Disjunctive Normal Level Set: An Efficient Parametric Implicit Method

TL;DR

This paper introduces the Disjunctive Normal Level Set (DNLS), a novel parametric level set method that enables faster, more stable, and less initialization-sensitive image segmentation, especially for multiple objects.

Contribution

The paper presents DNLS, a new parametric level set approach using unions of polytopes, improving segmentation speed, stability, and scalability for multi-object segmentation.

Findings

Faster convergence compared to existing methods.

Maintains regularity of the level set function during evolution.

Less sensitive to initialization with constant computational cost for multiple objects.

Abstract

Level set methods are widely used for image segmentation because of their capability to handle topological changes. In this paper, we propose a novel parametric level set method called Disjunctive Normal Level Set (DNLS), and apply it to both two phase (single object) and multiphase (multi-object) image segmentations. The DNLS is formed by union of polytopes which themselves are formed by intersections of half-spaces. The proposed level set framework has the following major advantages compared to other level set methods available in the literature. First, segmentation using DNLS converges much faster. Second, the DNLS level set function remains regular throughout its evolution. Third, the proposed multiphase version of the DNLS is less sensitive to initialization, and its computational cost and memory requirement remains almost constant as the number of objects to be simultaneously segmented grows. The experimental results show the potential of the proposed method.