Topology-Constrained Surface Reconstruction From Cross-sections

摘要

In this work we detail the first algorithm that provides topologicalrncontrol during surface reconstruction from an input set of planarrncross-sections. Our work has broad application in a numberrnof fields including surface modeling and biomedical image analysis,rnwhere surfaces of known topology must be recovered. Givenrncurves on arbitrarily oriented cross-sections, our method produces arnmanifold interpolating surface that exactly matches a user-specifiedrngenus. The key insight behind our approach is to formulate therntopological search as a divide-and-conquer optimization processrnwhich scores local sets of topologies and combines them to satisfyrnthe global topology constraint. We further extend our methodrnto allow image data to guide the topological search, achieving evenrnbetter results than relying on the curves alone. By simultaneouslyrnsatisfying both geometric and topological constraints, we are ablernto produce accurate reconstructions with fewer input cross-sections,rnhence reducing the manual time needed to extract the desired shape.