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：拓扑结构的最小路径曲面


我们提出了 SurfCut，一种用于从嘈杂的 3D 图像和种子点中提取具有未知 3D 曲线边界的平滑、简单表面的算法。我们的方法建立在新的观察之上，即终止于 Eikonal 方程解的水平集的最小路径的欧几里得长度的脊线位于表面上。我们的方法提取这些脊并切割它们以形成表面边界。我们的表面提取算法建立在表面位于 Ekonal 方程解的山谷中的新颖观察之上。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，我们设计了鲁棒地提取山脊和山谷的算法。对三个 3D 数据集的实验表明了我们方法的稳健性，并且与最先进的方法相比，它以更低的计算成本实现了更高的精度。