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Scene illumination and surface albedo recovery via L1-norm total variation minimization Hong-Ming Chen hc2599@columbia.edu Advised by: John Wright

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Decomposition of a scene 2 =.* sceneReflectance (albedo) illumination.* : Matlab element multiplication operation

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Image Formation 3 =.* scenereflectanceillumination Sensor response (camera or eyes) Light source power spectrum Object reflectance intensityresponseSensor response integration Pixel i signals : shutter speed, aperture size, quantization factor etc

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It is VERY HARD to directly model / simulate / solve this problem! 4

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Narrowing down our target problem Simplification: – mean wavelength response (impulse response) Assumption (on surface reflectance) : – Lambertian Surface (Perfect diffuse reflection, no specular light) Simulation (of light source model) : – We need a formula to describe the behavior of the light source – Blackbody radiation: parameterize the light source with: Light color (color temperature) Light intensity 5

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Problem formulation: 6

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7 log Assume: λ R λ G λ G are known If there are N pixels in an image: 3N observations 5N unknowns (I, T, ref ) + 3 quantize factors underdetermined system!

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Recovering unknown x Previous approach – Introducing regularization terms into objective function Current approach – Minimizing L1-norm total variation 9

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Previous Approach 10 1-D grayscale visualization A segmentation-like result A result of: Intrinsic images by entropy minimization, Finlayson, ECCV2004 psps p ps 0 255

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Drawbacks of this approach There are at least 2 parameters (λ, σ) to be fine tuned. The results of Finlayson’s approach heavily affects the accurateness of our prior. – 1. Its Achilles heel: projection problem – 2. it is still an open problem to find the best rotation angle. 11

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12 (λ =50, σ = 10)(λ =10, σ = 30) (λ =120, σ = 5)(λ =120, σ = 8)

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A brief review of Finlayson’ solution Its Achilles heel: 13

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L1 norm Total Variation Minimization 14 Image From Wikipedia

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L1 norm Total Variation Minimization Widely used in image denoise / Compressive sensing – E(x, y) + λTV(y). 15 Image From Wikipedia

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Current approach: L1 TV norm Applying L1-norm total variation on albedo term, The L1-norm encourages a spiky result on gradient – Which means: we want most of the albedo gradients are 0 unless necessary => when albedo changes 16

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17 Results Original image Light color (temperature) imageLight intensity image Albedo (reflectance) image

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18 Results Original image Light color (temperature) imageLight intensity image Albedo (reflectance) image

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19 Results Original image Light color (temperature) imageAlbedo (reflectance) image

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20 Results Original image Light color (temperature) imageAlbedo (reflectance) image

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Editing 21 Original imageAverage T-1000Average T+1000 Average T+2000Average T+3000Average T+4000 Average T = 3940

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THANK YOU 22

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