Manhattan-world urban scenes are common in the real world. We propose a fully automatic approach for reconstructing such scenes from 3D point samples. Our key idea is to represent the geometry of the buildings in the scene using a set of well-aligned boxes. We first extract plane hypothesis from the points followed by an iterative refinement step. Then, candidate boxes are obtained by partitioning the space of the point cloud into a non-uniform grid. After that, we choose an optimal subset of the candidate boxes to approximate the geometry of the buildings. The contribution of our work is that we transform scene reconstruction into a labeling problem that is solved based on a novel Markov Random Field formulation. Unlike previous methods designed for particular types of input point clouds, our method can obtain faithful reconstructions from a variety of data sources. Experiments demonstrate that our method is superior to state-of-the-art methods.

Non-rigid registration of 3D shapes is an essential task of increasing importance as commodity depth sensors become more widely available for scanning dynamic scenes. Non-rigid registration is much more challenging than rigid registration as it estimates a set of local transformations instead of a single global transformation, and hence is prone to the overfitting issue due to underdetermination. The common wisdom in previous methods is to impose an l2-norm regularization on the local transformation differences. However, the l2-norm regularization tends to bias the solution towards outliers and noise with heavy-tailed distribution, which is verified by the poor goodness- of-fit of the Gaussian distribution over transformation differences. On the contrary, Laplacian distribution fits well with the transformation differences, suggesting the use of a sparsity prior. We propose a sparse non-rigid registration (SNR) method with an l1-norm regularized model for transformation estimation, which is effectively solved by an alternate direction method (ADM) under the augmented Lagrangian framework. We also devise a multi-resolution scheme for robust and progressive registration. Results on both public datasets and our scanned datasets show the superiority of our method, particularly in handling large-scale deformations as well as outliers and noise.

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Intrinsic Delaunay triangulation (IDT) naturally generalizes Delaunay triangulation from R^2 to curved surfaces. Due to many favorable properties, the IDT whose vertex set includes all mesh vertices is of particular interest in polygonal mesh processing. To date, the only way for constructing such IDT is the edge-flipping algorithm, which iteratively flips non-Delaunay edges to become locally Delaunay. Although this algorithm is conceptually simple and guarantees to terminate in finite steps, it has no known time complexity and may also produce triangulations containing faces with only two edges. This article develops a new method to obtain proper IDTs on manifold triangle meshes.We first compute a geodesic Voronoi diagram (GVD) by taking all mesh vertices as generators and then find its dual graph. The sufficient condition for the dual graph to be a proper triangulation is that all Voronoi cells satisfy the so-called closed ball property. To guarantee the closed ball property everywhere, a certain sampling criterion is required. For Voronoi cells that violate the closed ball property, we fix them by computing topologically safe regions, inwhich auxiliary sites can be addedwithout changing the topology of theVoronoi diagram beyond them.Given a meshwith n vertices, we prove that by adding at most O(n) auxiliary sites, the computed GVD satisfies the closed ball property, and hence its dual graph is a proper IDT. Our method has a theoretical worst-case time complexity O(n^2 + tn log n), where t is the number of obtuse angles in the mesh. Computational results show that it empirically runs in linear time on real-world models.

In 3D printing, it is critical to use as few as possible supporting materials for efficiency and material saving. Multiple model decomposition methods and multi-DOF (degrees of freedom) 3D printers have been developed to address this issue. However, most systems utilize model decomposition and multi-DOF independently. Only a few existing approaches combine the two, i.e. partitioning the models for multi-DOF printing. In this paper, we present a novel model decomposition method for multidirectional 3D printing, allowing consistent printing with the least cost of supporting materials. Our method is based on a global optimization that minimizes the surface area to be supported for a 3D model. The printing sequence is determined inherently by minimizing a single global objective function. Experiments on various complex 3D models using a five-DOF 3D printer have demonstrated the effectiveness of our approach.