Deriving intrinsic images from image sequences. Yair Weiss, 2001

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Deriving intrinsic images from image sequences.
Yair Weiss, 2001

• 6.899 Presentation by
• Leonid Taycher

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Objective

• Recover intrinsic images from multiple
  observations.

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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 R1, LI
• Multiple images I(x,y,t) L(x,y,t)R(x,y)
• N equations and N1 unknowns
• Trivial solution R1, 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)a(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