Active Contour Models Driven by Hyperbolic Mean Curvature Flow for Image Segmentation

2025-06-07

AI Summary

Traditional parabolic mean curvature flow-based active contour models (PMCF-ACMs) suffer from high sensitivity to initial contour placement and poor robustness in segmenting weak boundaries. To address these limitations, this paper proposes a novel hyperbolic mean curvature flow-based active contour framework. Methodologically, it integrates level-set representation, signed distance function regularization, a smoothed Heaviside function, and a hybrid numerical solver combining weighted fourth-order Runge–Kutta time integration with a nine-point spatial finite difference scheme. Key contributions include: (1) introducing a tunable initial velocity field to substantially improve initialization robustness; (2) establishing numerical equivalence between the dissipative hyperbolic flow and the wave equation to ensure physical consistency; and (3) designing an edge-aware dual-mode regularization mechanism to suppress spurious diffusion near weak boundaries. Experiments demonstrate superior segmentation accuracy under noise, significantly enhanced numerical stability, and improved task adaptability compared to conventional approaches.

Technology Category

• Machine Learning: Active Learning
• Computer Vision: Segmentation
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Web Mining and Content Analysis: Models for Web evolution

Abstract

Parabolic mean curvature flow-driven active contour models (PMCF-ACMs) are widely used in image segmentation, which however depend heavily on the selection of initial curve configurations. In this paper, we firstly propose several hyperbolic mean curvature flow-driven ACMs (HMCF-ACMs), which introduce tunable initial velocity fields, enabling adaptive optimization for diverse segmentation scenarios. We shall prove that HMCF-ACMs are indeed normal flows and establish the numerical equivalence between dissipative HMCF formulations and certain wave equations using the level set method with signed distance function. Building on this framework, we furthermore develop hyperbolic dual-mode regularized flow-driven ACMs (HDRF-ACMs), which utilize smooth Heaviside functions for edge-aware force modulation to suppress over-diffusion near weak boundaries. Then, we optimize a weighted fourth-order Runge-Kutta algorithm with nine-point stencil spatial discretization when solving the above-mentioned wave equations. Experiments show that both HMCF-ACMs and HDRF-ACMs could achieve more precise segmentations with superior noise resistance and numerical stability due to task-adaptive configurations of initial velocities and initial contours.

Problem

• Overcoming initial curve dependency in image segmentation models
• Enhancing segmentation precision with adaptive velocity fields
• Suppressing over-diffusion near weak boundaries in segmentation

Innovation

• Hyperbolic mean curvature flow-driven ACMs
• Edge-aware force modulation with Heaviside functions
• Weighted fourth-order Runge-Kutta algorithm optimization