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 ℓ0gradient minimization problem. To solve this problem efficiently, we adopt a coarse-to-fine strategy. A fast heuristic algorithm is first 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.

3D printers have become popular in recent years and enable fabrication of custom objects for home users. However, the cost of the material used in printing remains high. In this paper, we present an automatic solution to design a skin-frame structure for the purpose of reducing the material cost in printing a given 3D object. The frame structure is designed by an optimization scheme which significantly reduces material volume and is guaranteed to be physically stable, geometrically approximate, and printable. Furthermore, the number of struts is minimized by solving an l 0 sparsity optimization. We formulate it as a multi-objective programming problem and an iterative extension of the preemptive algorithm is developed to find a compromise solution. We demonstrate the applicability and practicability of our solution by printing various objects using both powder-type and extrusion-type 3D printers. Our method is shown to be more cost-effective than previous works.