三维沃罗诺伊图中基于最小权曲面的裂纹建模
Crack Modeling via Minimum-Weight Surfaces in 3d Voronoi Diagrams
摘要：
最短路径在数学建模和图像处理中起着重要的作用。通常，最短路问题是在由顶点和带权弧组成的平面图上进行求解的。在这种情况下，人们感兴趣的是找到一条从起始顶点到结束顶点的最小权重路径。最小权曲面的概念将最短路径扩展到3d。最小重量表面问题制定的细胞复杂的加权方面。一个循环的弧的复杂的作为输入和一个感兴趣的是找到一个表面的最小重量所界定的循环。在实践中，最小权重表面可以用来分割3d图像。反之亦然，它是可以使用它们作为几何结构，如裂缝的建模工具。在这项工作中，我们提出了一种方法，使用最小重量的表面有界沃罗诺伊图生成合成的三维图像的裂缝。
英文摘要：
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.
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