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CVPR
2010
IEEE

An Approach to Vectorial Total Variation based on Geometric Measure Theory

14 years 7 months ago
An Approach to Vectorial Total Variation based on Geometric Measure Theory
We analyze a previously unexplored generalization of the scalar total variation to vector-valued functions, which is motivated by geometric measure theory. A complete mathematical characterization is given, which proves important invariance properties as well as existence of solutions of the vectorial ROF model. As an important feature, there exists a dual formulation for the proposed vectorial total variation, which leads to a fast and stable minimization algorithm. The main difference to previous approaches with similar properties is that we penalize across a common edge direction for all channels, which is a major theoretical advantage. Experiments show that this leads to a significiantly better restoration of color edges in practice.
Bastian Goldluecke, Daniel Cremers
Added 03 Apr 2010
Updated 14 May 2010
Type Conference
Year 2010
Where CVPR
Authors Bastian Goldluecke, Daniel Cremers
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