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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 Slide 2 Decomposition of a scene 2 =.* sceneReflectance (albedo) illumination.* : Matlab element multiplication operation Slide 3 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 Slide 4 It is VERY HARD to directly model / simulate / solve this problem! 4 Slide 5 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 Slide 6 Problem formulation: 6 Slide 7 7 log Assume: R G G are known If there are N pixels in an image: 3N observations 5N unknowns (I, T, ref ) + 3 quantize factors underdetermined system! Slide 8 8 Slide 9 Recovering unknown x Previous approach Introducing regularization terms into objective function Current approach Minimizing L1-norm total variation 9 Slide 10 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 Slide 11 Drawbacks of this approach There are at least 2 parameters (, ) to be fine tuned. The results of Finlaysons 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 Slide 12 12 ( =50, = 10)( =10, = 30) ( =120, = 5)( =120, = 8) Slide 13 A brief review of Finlayson solution Its Achilles heel: 13 Slide 14 L1 norm Total Variation Minimization 14 Image From Wikipedia Slide 15 L1 norm Total Variation Minimization Widely used in image denoise / Compressive sensing E(x, y) + TV(y). 15 Image From Wikipedia Slide 16 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 Slide 17 17 Results Original image Light color (temperature) imageLight intensity image Albedo (reflectance) image Slide 18 18 Results Original image Light color (temperature) imageLight intensity image Albedo (reflectance) image Slide 19 19 Results Original image Light color (temperature) imageAlbedo (reflectance) image Slide 20 20 Results Original image Light color (temperature) imageAlbedo (reflectance) image Slide 21 Editing 21 Original imageAverage T-1000Average T+1000 Average T+2000Average T+3000Average T+4000 Average T = 3940 Slide 22 THANK YOU 22