Sublabel-Accurate Discretization of Nonconvex Free-Discontinuity Problems
This work addresses discretization challenges in computer vision and image processing, offering incremental improvements for tasks like segmentation and denoising.
The paper tackles the discretization of nonconvex free-discontinuity problems by deriving sublabel-accurate multilabeling approaches from convex relaxations, extending them to general regularizations and applying them to the vectorial Mumford-Shah functional, resulting in more precise solutions with fewer labels in experiments.
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.