Image Reconstruction via Discrete Curvatures

TL;DR

This paper introduces a novel method for image reconstruction that estimates discrete curvatures using differential geometry, leading to an efficient variational model solved by ADMM, demonstrating superior results.

Contribution

It proposes a new approach to estimate discrete curvatures for image reconstruction, transforming curvature regularities into a weighted total variation minimization problem.

Findings

Effective in various image reconstruction tasks

Outperforms existing methods in accuracy and efficiency

Demonstrates the practicality of curvature-based regularization

Abstract

The curvature regularities are well-known for providing strong priors in the continuity of edges, which have been applied to a wide range of applications in image processing and computer vision. However, these models are usually non-convex, non-smooth and highly non-linear, the first-order optimal condition of which are high-order partial differential equations. Thus, the numerical computation are extremely challenging. In this paper, we propose to estimate the discrete curvatures, i.e., mean curvature and Gaussian curvature, in the local neighborhood according to differential geometry theory. By minimizing certain functions of curvatures on all level curves of an image, it yields a kind of weighted total variation minimization problem, which can be efficiently solved by the proximal alternating direction method of multipliers (ADMM). Numerical experiments are implemented to demonstrate the effectiveness and superiority of our proposed variational models for different image reconstruction tasks.