We present SurfCut , an algorithm for extracting a smooth, simple surface with an unknown 3D curve boundary from a noisy 3D image and a seed point. Our method is built on the novel observation that ridge curves of the Euclidean length of minimal paths ending on a level set of the solution of the eikonal equation lie on the surface. Our method extracts these ridges and cuts them to form the surface boundary. Our surface extraction algorithm is built on the novel observation that the surface lies in a valley of the eikonal equation solution. The resulting surface is a collection of minimal paths. Using the framework of cubical complexes and Morse theory, we design algorithms to extract ridges and valleys robustly. Experiments on three 3D datasets show the robustness of our method, and that it achieves higher accuracy with lower computational cost than state-of-the-art.

中文翻译：

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SurfCut：来自拓扑结构的最小路径的表面

我们提出 冲浪切割 ，一种用于从嘈杂的3D图像和种子点提取具有未知3D曲线边界的光滑，简单曲面的算法。我们的方法建立在新颖的观察之上，即最小路径的欧几里得长度的脊曲线以表面上的方程组方程解的水平集结尾。我们的方法提取这些脊并将其切割以形成表面边界。我们的表面提取算法是建立在新颖的观察之上的，即表面位于方程方程解的谷底。生成的表面是最小路径的集合。利用立方复合体和莫尔斯理论的框架，我们设计了算法来稳健地提取山脊和山脊。在3个3D数据集上进行的实验表明了我们方法的鲁棒性，