# Sublabel-Accurate Discretization of Nonconvex Free-Discontinuity Problems

arXiv: https://arxiv.org/abs/1611.06987 · HTML: https://mlsanity.com/paper/1611.06987/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Nov 2016.

## Built on by (most cited first, 2 of 2)

- [Lifting the Convex Conjugate in Lagrangian Relaxations: A Tractable Approach for Continuous Markov Random Fields](https://mlsanity.com/paper/2107.06028/) (2021)
- [Efficient and Flexible Sublabel-Accurate Energy Minimization](https://mlsanity.com/paper/2206.09596/) (2022)

## Abstract (arXiv)

In this work we show how sublabel-accurate multilabeling approaches can be derived by approximating a classical label-continuous convex relaxation of nonconvex free-discontinuity problems. This insight allows to extend these sublabel-accurate approaches from total variation to general convex and nonconvex regularizations. Furthermore, it leads to a systematic approach to the discretization of continuous convex relaxations. We study the relationship to existing discretizations and to discrete-continuous MRFs. Finally, we apply the proposed approach to obtain a sublabel-accurate and convex solution to the vectorial Mumford-Shah functional and show in several experiments that it leads to more precise solutions using fewer labels.