield a function S(r, q) where S is the spectrum function and r and q are the polar coordinates. For each direction q, S(r, q) = a 1-D function S q (r) For each frequency r, S(r, q) = a 1-D function S r (q) Analyzing S q (r) for a fixed q, gives the distance from the origin and thus the scale of repetition of a texture pattern. Analyzing S r (q) for a fixed r, gives the direction and thus the orientation of the periodic texture pattern. To measure this analysis, we define two quantities S( r) q 0 S q ( r), S( q ) r 1 ( q ). These quantities measure the spectral response and give the dominant directions and scales of periodic texture patterns. R o S r 51

52 Spectral techniques: Fourier transform (example) Image showing periodic texture Spectrum Plot of S(r) Plot of S(q) 52

53 Spectral techniques: Fourier transform (example) Another image showing periodic texture Plot of S(q) 53

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56 Readings from Book (3 rd Edn.) Texture (Chapter-11) Reading Assignment: Table-11.3, 11.4

57 Material in these slides has been taken from, the following resources Acknowledgements Digital Image Processing, Rafael C. Gonzalez & Richard E. Woods, Addison-Wesley, 2002 Computer Vision for Computer Graphics, Mark Borg 57