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Multiresolution Histograms and their Use for Texture Classification

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. Q: Is there a fast feature which captures spatial information?. Same Histogram.

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Multiresolution Histograms and their Use for Texture Classification

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

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

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

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

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

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

  8. Shape Elongation and Fisher Information • Gaussian: • Pyramid: St. dev. along axes: sx, sy. Sides of base: rx, ry. Elongation: Elongation: 6 5 (analytically) 4 J 3 2 1 2 3 4 5 r

  9. h=0.56 h=1.00 h=1.48 h=2.00 h=6.67 (numerically) Complex boundary Shape Boundary and Fisher Information Superquadrics: 6 5 J 4 3 2 0 2 4 6 h

  10. Texel Repetition and Fisher Information Tileing 8 6 4 J 2 0 1 2 3 4 5 6 Tileing p x 103 8 6 4 J 2 0 1 2 3 4 5 6 Tileing p (analytically).

  11. Randomness (numerically) Texel Placement and Fisher Information Stand. dev. of perturbation x 103 6.6 6.4 6.2 J 6 5.8 0 5 10 15 20 St. Dev (% of Texel Width) 2.9 2.8 2.7 J 2.6 2.5 0 5 10 15 20 Average of 20 trials St. Dev (% of Texel Width)

  12. Matching Algorithm Multiresolution histogram with Burt-Adelson Pyramid Cumulative histograms Compute Feature Difference histograms between consecutive resolutions Concatenate to form feature vector L1 norm

  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 Brodatz textures[Brodatz, 66]: • 91 images; 7 images • Histogram equalized • Database of CUReT textures[Dana et al, 99]: • 8,046 images; 61 materials • 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. Number of bins 256 128 62 32 16 8 Class Matching Sensitivity: Brodatz Textures 100 80 60 Class matched 40 20 0 0 10 20 30 40 50 60 St dev. of noise sn

  19. Class Matching Sensitivity: Brodatz Textures 100 95 90 85 80 75 70 65 60 0 10 20 30 40 50 60 St dev. of noise sn 256 Constant 256, Higher Subsampling= 22/3 256, Lower Subsampling = 21/2 smoothing & adaptive bin size

  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. Class Matching Sensitivity: CUReT Textures 100 90 80 Class matched 70 60 50 0 10 20 30 40 50 St dev. of noise sn 256 Constant 256, Higher Subsampling= 22/3 256, Lower Subsampling = 21/2 Difference norm & Smoothing • Match 100 randomly selected images per noise level

  23. Comparison with Low-level Features • Fourier power spectrum annuli • Gabor features • Daubechies wavelet features • Auto-cooccurrence matrix • Markov random field parameters

  24. Comparison with Low-Level Features • Fourier power spectrum annuli: h z r1 r2 • Gabor features • Auto-cooccurrence matrix

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

  26. Comparison of Computation Costs decreasing cost n- number of pixels l- window width l- resolution levels

  27. Sensitivity Comparison to Transformations

  28. Matching Comparison of Features: Brodatz • Brodatz textures database: 100 80 Multiresolution Diff. Histograms Fourier Power Spectrum Gabor Features Wavelet Packets Cooccurence Matrix Markov Random Fields 60 Class matched 40 20 0 0 10 20 30 40 50 60 St dev. of noise sn

  29. Matching Comparison of Features: CUReT • Curet textures database: 100 80 Multiresolution Diff. Histograms Fourier Power Spectrum Gabor Features Wavelet Packets Cooccurence Matrix Markov Random Fields 60 Class matched 40 r1 20 0 0 10 20 30 40 50 St dev. of noise sn • Match 100 randomly selected images per noise level

  30. Sensitivity of Features to Recognition

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