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Illumination Estimation via Non-Negative Matrix Factorization

Illumination Estimation via Non-Negative Matrix Factorization. By Lilong Shi, Brian Funt, Weihua Xiong, ( Simon Fraser University, Canada) Sung-Su Kim, Byoung-Ho Kang, Sung-Duk Lee, and Chang-Yeong Kim ( Samsung Advanced Institute of Technology, Korea ). Presented by: Lilong Shi.

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Illumination Estimation via Non-Negative Matrix Factorization

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  1. Illumination Estimation via Non-Negative Matrix Factorization ByLilong Shi, Brian Funt, Weihua Xiong, (Simon Fraser University, Canada) Sung-Su Kim, Byoung-Ho Kang, Sung-Duk Lee, and Chang-Yeong Kim (Samsung Advanced Institute of Technology, Korea) Presented by: Lilong Shi

  2. Automatic White Balance Problem AWB Colour constancy accounting for differences in illumination colour

  3. Overview N sub-windows Take log and apply NMFsc Illumination component (low sparseness) M Reflectance basis (high sparseness) Illumination image by anti-log Reflectance images by anti-log With this we can do AWB

  4. The Model of Illumination and Feature Reflectances • RGB sensor response is defined by • E(λ): illumination spectral power distribution • S(λ): matte surface reflectance function • Rk(λ): sensor sensitivity function of channel k • Assumingnarrowband sensors:

  5. The Model of Illumination and Feature Reflectances • In logarithm space • Linear combination of illumination and reflectance • For an entire colour image I, with E and S the illumination and reflectance

  6. Linear Reflectance Features • Illumination log E • Changes slowly cross an image • Reflectance log S • Linear combination of M “features” Fi weights hi

  7. Linear Reflectance Features • “Feature” Reflectances • “building blocks” e.g. basis images derived from the ORL face image database following Li et al. (2001) • Independent • No non-zero pixels in common • Dot product of 2 blocks is zero • The complete model

  8. Non-Negative Matrix Factorization • NMF Input data matrix Factored result Basisvectors Weights • A data instance v is a weighted combination of basis

  9. Constraints on the Factorization • Illumination & reflectance non-negative => NMF basis non-negative • E smooth, R non-smooth • Sparseness vs. Smoothness Increasing smoothness 1D example Increasing sparseness

  10. Sparseness Constraint • Sparseness implies most entries zero 2D example Increasing sparseness

  11. L-1 norm L-2 norm Sparseness Measure • Sparseness s(x) of x=<x1…xn> • Sparseness constraint is enforced during matrix factorization

  12. NMFsc Using Non-Negative Matrix Factorization with sparseness constraint Calling it NMFsc

  13. NMFsc for Auto White Balancing • The Illumination-Reflectance model • NMFsc form • In combination

  14. Incorporating Sparseness • Finding M+1 basis vectors • Set low sparseness for 1st basis vector (illumination) • Set high sparseness for 2nd-(M+1)th basis (feature reflectance)

  15. The Algorithm N sub-windows Take log and apply NMFsc Illumination basis (low sparseness) M Reflectance basis (high sparseness) Illumination image by anti-log Reflectance images by anti-log

  16. Experiment on MNFsc (M=4) Input Ground Truth NMFsc result

  17. Experiment on MNFsc (M=4) Illumination Image Reflectance Images

  18. More Experiment on NMFsc (M=4) Input Ground Truth NMFsc result

  19. Experiment on MNFsc (M=4) Illumination Image Reflectance Images

  20. Experiment on MNFsc (M=1) Ground Truth Input Illumination Image NMFsc Result Reflectance Image

  21. More Experiments (M=1) Ground Truth Input Illumination Image NMFsc Result Reflectance Image

  22. Tests on Large Dataset (M=4) 16 sub-windows (16x16) Take log and apply NMFsc 7661 images (64x64) Illumination basis (sparseness=0.001) 4 Reflectance basis (sparseness = 0.45) Illumination image by anti-log Reflectance images by anti-log Average to estimate illumination

  23. Tests on Large Dataset (M=1) Single sub-window (64x64) Take log and apply NMFsc 7661 images (64x64) Illumination basis (sparseness=0.001) One reflectance basis (sparseness = 0.45) Illumination image by anti-log Reflectance images by anti-log Average to estimate illumination

  24. Results • Processing Time: • 0.83 sec/image for M = 4; • 2.43 sec/image for M = 1;

  25. Algorithm Comparison via Wilcoxon NMFsc better than Greyworld, Shades of Gray, Max RGB

  26. Conclusions • New AWB method using NMF • NMF ‘factors’ illumination from reflectance • Provides separate estimate for each pixel • Globally minimizes objective function across all three colour channels • Incorporates both colour and spatial (sparseness) information • Assumptions • spatially smooth illumination variation • non-smooth reflectance variation

  27. Conclusions • Insensitive to sparseness setting • NMFsc converges quickly • 20-30 iterations • Good AWB results • Tested on large data set of natural images

  28. Financial support provided by Samsung Advanced Institute of Technology

  29. Thank you! Yoho National Park British Columbia, Canada

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