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.

• Type: Conference
• Year: 2010
• Where: CVPR
• Authors: Bastian Goldluecke, Daniel Cremers
• Keywords: Computer Vision, CVPR 2010, Scalar Total Variation, Total Variation, Vectorial Total Variation