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Unformatted text preview: Vector Valued Image Regularization with PDEs: A Common Framework for Different Applications CVPR 2003 Best Student Paper Award Definitions Scalar images: Intensity images Vector valued images: RGB, HSV, YIQ Regularization: Finding approximate solution for illposed problems. Let G be 2x2 matrix = d c b a G = = 2 1 , ) ( i i i g trace G Divergence and Curl Vectors are obtained from image gradients I y A x A A A div y x + = = ) ( Divergence defines expansion or contraction per unit volume ) , ( y x A vector function yy xx y x I I I I div I div I + = = = ) ( Curl of a vector field is defined by cross product between vectors Structure Tensor [ ] = = = = n i y x y x n i T i i I I I I I I 1 1 G Structure Tensor [ ] = = = = n i y x y x n i T i i I I I I I I 1 1 G One dimensional image (gray level) = y y y x y x x x gray I I I I I I I I G ) 1 , ( ) , ( ) , 1 ( ) , ( = = y x I y x I I y x I y x I I y x Structure Tensor + + = + + = y y y x y x x x y y y x y x x x y y y x y x x x color T T T color B B B B B B B B G G G G G G G G R R R R R R R R B B G G R R G G r eigenvecto eigenvalue color = + + + + + 2 1 2 1 G Eigenvalue and eigenvectors of G (spectral elements) Can be computed using Matlab functions x derivative y derivative More Insight (hessian&tensor) Hessian of image I Laplacian of I Tensor: Matrix of matrices. They abuse Matrix of matrices....
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This note was uploaded on 06/13/2011 for the course CAP 6412 taught by Professor Staff during the Spring '08 term at University of Central Florida.
 Spring '08
 Staff

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