English

Image Decomposition with G-norm Weighted by Total Symmetric Variation

Computer Vision and Pattern Recognition 2025-03-31 v1

Abstract

In this paper, we propose a novel variational model for decomposing images into their respective cartoon and texture parts. Our model characterizes certain non-local features of any Bounded Variation (BV) image by its Total Symmetric Variation (TSV). We demonstrate that TSV is effective in identifying regional boundaries. Based on this property, we introduce a weighted Meyer's GG-norm to identify texture interiors without including contour edges. For BV images with bounded TSV, we show that the proposed model admits a solution. Additionally, we design a fast algorithm based on operator-splitting to tackle the associated non-convex optimization problem. The performance of our method is validated by a series of numerical experiments.

Keywords

Cite

@article{arxiv.2503.22560,
  title  = {Image Decomposition with G-norm Weighted by Total Symmetric Variation},
  author = {Roy Y. He and Martin Huska and Hao Liu},
  journal= {arXiv preprint arXiv:2503.22560},
  year   = {2025}
}
R2 v1 2026-06-28T22:38:13.839Z