An Approach to Vectorial Total Variation based on Geometric Measure Theory

作者:Goldluecke Bastian*; Cremers Daniel
来源:23rd IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2010-06-13 to 2010-06-18.
DOI:10.1109/CVPR.2010.5540194

摘要

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.

  • 出版日期2010