用双自由度曲线演化提升图像分割抗噪能力
Active Contour Models Driven by Hyperbolic Mean Curvature Flow for Image Segmentation
- 引入双曲型曲率流驱动轮廓演化，可自适应调节平滑性
- 在高噪声下分割准确率显著提升，参数敏感度降低
- 适合医学图像等噪声严重的实际场景使用
基于抛物型平均曲率流的主动轮廓模型（PMCF-ACMs）广泛用于图像分割，但在高强度噪声下因梯度下降演化出现著名的锯齿现象而性能严重退化。为克服此问题，本文提出双曲型平均曲率流驱动的主动轮廓模型（HMCF-ACMs）。该框架引入可调加速度场，自主调控曲线演化平滑性，提供初始轮廓和速度场的双重自适应选择自由度。严格证明了HMCF-ACMs为法向流，并通过带符号距离函数的水平集形式建立其与波动方程的数值等价性。开发了结合谱离散与优化时间积分的高效数值求解方案，通过傅里叶分析推导出稳定性条件。在自然图像和医学图像上的大量实验表明，与PMCF-ACMs相比，HMCF-ACMs在高噪声条件下表现出更优性能，具有更低的参数敏感性、更强的抗噪能力和更高的分割精度。
原文摘要 · Abstract (English)
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.
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