Fast Regularization of Matrix-Valued Images
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- 作者：Guy Rosman (18)
Yu Wang (18)
Xue-Cheng Tai (19)
Ron Kimmel (18)
Alfred M. Bruckstein (18) - 关键词：Regularization ; Matrix ; manifolds ; Lie ; groups ; Total ; variation ; Segmentation
- 刊名：Lecture Notes in Computer Science
- 出版年：2014
- 出版时间：2014
- 年：2014
- 卷：1
- 期：1
- 页码：19-43
- 全文大小：2,064 KB
- 参考文献：1. Fingerprints Verification Competition database
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Yu Wang (18)
Xue-Cheng Tai (19)
Ron Kimmel (18)
Alfred M. Bruckstein (18)
18. Department of Computer Science, Technion, 32000, Haifa, Israel
19. Department of Mathematics, University of Bergen, Johaness Brunsgate 12, 5007, Bergen, Norway - ISSN：1611-3349
文摘
Regularization of matrix-valued data is important in many fields, such as medical imaging, motion analysis and scene understanding, where accurate estimation of diffusion tensors or rigid motions is crucial for higher-level computer vision tasks. In this chapter we describe a novel method for efficient regularization of matrix- and group-valued images. Using the augmented Lagrangian framework we separate the total-variation regularization of matrix-valued images into a regularization and projection steps, both of which are fast and parallelizable. Furthermore we extend our method to a high-order regularization scheme for matrix-valued functions. We demonstrate the effectiveness of our method for denoising of several group-valued image types, with data in $SO(n)$ , $SE(n)$ , and $SPD(n)$ , and discuss its convergence properties.