@inproceedings{2dd8a0b5479b4e2a987456954d5cd45b,
title = "Fast regularization of matrix-valued images",
abstract = "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, and, and discuss its convergence properties.",
keywords = "Lie-groups, Matrix-manifolds, Regularization, Segmentation, Total-variation",
author = "Guy Rosman and Yu Wang and Tai, {Xue Cheng} and Ron Kimmel and Bruckstein, {Alfred M.}",
note = "Funding Information: This research was supported by European Community{\textquoteright}s FP7-ERC program, grant agreement no. 267414.; 2011 International Dagstuhl Seminar 11471 on Efficient Algorithms for Global Optimization Methods in Computer Vision ; Conference date: 20-11-2011 Through 25-11-2011",
year = "2014",
doi = "10.1007/978-3-642-54774-4_2",
language = "الإنجليزيّة",
isbn = "9783642547737",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
pages = "19--43",
booktitle = "Efficient Algorithms for Global Optimization Methods in Computer Vision - International Dagstuhl Seminar, Revised Selected Papers",
}