In the domain of point cloud registration, the coarse-to-fine feature matching paradigm has received significant attention due to its impressive performance. This paradigm involves a two-step process: first, the extraction of multi-level features, and subsequently, the propagation of correspondences from coarse to fine levels. However, this approach faces two notable limitations. Firstly, the use of the Dual Softmax operation may promote one-to-one correspondences between superpoints, inadvertently excluding valuable correspondences. Secondly, it is crucial to closely examine the overlapping areas between point clouds, as only correspondences within these regions decisively determine the actual transformation. Considering these issues, we propose OAAFormer to enhance correspondence quality. On the one hand, we introduce a soft matching mechanism to facilitate the propagation of potentially valuable correspondences from coarse to fine levels. On the other hand, we integrate an overlapping region detection module to minimize mismatches to the greatest extent possible. Furthermore, we introduce a region-wise attention module with linear complexity during the fine-level matching phase, designed to enhance the discriminative capabilities of the extracted features. Tests on the challenging 3DLoMatch benchmark demonstrate that our approach leads to a substantial increase of about 7% in the inlier ratio, as well as an enhancement of 2%–4% in registration recall. Finally, to accelerate the prediction process, we replace the Conventional Random Sample Consensus (RANSAC) algorithm with the selection of a limited yet representative set of high-confidence correspondences, resulting in a 100 times speedup while still maintaining comparable registration performance.

Voronoi diagrams on triangulated surfaces based on the geodesic metric play a key role in many applications of computer graphics. Previous methods of constructing such Voronoi diagrams generally depended on having an exact geodesic metric. However, exact geodesic computation is time-consuming and has high memory usage, limiting wider application of geodesic Voronoi diagrams (GVDs). In order to overcome this issue, instead of using exact methods, we reformulate a graph method based on Steiner point insertion, as an effective way to obtain geodesic distances. Further, since a bisector comprises hyperbolic and line segments, we utilize Apollonius diagrams to encode complicated structures, enabling Voronoi diagrams to encode a medial-axis surface for a dense set of boundary samples. Based on these strategies, we present an approximation algorithm for efficient Voronoi diagram construction on triangulated surfaces. We also suggest a measure for evaluating similarity of our results to the exact GVD. Although our GVD results are constructed using approximate geodesic distances, we can get GVD results similar to exact results by inserting Steiner points on triangle edges. Experimental results on many 3D models indicate the improved speed and memory requirements compared to previous leading methods.

We present a simple yet effective method for constructing 3D self-supporting surfaces with planar quadrilateral (PQ) elements. Starting with a triangular discretization of a self-supporting surface, we firstcompute the principal curvatures and directions of each triangular face using a new discrete differential geometryapproach, yielding more accurate results than existing methods. Then, we smooth the principal direction field to reduce the number of singularities. Next, we partition all faces into two groups in terms of principalcurvature difference. For each face with small curvature difference, we compute a stretch matrix that turns the principal directions into a pair of conjugate directions. For the remaining triangular faces, we simply keep their smoothed principal directions. Finally, applying a mixed-integer programming solver to the mixed principal and conjugate direction field, we obtain a planar quadrilateral mesh. Experimental results show that our method is computationally efficient and can yield high-quality PQ meshes that well approximate the geometry of the input surfaces and maintain their self-supporting properties.