Topology Repair of Solid Models Using Skeletons

1. Data structure For each minimal element in the OcTree, we give it a +/- sign to represent if it belongs to the object. Topology Repair of Solid Models Using Skeletons Qian-Yi Zhou1, Tao Ju2, Shi-Min Hu1 1 Computer Science and Technology Department, Tsinghua University 2 Department of Computer Science and Engineering Washington University in St. Louis Abstract Genus 75 Genus 17 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. Method overview Thinning To avoid introducing invalid geometry (e.g., self-intersections) as the result of topology repair, we represent an input model as an implicit volume. The surface of the model, represented as the iso-surface on the volume, partitions the volume into the object (e.g., interior) and the background (e.g., exterior). To remove surface handles, our method involves three conceptually simple steps: • Simple pairs : A N-D element contained in exactly one (N+1)-D element, removal of a simple pair does NOT change the topology of object • At each step of thinning, we remove a simple pair together. By iteratively peeling off the elements, we can reach a skeleton in the centre of the object. Thin Re- move Grow A thinning sequence • Thin the object into a skeleton that reserves the topology of the object. • Remove cycles in the skeleton by computing the spanning tree of the graph defined by the skeleton. • Grow the modified skeleton to form a new object that preserves the topology of the skeleton. Removing handles and growing Generating set: the minimum set so that V \W[e] is a cellular complex, and thinning V \W[e] yields Skeleton\{e}. The above steps can be applied to both the object and the background. When applied to the background, a cycle in the background skeleton corresponds to a tunnel-like handle on the original surface, and removing a skeleton cycle results in “filling” of the tunnel. Like cutting, filling is guaranteed not to introduce additional handles, and tunnels can be selectively filled based on their sizes. Removing handles: the skeleton consisting of edges and points can be regarded as a graph, with weight measuring the size of generating set for each edge. Generate the Maximum Spanning Tree of the graph. Growing: We simply subtract the generating sets associated with edges which is removed in the last step with a weight smaller than a user-given threshold. Experiment results Topology preserving contouring Perform Dual Contouring on a composite grid ˜G constructed by overlaying G with ˆG and the iso-surface (solid lines). In this way, the final mesh has the same topology as the volume. Algorithm details please refer to the paper. Models with complex topology: Removing handles on a mug with both an outside knot r1 and an inside knot complement h1 Paper and software Software available! Please visit website: http://graphics.usc.edu/~qianyizh/software.htm Paper download: Please visit website: http://graphics.usc.edu/~qianyizh/research.htm