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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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Automatic White Balance Problem AWB Colour constancy accounting for differences in illumination colour
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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
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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 R k (λ) : sensor sensitivity function of channel k Assuming narrowband sensors:
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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
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Linear Reflectance Features Illumination log E Changes slowly cross an image Reflectance log S Linear combination of M “features” F i weights h i
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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
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Non-Negative Matrix Factorization NMF Input data matrix Basis vectorsWeights Factored result A data instance v is a weighted combination of basis
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Constraints on the Factorization Illumination & reflectance non-negative => NMF basis non-negative E smooth, R non-smooth Sparseness vs. Smoothness 1D example Increasing smoothness Increasing sparseness
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Sparseness Constraint Sparseness implies most entries zero 2D example Increasing sparseness
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Sparseness Measure Sparseness s(x) of x= Sparseness constraint is enforced during matrix factorization L-1 norm L-2 norm
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NMFsc Using Non-Negative Matrix Factorization with sparseness constraint Calling it NMFsc
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NMFsc for Auto White Balancing The Illumination-Reflectance model NMFsc form In combination
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Incorporating Sparseness Finding M+1 basis vectors Set low sparseness for 1 st basis vector (illumination) Set high sparseness for 2 nd -(M+1) th basis (feature reflectance)
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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
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Experiment on MNFsc (M=4) Input Ground Truth NMFsc result
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Experiment on MNFsc (M=4) Illumination Image Reflectance Images
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More Experiment on NMFsc (M=4) Input Ground Truth NMFsc result
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Experiment on MNFsc (M=4) Illumination Image Reflectance Images
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Experiment on MNFsc (M=1) Ground Truth Input Illumination Image NMFsc Result Reflectance Image
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More Experiments (M=1) NMFsc Result Reflectance Image Ground Truth Input Illumination Image
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Tests on Large Dataset (M=4) 16 sub-windows (16x16) Take log and apply NMFsc Illumination basis (sparseness=0.001) 4 Reflectance basis (sparseness = 0.45) Illumination image by anti-log Reflectance images by anti-log 7661 images (64x64) Average to estimate illumination
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Tests on Large Dataset (M=1) Single sub-window (64x64) Take log and apply NMFsc Illumination basis (sparseness=0.001) One reflectance basis (sparseness = 0.45) Illumination image by anti-log Reflectance images by anti-log 7661 images (64x64) Average to estimate illumination
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Results Processing Time: 0.83 sec/image for M = 4; 2.43 sec/image for M = 1; Method Angular DegreesL-2 Distance (x10 2 ) MeanMaxMeanMax GW7.6942.285.9738.33 SoG7.5034.525.5027.67 MAX RGB9.9927.427.2421.72 NMFsc (M = 4)7.66 8.9634.79 5.59 NMFsc (M = 1)6.82 8.1538.27 5.11
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Algorithm Comparison via Wilcoxon MethodGWSoGMAX NMFsc (M=4) NMFsc (M=1) GW =+=- SoG =++- MAX ---- NMFsc (M=4) =-+- NMFsc (M=1) ++++ NMFsc better than Greyworld, Shades of Gray, Max RGB
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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
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Conclusions Insensitive to sparseness setting NMFsc converges quickly 20-30 iterations Good AWB results Tested on large data set of natural images
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Financial support provided by Samsung Advanced Institute of Technology
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Thank you! Yoho National Park British Columbia, Canada
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