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Deriving intrinsic images from image sequences. Yair Weiss, 2001 6.899 Presentation by Leonid Taycher
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6.899 Presentation2 Objective Recover intrinsic images from multiple observations. Intrinsic images reflectance R(x, y) illumination L(x,y) I(x,y)=L(x,y)R(x,y)
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6.899 Presentation3 Intrinsic Images
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6.899 Presentation4 Ill-Posed problem Single image: I(x,y) = L(x,y)R(x,y) N equations and 2N unknowns Trivial solution: R=1, L=I Multiple images: I(x,y,t) = L(x,y,t)R(x,y) N equations and N+1 unknowns Trivial solution: R=1, L(t)=I(t)
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6.899 Presentation5 Previous Approaches L(x,y,t) are attached shadows Yuille et. al., 1999 (SVD) L(x,y,t)= (t)L(x,y) Farid and Adelson, 1999 (ICA) I(x,y,t)=R(x,y)+L(x-tv x,y-tv y ) (transparency) Szeliski et. al., 2000
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6.899 Presentation6 Main Assumption Large illumination variations are sparse, and can be approximated by a Laplacian distribution (even in the log domain).
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6.899 Presentation7 Real main assumption The illumination variations are Laplacian distributed in both space and time.
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6.899 Presentation8 Intuition If you often see an intensity variation at (x 0, y 0 ), then it is probably caused by reflectance properties. Otherwise it is caused by illumination.
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6.899 Presentation9 Example
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6.899 Presentation10 Maximum Likelihood Estimation In log domain i(x,y,t)=r(x,y)+l(x,y,t) Assuming filters {f n } o n (x,y,t)=i(x,y,t)*f n r n (x,y)=r(x,y)*f n Assuming that l_n(x,y,t)=l(x,y,t)*f_n are Laplacian distributed in time and space…
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6.899 Presentation11 Maximum Likelihood Estimation
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6.899 Presentation12 Results
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6.899 Presentation13 More Results
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6.899 Presentation14 Even More Results
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