Mesh segmentation is a process of partitioning a mesh model into meaningful parts --- a fundamental problem in various disciplines. This paper introduces a novel mesh segmentation method inspired by sparsity pursuit. Based on the local geometric and topological information of a given mesh, we build a Laplacian matrix whose Fiedler vector is used to characterize the uniformity among elements of the same segment. By analyzing the Fiedler vector, we reformulate the mesh segmentation problem as a $\ell_0$ gradient minimization problem. To solve this problem efficiently, we adopt a coarse-to-fine strategy. A fast heuristic algorithm is firstly devised to find a rational coarse segmentation, and then an optimization algorithm based on the alternating direction method of multiplier (ADMM) is proposed to refine the segment boundaries within their local regions. To extract the inherent hierarchical structure of the given mesh, our method performs segmentation in a recursive way. Experimental results demonstrate that the presented method outperforms the state-of-the-art segmentation methods when evaluated on the Princeton Segmentation Benchmark, the LIFL/LIRIS Segmentation Benchmark and a number of other complex meshes.

中文翻译：

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通过10梯度最小化进行光谱网格分割。

网格分割是将网格模型划分为有意义的部分的过程，这是各个学科的基本问题。本文介绍了一种新的基于稀疏性追求的网格分割方法。基于给定网格的局部几何和拓扑信息，我们构建了一个拉普拉斯矩阵，该矩阵的Fiedler向量用于表征同一段元素之间的均匀性。通过分析Fiedler向量，我们将网格分割问题重新构造为$ \ ell_0 $梯度最小化问题。为了有效解决此问题，我们采用了从粗到精的策略。首先设计了一种快速启发式算法来找到合理的粗略分割，然后提出了一种基于乘法器交替方向法的优化算法，对局部区域内的边界进行细化。为了提取给定网格的固有层次结构，我们的方法以递归方式执行分段。实验结果表明，在普林斯顿分割基准，LIFL / LIRIS分割基准和许多其他复杂网格物体上进行评估时，所提出的方法优于最新的分割方法。