Deriving intrinsic images from image sequences. Yair Weiss, 2001

6.899 Presentation byLeonid Taycher

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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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Intrinsic Images

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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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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-tvx,y-tvy) (transparency) Szeliski et. al., 2000

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Main Assumption

Large illumination variations are sparse, and can be approximated by a Laplacian distribution (even in the log domain).

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Real main assumption

The illumination variations are Laplacian distributed in both space and time.

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Intuition

If you often see an intensity variation at (x0, y0), then it is probably caused by reflectance properties. Otherwise it is caused by illumination.

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Example

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Maximum Likelihood Estimation

In log domain i(x,y,t)=r(x,y)+l(x,y,t)Assuming filters {fn}

on(x,y,t)=i(x,y,t)*fn

rn(x,y)=r(x,y)*fn

Assuming that l_n(x,y,t)=l(x,y,t)*f_n are Laplacian distributed in time and space…

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Maximum Likelihood Estimation

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Results

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More Results

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Even More Results