This work presents a technique that allows quick conversion of acquired low-quality data from consumer-level scanning devices to high-quality 3D models with labeled semantic parts and meanwhile their assembly reasonably close to the underlying geometry. This is achieved by a novel structure recovery approach that is essentially local to global and bottom up, enabling the creation of new structures by assembling existing labeled parts with respect to the acquired data. We demonstrate that using only a small-scale shape repository, our part assembly approach is able to faithfully recover a variety of high-level structures from only a single-view scan of man-made objects acquired by the Kinect system, containing a highly noisy, incomplete 3D point cloud and a corresponding RGB image.

We present a method for repairing topological errors on solid models in the form of small surface handles, which often arise from surface reconstruction algorithms. We utilize a skeleton representation that offers a new mechanism for identifying and measuring handles. Our method presents two unique advantages over previous approaches. First, handle removal is guaranteed not to introduce invalid geometry or additional handles. Second, by using an adaptive grid structure, our method is capable of processing huge models efficiently at high resolutions.

Delaunay meshes (DM) are a special type of triangle mesh where the local Delaunay condition holds everywhere. We present an efficient algorithm to convert an arbitrary manifold triangle mesh M into a Delaunay mesh. We show that the constructed DM has O(Kn) vertices, where n is the number of vertices in M and K is a model-dependent constant. We also develop a novel algorithm to simplify Delaunay meshes, allowing a smooth choice of detail levels. Our methods are conceptually simple, theoretically sound and easy to implement. The DM construction algorithm also scales well due to its O(nK logK) time complexity. Delaunay meshes have many favorable geometric and numerical properties. For example, a DM has exactly the same geometry as the input mesh, and it can be encoded by any mesh data structure. Moreover, the empty geodesic circumcircle property implies that the commonly used cotangent Laplace-Beltrami operator has non-negative weights. Therefore, the existing digital geometry processing algorithms can benefit the numerical stability of DM without changing any codes. We observe that DMs can improve the accuracy of the heat method for computing geodesic distances. Also, popular parameterization techniques, such as discrete harmonic mapping, produce more stable results on the DMs than on the input meshes.

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