1. Deriving intrinsic images from image sequences. Yair Weiss, 2001 6.899 Presentation by Leonid Taycher

2. 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)

3. 6.899 Presentation3 Intrinsic Images

4. 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)

5. 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

6. 6.899 Presentation6 Main Assumption Large illumination variations are sparse, and can be approximated by a Laplacian distribution (even in the log domain).

7. 6.899 Presentation7 Real main assumption The illumination variations are Laplacian distributed in both space and time.

8. 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.

9. 6.899 Presentation9 Example

10. 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…

11. 6.899 Presentation11 Maximum Likelihood Estimation

12. 6.899 Presentation12 Results

13. 6.899 Presentation13 More Results

14. 6.899 Presentation14 Even More Results