Thin Structure Estimation with Curvature Regularization

TL;DR

This paper introduces a novel method for detecting and delineating thin structures in images by jointly optimizing their location and orientation using curvature regularization, applicable to 2D and 3D data.

Contribution

It presents a new joint optimization algorithm for thin structure detection that effectively handles curvature regularization, improving over previous methods.

Findings

Effective detection of thin structures in 2D and 3D images.

Joint optimization improves localization and orientation accuracy.

Applicable to various vision tasks involving thin structures.

Abstract

Many applications in vision require estimation of thin structures such as boundary edges, surfaces, roads, blood vessels, neurons, etc. Unlike most previous approaches, we simultaneously detect and delineate thin structures with sub-pixel localization and real-valued orientation estimation. This is an ill-posed problem that requires regularization. We propose an objective function combining detection likelihoods with a prior minimizing curvature of the center-lines or surfaces. Unlike simple block-coordinate descent, we develop a novel algorithm that is able to perform joint optimization of location and detection variables more effectively. Our lower bound optimization algorithm applies to quadratic or absolute curvature. The proposed early vision framework is sufficiently general and it can be used in many higher-level applications. We illustrate the advantage of our approach on a range of 2D and 3D examples.