论文标题
通过3D Voronoi图中的最小重量表面进行裂纹建模
Crack Modeling via Minimum-Weight Surfaces in 3d Voronoi Diagrams
论文作者
论文摘要
最短的路径在数学建模和图像处理中起着重要作用。通常，最短的路径问题是在由顶点和加权弧组成的平面图上提出的。在这种情况下，人们有兴趣找到从启动顶点到末端顶点的最小重量的路径。最小重量表面的概念将最短的路径扩展到3D。最小重量的表面问题是在带有加权面的细胞复合物上提出的。复合物的弧线上的一个循环是输入的，并且有兴趣找到由该周期界定的最小重量表面。实际上，最小重量表面可用于细分3D图像。反之亦然，可以将它们用作裂缝等几何结构的建模工具。在这项工作中，我们提出了一种方法，用于使用有界Voronoi图中的最小重量表面来生成裂纹的合成3D图像。
Shortest paths play an important role in mathematical modeling and image processing. Usually, shortest path problems are formulated on planar graphs that consist of vertices and weighted arcs. In this context, one is interested in finding a path of minimum weight from a start vertex to an end vertex. The concept of minimum-weight surfaces extends shortest paths to 3d. The minimum-weight surface problem is formulated on a cellular complex with weighted facets. A cycle on the arcs of the complex serves as input and one is interested in finding a surface of minimum weight bounded by that cycle. In practice, minimum-weight surfaces can be used to segment 3d images. Vice versa, it is possible to use them as a modeling tool for geometric structures such as cracks. In this work, we present an approach for using minimum-weight surfaces in bounded Voronoi diagrams to generate synthetic 3d images of cracks.
