Texture Similarity Measure. Pavel Vácha. Institute of Information Theory and Automation, AS CR Faculty of Mathematics and Physics, Charles University

Transcription

1 Texture Similarity Measure Pavel Vácha Institute of Information Theory and Automation, AS CR Faculty of Mathematics and Physics, Charles University

2 What is texture similarity?

3 Outline 1. Introduction Julesz conjecture 2. Texture similarity Cumulative histogram Gabor filters Steerable pyramids Markov random fields 3. Comparison of methods Results 4. Conclusion

4 Introduction Texture: homogenous translation invariant realization of random field or texture elements placed according to rules Motivation: content based image retrieval segmentation texture modeling and synthesis

5 Joulesz conjecture Textures cannot by spontaneously discriminated if they have the same first-order and second-order statistics and differ only in higher statistics [Julesz, 62]. disproved! The third-order statistics of any image of finite size uniquely determine that image up to translation. It do not says that images with close statistics up to third-order look similar [Yellot, 93]. proved!

6 Texture similarity based on texture features (randomness, directionality, periodicity, spatial relations, statistics, etc. ) feature vector: f = (f 1, f 2,..., f n ) features are at least translation invariant similarity of textures is distance of feature vectors distance measures: L 1std (Y 1, Y 2 ) = f (Y 1) i f (Y 2) i σ(f i ), i L (Y 1, Y 2 ) = max f (Y 1) i f (Y 2) i i

7 Cumulative histogram 1. ordinary histogram Q = (h 1, h 2,..., h n ) 2. cumulative histogram Q = ( h 1, h 2,..., h n ), where h j = k j h k more robust than ordinary histogram rotation invariant and fairly insensitive to resolution change no spatial relations computational complexity: linear

8 Gabor filters Gabor filters are orientation and scale tunable edge and line detectors. two dimensional Gabor function [ 1 g(x, y) = exp 1 ( x 2 2πσ x σ y 2 σ 2 x + y ) ] 2 + 2πiWx, σy 2 Fourier transform of Gabor function [ G(u, v) = exp 1 ( (u W ) 2 2 σ 2 u + v )] 2 σv 2 filter set g mn (x, y) are dilatations and rotations of g(x, y)

9 Gabor filters Two dimensional Gabor function g(x, y): spatial domain frequency domain

10 Gabor filters The covering of the half of frequency domain by 4 dilatations and 6 rotations of g(x, y).

11 Gabor filters Gabor wavelet transformation of the image: W mn (x, y) = Y (x 1, y 1 )gmn(x x 1, y y 1 )dx 1 dy 1 feature vector: f = (µ00, σ 00, µ 01, σ 01,..., µ MN, σ MN ) computational complexity: O(n log n) heavily used, maybe not optimal

12 Steerable pyramids over-complete form of wavelet transformation system diagram for steerable pyramid

13 Steerable pyramids A complex steerable representation of a disk image [Portilla and Simoncelli, 2000] real magnitude Feature vector: marginal statistics coefficient autocorrelation periodicity coefficient crosscorrelation structures in images cross-scale phase statistics lighting effects

14 Markov random fields Assumptions about image density function: homogeneity pixel value depends only on relative spatial position locality pixel value depends only on its neighbors density sometimes, e.g. Gaussian Models: Gaussian Markov Random Fields (GMRF) Causal simultaneous AutoRegressive random field (2D CAR)

15 Markov random fields Model: Y r = s I r a s Y r s + e r, r = (x, y) neighborhood I r : symmetric (GMRF), causal (2D CAR) GMRF: joint Gaussian distribution of pixel value feature vector f formed by model parameters computational complexity: linear

16 Comparison of methods Test texture synthesis: 1. fully known GMRF model of 11 th order 2. parameter estimation for GMRF models of orders: textures synthesized by different the GMRF models Texture similarity: 1. feature vectors computation 2. distance among feature vectors

17 Outline Introduction Texture similarity Comparison Conclusion 12 References

18 Results

19 Conclusion According to the experiment it seams: histogram features are not suitable Gabor features and 2D CAR are superior 2D CAR features are faster

20 References B. Julesz. Visual pattern discrimination. IRE Transactions on Information Theory, pages 84 92, February 1962 J. Yellot, John I. Implications of triple correlation uniqueness for texture statistics and the julesz conjecture. Journal of the Optical Society of America A, 10(5): , May 1993.

21 References B. S. Manjunath and W. Y. Ma. Texture features for browsing and retrieval of image data. IEEE Transactions on Pattern Analysis and Machine Intelligence, 18(8): , August J. Portilla and E. P. Simoncelli. A parametric texture model based on joint statistics of complex wavelet coefficients. International Journal of Computer Vision, 40(1):49 71, 2000.