软Mumford-Shah分割的随机变分模型
A stochastic-variational model for soft Mumford-Shah segmentation
摘要：
在当代图像和视觉分析中，随机方法在表示和建模复杂现象方面表现出极大的灵活性，而变分PDE方法相对于Monte-Carlo或其他随机算法获得了巨大的计算优势。两者结合起来，可以产生更强大的新模型和有效的算法。在目前的工作中，我们提出了一个随机变分模型的软（或模糊）Mumford-Shah分割的混合图像模式。与经典的硬Mumford-Shah分割不同，新模型允许每个像素以一定的概率属于每个图像模式。我们表明，软分割导致硬分割，因此是更普遍的。新模型的建模过程，数学分析和计算实现进行了详细的探讨，合成和自然图像的数值例子。
英文摘要：
In contemporary image and vision analysis, stochastic approaches demonstrate great flexibility in representing and modeling complex phenomena, while variational-PDE methods gain enormous computational advantages over Monte-Carlo or other stochastic algorithms. In combination, the two can lead to much more powerful novel models and efficient algorithms. In the current work, we propose a stochastic-variational model for soft (or fuzzy) Mumford-Shah segmentation of mixture image patterns. Unlike the classical hard Mumford-Shah segmentation, the new model allows each pixel to belong to each image pattern with some probability. We show that soft segmentation leads to hard segmentation, and hence is more general. The modeling procedure, mathematical analysis, and computational implementation of the new model are explored in detail, and numerical examples of synthetic and natural images are presented.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
