Robust optimization for topological surface reconstruction
Robust optimization for topological surface reconstruction
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DOI：
10.1145/3197517.3201348
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发表时间：
2018-07
期刊：
影响因子：
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通讯作者：
R. Lazar;Nadav Dym;Y. Kushinsky;Zhiyang Huang;T. Ju;Y. Lipman
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文献类型：
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作者：
R. Lazar;Nadav Dym;Y. Kushinsky;Zhiyang Huang;T. Ju;Y. Lipman
曲面重建是计算机图形学的核心问题之一。对该问题的现有研究主要集中在改进重建的几何方面（例如，平滑度、特征、元件质量等），并且很少注意确保它也具有期望的拓扑性质（例如，连通性和属）。提出了一种新的拓扑约束下曲面重构的通用优化方法。我们的方法的输入是一个规定的属的重建表面，一个分区的环境体积到细胞，和一组可能的表面候选人和他们在每个细胞内的相关能量。我们的方法计算每个细胞的一个候选人，使他们的工会是一个连接的表面与规定的亏格，最大限度地减少总能量。我们制定的任务作为一个整数规划，并提出了一种新的解决方案，结合凸松弛内的分支和绑定框架。由于我们的方法不考虑输入细胞的类型，表面候选者和能量，因此它可以应用于各种重建场景，我们将在本文中探索其中两种：从横截面切片重建和等值面强度体积。在第一种情况下，我们的方法优于现有的拓扑感知方法，特别是对于复杂的输入和更高的属约束。在第二种情况下，我们展示了经典的拓扑无关的方法，如行军立方体的拓扑控制的好处。
Surface reconstruction is one of the central problems in computer graphics. Existing research on this problem has primarily focused on improving the geometric aspects of the reconstruction (e.g., smoothness, features, element quality, etc.), and little attention has been paid to ensure it also has desired topological properties (e.g., connectedness and genus). In this paper, we propose a novel and general optimization method for surface reconstruction under topological constraints. The input to our method is a prescribed genus for the reconstructed surface, a partition of the ambient volume into cells, and a set of possible surface candidates and their associated energy within each cell. Our method computes one candidate per cell so that their union is a connected surface with the prescribed genus that minimizes the total energy. We formulate the task as an integer program, and propose a novel solution that combines convex relaxations within a branch and bound framework. As our method is oblivious of the type of input cells, surface candidates, and energy, it can be applied to a variety of reconstruction scenarios, and we explore two of them in the paper: reconstruction from cross-section slices and iso-surfacing an intensity volume. In the first scenario, our method outperforms an existing topology-aware method particularly for complex inputs and higher genus constraints. In the second scenario, we demonstrate the benefit of topology control over classical topology-oblivious methods such as Marching Cubes.