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

TL;DR

This paper introduces hyperbolic mean curvature flow-driven active contour models (HMCF-ACMs) that improve image segmentation robustness under high noise by incorporating an adjustable acceleration field and advanced numerical schemes.

Contribution

It proposes a novel hyperbolic mean curvature flow framework with an acceleration field, providing adaptive control and improved noise robustness over traditional models.

Findings

HMCF-ACMs outperform PMCF-ACMs in noisy environments.

The model is proven to be a normal flow and equivalent to wave equations.

The numerical scheme is stable and efficient for practical use.

Abstract

Parabolic mean curvature flow-driven active contour models (PMCF-ACMs) are widely used for image segmentation, yet they suffer severe degradation under high-intensity noise because gradient-descent evolutions exhibit the well-known zig-zag phenomenon. To overcome this drawback, we propose hyperbolic mean curvature flow-driven ACMs (HMCF-ACMs). This novel framework incorporates an adjustable acceleration field to autonomously regulate curve evolution smoothness, providing dual degrees of freedom for adaptive selection of both initial contours and velocity fields. We rigorously prove that HMCF-ACMs are normal flows and establish their numerical equivalence to wave equations through a level set formulation with signed distance functions. An efficient numerical scheme combining spectral discretization and optimized temporal integration is developed to solve the governing equations, and its stability condition is derived through Fourier analysis. Extensive experiments on natural and medical images validate that HMCF-ACMs achieve superior performance under high-noise conditions, demonstrating reduced parameter sensitivity, enhanced noise robustness, and improved segmentation accuracy compared to PMCF-ACMs.