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Shadow removal algorithms

Shadow removal algorithms. Shadow removal seminar Pavel Knur. Deriving intrinsic images from image sequences. Yair Weiss July 2001. History. “ intrinsic images ” by Barrow and Tenenbaum , 1978. Constraints. Fixed viewpoint Works only for static objects Cast shadows.

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Shadow removal algorithms

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  1. Shadow removal algorithms Shadow removal seminar Pavel Knur

  2. Deriving intrinsic images from image sequences Yair Weiss July 2001.

  3. History • “intrinsic images” by Barrow and Tenenbaum , 1978

  4. Constraints • Fixed viewpoint • Works only for static objects • Cast shadows

  5. Classic ill-posed problem • Denote • the input image • the reflectance image • the illumination image Number of Unknowns is twice the number of equations.

  6. The problem Given a sequence of T images in which reflectance is constant over the time and only the illumination changes, can we solve for a single reflectance image and T illumination images ? Still completely ill-posed : at every pixel there are T equations and T+1 unknowns.

  7. Maximum-likelihood estimation • Log domain :

  8. Assumptions When derivative filters are applied to natural images, the filter outputs tend to be sparse.

  9. Laplacian distribution Can be well fit by laplacian distribution

  10. Claim 1 Denote : • N filters – • Filter outputs – • Filtered reflectance image – ML estimation of filtered reflectance image is given by

  11. Estimated reflectance function Recover ML estimation of r is reversed filter of

  12. ML estimation algorithm

  13. ML estimation algorithm – cont. • Ones we have estimated

  14. Claim 2 • What if does not have exactly a Laplasian distribution ? Let Then estimated filtered reflectance are within with probability at least:

  15. Claim 2 - proof If more than 50% of the samples of are within of some value, then by definition of median, the median must be within of that value.

  16. Example 1 • Einstein image is translated diagonally • 4 pixels per frame

  17. Example 2 • 64 images with variable lighting from Yale Face Database

  18. Illumination Normalization with Time-Dependent Intrinsic Images for Video Surveillance Y.Matsushita,K.Nishito,K.Ikeuchi Oct. 2004

  19. Illumination Normalization algorithm • Preprocessing stage for robust video surveillance. • Causes • Illumination conditions • Weather conditions • Large buildings and trees • Goal • To “normalize” the input image sequence in terms of incident lighting.

  20. Constraints • Fixed viewpoint • Works only for static objects • Cast shadows

  21. Background images Input images • Remove moving objects from the input image sequence Off-line Background images

  22. Estimation of Intrinsic Images Input images Denote • input image • time-varying reflectance image • time-varying illumination image • reflectance image estimated by ML • illumination image estimated by ML • Filters • Log domain Off-line Background images Estimation of Intrinsic Images

  23. Estimation of Intrinsic Images – cont. Input images • In Weiss’s original work • The goal is to find estimation of and Off-line Background images Estimation of Intrinsic Images

  24. Estimation of Intrinsic Images – cont. Input images Basic idea: • Estimate time-varying reflectance components by canceling the scene texture from initial illumination images Define: Off-line Background images Estimation of Intrinsic Images

  25. Estimation of Intrinsic Images – cont. Input images Finally : Where : is reversed filter of Off-line Background images Estimation of Intrinsic Images

  26. Shadow Removal Input images Denote - background image - illuminance-invariant image Off-line Background images Estimation of Intrinsic Images

  27. Illumination Eigenspace Input images • PCA – Principle component analysis Basic components - Off-line Background images Illumination Eigenspace Estimation of Intrinsic Images

  28. Illumination Eigenspace – cont. Input images • Average is • P is MxN matrix where • N – number of pixels in illumination image • M – number of illumination images • Covariance matrix Q of P is Off-line Background images Illumination Eigenspace Estimation of Intrinsic Images

  29. Direct Estimation of Illumination Images Input images • Pseudoillumination image • Direct Estimation is • Where • F is a projection function onto the j’s eigenvector - Off-line Background images Illumination Eigenspace Estimation of Intrinsic Images

  30. Direct Estimation of Illumination Images Input images • Results Off-line Background images Illumination Eigenspace Estimation of Intrinsic Images

  31. Shadow interpolation Input images probability density function cumulative probability function shadowed area lit area mean optimum threshold value Off-line Background images Illumination Eigenspace Estimation of Intrinsic Images Shadow Interpolation

  32. The whole algorithm Input images Off-line Background images Illumination Eigenspace Estimation of Intrinsic Images Shadow Interpolation Illumination Images / Normalization

  33. Example

  34. Questions ?

  35. References [1] Y.Weiss,”Deriving Intrinsic Images from Image Sequences”, Proc. Ninth IEEE Int’l Conf. Computer Vision, pp. 68-75, July 2001. [2] Y.Matsushita,K.Nishito,K.Ikeuchi,“Illumination Normalization with Time-Dependent Intrinsic Images for Video Surveillance”,Oct. 2004.

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