基于区域强度差异的图像分割模型，适合噪声大或边界弱的图像。
Image Segmentation using Chan-Vese Active Contours
- 用区域平均强度差驱动轮廓演化，不依赖边缘梯度。
- 在医学和合成图像上实现高精度分割，抗噪性强。
- 适合医学影像等真实场景，数值稳定设计值得借鉴。
本文系统推导并实现了基于Mumford-Shah变分框架的Chan-Vese活动轮廓模型用于图像分割。该模型通过区域强度差异驱动轮廓演化，而非依赖图像梯度，因此对噪声图像或边界微弱的图像具有优异表现。我们提供了水平集形式的严格数学推导，包括利用散度定理和曲线演化理论对各项能量项的详细处理。算法采用有限差分法在Python中实现，特别关注数值稳定性，引入迎风熵格式与基于曲率的正则化。在医学图像和合成图像上的实验结果表明，该方法能实现精准分割，对噪声具有强鲁棒性，性能优于经典基于边缘的方法。本研究证实了Chan-Vese模型在复杂分割任务中的适用性，并凸显其在实际成像应用中的潜力。
原文摘要 · Abstract (English)
This paper presents a comprehensive derivation and implementation of the Chan-Vese active contour model for image segmentation. The model, derived from the Mumford-Shah variational framework, evolves contours based on regional intensity differences rather than image gradients, making it highly effective for segmenting noisy images or images with weak boundaries. We provide a rigorous mathematical derivation of the level set formulation, including detailed treatment of each energy term using the divergence theorem and curve evolution theory. The resulting algorithm is implemented in Python using finite difference methods with special care to numerical stability, including an upwind entropy scheme and curvature-based regularization. Experimental results on medical and synthetic images demonstrate accurate segmentation, robustness to noise, and superior performance compared to classical edge-based methods. This study confirms the suitability of the Chan-Vese model for complex segmentation tasks and highlights its potential for use in real-world imaging applications.
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