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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 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
Automatic White Balance Problem AWB Colour constancy accounting for differences in illumination colour
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
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:
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
Linear Reflectance Features • Illumination log E • Changes slowly cross an image • Reflectance log S • Linear combination of M “features” Fi weights hi
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
Non-Negative Matrix Factorization • NMF Input data matrix Factored result Basisvectors Weights • A data instance v is a weighted combination of basis
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
Sparseness Constraint • Sparseness implies most entries zero 2D example Increasing sparseness
L-1 norm L-2 norm Sparseness Measure • Sparseness s(x) of x=<x1…xn> • Sparseness constraint is enforced during matrix factorization
NMFsc Using Non-Negative Matrix Factorization with sparseness constraint Calling it NMFsc
NMFsc for Auto White Balancing • The Illumination-Reflectance model • NMFsc form • In combination
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)
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
Experiment on MNFsc (M=4) Input Ground Truth NMFsc result
Experiment on MNFsc (M=4) Illumination Image Reflectance Images
More Experiment on NMFsc (M=4) Input Ground Truth NMFsc result
Experiment on MNFsc (M=4) Illumination Image Reflectance Images
Experiment on MNFsc (M=1) Ground Truth Input Illumination Image NMFsc Result Reflectance Image
More Experiments (M=1) Ground Truth Input Illumination Image NMFsc Result Reflectance Image
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
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
Results • Processing Time: • 0.83 sec/image for M = 4; • 2.43 sec/image for M = 1;
Algorithm Comparison via Wilcoxon NMFsc better than Greyworld, Shades of Gray, Max RGB
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
Conclusions • Insensitive to sparseness setting • NMFsc converges quickly • 20-30 iterations • Good AWB results • Tested on large data set of natural images
Financial support provided by Samsung Advanced Institute of Technology
Thank you! Yoho National Park British Columbia, Canada