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Discovering Structural Regularity In 3d Geometry

机译:在3d几何中发现结构规律

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We introduce a computational framework for discovering regular or repeated geometric structures in 3D shapes. We describe and classify possible regular structures and present an effective algorithm for detecting such repeated geometric patterns in point- or mesh-based models. Our method assumes no prior knowledge of the geometry or spatial location of the individual elements that define the pattern. Structure discovery is made possible by a careful analysis of pairwise similarity transformations that reveals prominent lattice structures in a suitable model of transformation space. We introduce an optimization method for detecting such uniform grids specifically designed to deal with outliers and missing elements. This yields a robust algorithm that successfully discovers complex regular structures amidst clutter, noise, and missing geometry. The accuracy of the extracted generating transformations is further improved using a novel simultaneous registration method in the spatial domain. We demonstrate the effectiveness of our algorithm on a variety of examples and show applications to compression, model repair, and geometry synthesis.
机译:我们介绍了一种计算框架,用于发现3D形状中的规则或重复几何结构。我们描述并分类了可能的规则结构,并提出了一种有效的算法来检测基于点或网格的模型中的此类重复几何图案。我们的方法假设没有先验知识,这些知识不知道定义图案的各个元素的几何形状或空间位置。通过对成对相似性转换的仔细分析,可以发现结构,从而在合适的转换空间模型中揭示突出的晶格结构。我们介绍了一种优化方法,用于检测专门设计用于处理异常值和缺失元素的均匀网格。这产生了一种鲁棒的算法,可以成功地在杂波,噪声和缺少的几何图形中发现复杂的规则结构。在空间域中使用新颖的同步配准方法可以进一步提高提取的生成转换的精度。我们在各种示例中证明了我们算法的有效性,并展示了其在压缩,模型修复和几何综合中的应用。

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