Curvature Prior for MRF-based Segmentation and Shape Inpainting

TL;DR

This paper introduces a novel framework for efficiently learning and representing higher order image priors, specifically low curvature shape priors, to improve segmentation and inpainting tasks.

Contribution

It proposes a new method to learn compact, tractable representations of higher order priors using lower envelopes of linear functions, enabling efficient inference.

Findings

The framework effectively learns low curvature shape priors.

It approximates complex priors with high accuracy.

Demonstrates improved segmentation and inpainting results.

Abstract

Most image labeling problems such as segmentation and image reconstruction are fundamentally ill-posed and suffer from ambiguities and noise. Higher order image priors encode high level structural dependencies between pixels and are key to overcoming these problems. However, these priors in general lead to computationally intractable models. This paper addresses the problem of discovering compact representations of higher order priors which allow efficient inference. We propose a framework for solving this problem which uses a recently proposed representation of higher order functions where they are encoded as lower envelopes of linear functions. Maximum a Posterior inference on our learned models reduces to minimizing a pairwise function of discrete variables, which can be done approximately using standard methods. Although this is a primarily theoretical paper, we also demonstrate the practical effectiveness of our framework on the problem of learning a shape prior for image segmentation and reconstruction. We show that our framework can learn a compact representation that approximates a prior that encourages low curvature shapes. We evaluate the approximation accuracy, discuss properties of the trained model, and show various results for shape inpainting and image segmentation.