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.
Abstract (translated)
抛物型平均曲率流驱动的活动轮廓模型（PMCF-ACMs）在图像分割中被广泛应用，然而这些方法严重依赖于初始曲线配置的选择。在这篇论文中，我们首先提出了几种双曲平均曲率流驱动的活动轮廓模型（HMCF-ACMs），引入了可调的初始速度场，使它们能够针对不同的分割场景进行自适应优化。我们将证明HMCF-ACMs确实是规范流，并通过带符号距离函数的水平集方法建立了耗散型HMCF形式与某些波动方程之间的数值等价性。基于这一框架，我们进一步开发了双曲双模式正则化流动驱动的活动轮廓模型（HDRF-ACMs），利用平滑海维赛德函数进行边缘感知力调制以抑制弱边界附近的过度扩散现象。然后，我们在求解上述波动方程时优化了一种加权四阶龙格库塔算法，并采用了九点模板的空间离散化方法。 实验表明，由于初始速度和轮廓的配置可以根据任务需求进行自适应调整，HMCF-ACMs 和 HDRF-ACMs 都能够实现更精确的分割效果，并且具有更好的抗噪性能和数值稳定性。
URL
https://arxiv.org/abs/2506.06712
