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Fast Regularization of Matrix-Valued Images*
Guy Rosman1, Yu Wang1, Xue-Cheng Tai2, Ron Kimmel1, and Alfred M. Bruckstein1
1Dept. of Computer Science Technion - IIT Haifa 32000, Israel
rosman@cs.technion.ac.il
yuwang@cs.technion.ac.il
ron@cs.technion.ac.il
freddy@cs.technion.ac.il
2Dept. of Mathematics University of Bergen Johaness Brunsgate 12 Bergen 5007, Norway
tai@mi.uib.no
Abstract. Regularization of images with matrix-valued data is important in medical imaging, motion analysis and scene understanding. We propose a novel method for fast regularization of matrix group-valued images.
Using the augmented Lagrangian framework we separate total- variation regularization of matrix-valued images into a regularization and a projection steps. Both steps are computationally efficient and easily parallelizable, allowing real-time regularization of matrix valued images on a graphic processing unit.
We demonstrate the effectiveness of our method for smoothing several group-valued image types, with applications in directions diffusion, motion analysis from depth sensors, and DT-MRI denoising.
Keywords: Matrix-valued, Regularization, Total-variation, Optimization, Motion understanding, DT-MRI, Lie-groups
*This research was supported by Israel Science Foundation grant no.1551/09 and by the European Community’s FP7- ERC program, grant agreement no. 267414.
LNCS 7574, p. 173 ff.
lncs@springer.com
© Springer-Verlag Berlin Heidelberg 2012