1. Multiresolution Histograms and their Use for Texture Classification Stathis Hadjidemetriou, Michael Grossberg and Shree Nayar CAVE Lab, Columbia University Partially funded by NSF ITR Award, DARPA/ONR MURI

2. Fast and Simple Feature Q: Is there a fast feature which captures spatial information? A: Consider multiple resolutions. Same Histogram

3. Histograms of Filtered Images Graylevel Bin Count Graylevel Bin Count Histograms  Resolution

4. Analysis of Multiresolution Histograms Bin Count Graylevel Bin Count Change Shape and Texture Properties Difference Histograms Multiresolution Histograms Shape and Texture Images ?

5. Tools for Analysizing the Histogram Shanon Entropy Change in Shanon Entropy: Fisher Information Generalization: Tsallis Entropy/Generalized Fisher Information Resolution Multiresolution Histogram Bin Filter Dependent Constant

6. Relating Histogram Change to Image Fisher Information: Measure of image sharpness [Stam, 59, Plastino et al, 97]: Image Image Gradient Image Domain Edge filter never computed: Implicit

7. Analysis of Multiresolution Histograms Bin Count Graylevel Bin Count Change Shape and Texture Properties Difference Histograms Multiresolution Histograms Shape and Texture Images Fisher Information Resolution  Fisher Information Shape Elongation Shape Boundary Texel Repetition Texel Placement

8. Shape Elongation and Fisher Information Elongation: St. dev. along axes:  x,  y. Gaussian: Sides of base: r x, r y. Pyramid: (analytically) Elongation: 6 5 4 3 2 12345  J

9. Shape Boundary and Fisher Information Superquadrics:  =0.56  =1.00  =1.48  =2.00  =6.67 (numerically) Complex boundary J  2 3 4 5 6 2460

10. Texel Repetition and Fisher Information (analytically). 142356 0 2 4 6 8 Tileing 142356 Tileing p J 0 2 4 6 8 J x 10 3

11. Texel Placement and Fisher Information Stand. dev. of perturbation (numerically)Randomness Average of 20 trials 01551020 6.6 6.4 6.2 6 5.8 J St. Dev (% of Texel Width) 01551020 St. Dev (% of Texel Width) x 10 3 2.9 2.8 2.7 2.6 2.5 J

12. L 1 norm Matching Algorithm Multiresolution histogram with Burt-Adelson Pyramid Cumulative histograms Difference histograms between consecutive resolutions Concatenate to form feature vector Compute Feature

13. Histograms Bin Width Histogram bin width: Subsampling factor in pyramid:

14. Parameters of Multiresolution Histogram Histogram smoothing to avoid aliasing: –Database images –Test images Histogram normalization – Image size – Histogram size

15. Databases for Matching Database of CUReT textures [Dana et al, 99]: –8,046 images; 61 materials –Histogram equalized Database of Brodatz textures [Brodatz, 66]: –91 images; 7 images –Histogram equalized

16. Database of Brodatz Textures Samples of equalized images:

17. Match Results for Brodatz Textures Match under Gaussian noise of st.dev. 15 graylevels

18. Class Matching Sensitivity: Brodatz Textures 0102030405060 0 20 40 60 80 100 St dev. of noise  n Class matched 8 16 32 62 128 256 Number of bins

19. Class Matching Sensitivity: Brodatz Textures smoothing & adaptive bin size 0102030405060 100 St dev. of noise  n 95 90 85 80 75 70 65 60 256 Constant 256, Higher Subsampling= 2 2/3 256, Lower Subsampling = 2 1/2

20. Database of Curet Textures Samples of equalized images:

21. Match Results for Curet Textures Match under Gaussian noise of st.dev. 15 graylevels.

22. Match 100 randomly selected images per noise level Difference norm & Smoothing Class Matching Sensitivity: CUReT Textures 01020304050 60 70 80 90 100 St dev. of noise  n Class matched 256 Constant 256, Higher Subsampling= 2 2/3 256, Lower Subsampling = 2 1/2

23. Comparison with Low-level Features Fourier power spectrum annuliFourier power spectrum annuli Gabor featuresGabor features Daubechies wavelet featuresDaubechies wavelet features Auto-cooccurrence matrixAuto-cooccurrence matrix Markov random field parametersMarkov random field parameters

24. Comparison with Low-Level Features Auto-cooccurrence matrix Fourier power spectrum annuli: Gabor features r1r1   r2r2

25. Comparison with Low-Level Features Markov random field parameters Wavelets decomposition Wavelet packets decomposition Wavelet coefficient energies:

26. Comparison of Computation Costs 1 Markov random field parameters O(n( 2 -1) 2 -( 2 -1) 3 /3) 2 Gabor features  ( (logn+1)nlogn 1/2 ) 3 Fourier power spectrum features O(n 3/2 ) 4 Auto-cooccurrence matrix O(n  ) 5 Wavelet coefficient energies O(n l) 6 Multiresolution histograms  n n- number of pixels - window width l- resolution levels decreasing cost

27. Sensitivity Comparison to Transformations FeatureTranslationRotation Uniform Scaling 1 Fourier power spectrum annuli invariantrobustequivariant 2 Gabor features invariantvariantequivariant 3 Daubechies wavelet energies variantvariantvariant 4 Multiresolution histograms invariantinvariantequivariant 5 Auto-cooccurrence matrix invariantrobustequivariant 6 Markov random field parameters invariantvariantvariant

28. Matching Comparison of Features: Brodatz Brodatz textures database: 0102030405060 0 20 40 60 80 100 St dev. of noise  n Class matched Multiresolution Diff. Histograms Fourier Power Spectrum Gabor Features Wavelet Packets Cooccurence Matrix Markov Random Fields

29. Matching Comparison of Features: CUReT Curet textures database: Match 100 randomly selected images per noise level 01020304050 St dev. of noise  n 0 20 40 60 80 100 Class matched Multiresolution Diff. Histograms Fourier Power Spectrum Gabor Features Wavelet Packets Cooccurence Matrix Markov Random Fields r1r1

30. Sensitivity of Features to Recognition Feature Gaussian Noise Database size,#classes IlluminationParameter selection Fourier power spectrum annuli sensitive robustvery sensitive Gabor featuresrobust sensitive Daubechies wavelet energies sensitiverobust Multiresolution histogram robust Auto-cooccurrence matrix very sensitive Markov random field parameters very sensitive sensitiveN/A

31. Colors