Matrix-valued filters as convex programs

Authors:
Martin Welk;Florian Becker;Christoph Schnörr;Joachim Weickert
Affiliations:
Mathematical Image Analysis Group, Faculty of Mathematics and Computer Science, Bldg. 27, Saarland University, Saarbrücken, Germany;Computer Vision, Graphics, and Pattern Recognition Group, Faculty of Mathematics and Computer Science, University of Mannheim, Mannheim, Germany;Computer Vision, Graphics, and Pattern Recognition Group, Faculty of Mathematics and Computer Science, University of Mannheim, Mannheim, Germany;Mathematical Image Analysis Group, Faculty of Mathematics and Computer Science, Bldg. 27, Saarland University, Saarbrücken, Germany
Venue:
Scale-Space'05 Proceedings of the 5th international conference on Scale Space and PDE Methods in Computer Vision
Year:
2005

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Abstract

Matrix-valued images gain increasing importance both as the output of new imaging techniques and as the result of image processing operations, bearing the need for robust and efficient filters for such images. Recently, a median filter for matrix-valued images has been introduced. We propose a new approach for the numerical computation of matrix-valued median filters, and closely related mid-range filters, based on sound convex programming techniques. Matrix-valued medians are uniquely computed as global optima with interior point solvers. The robust performance is validated with experimental results for matrix-valued data including texture analysis and denoising.