Figure 1: Non-parallel cross-section curves delineating a developing chicken heart from a CT volume (a) and the reconstructed surfaces using the method of Lu et al. [2008] (b), method of Bermano et al. [2011, and our method with genus-1 constraint without utilizing the CT volume (d). The first two surfaces contain numerous topological tunnels, while ours correctly captures the shell-like shape of the object. AbstractIn this work we detail the first algorithm that provides topological control during surface reconstruction from an input set of planar cross-sections. Our work has broad application in a number of fields including surface modeling and biomedical image analysis, where surfaces of known topology must be recovered. Given curves on arbitrarily oriented cross-sections, our method produces a manifold interpolating surface that exactly matches a user-specified genus. The key insight behind our approach is to formulate the topological search as a divide-and-conquer optimization process which scores local sets of topologies and combines them to satisfy the global topology constraint. We further extend our method to allow image data to guide the topological search, achieving even better results than relying on the curves alone. By simultaneously satisfying both geometric and topological constraints, we are able to produce accurate reconstructions with fewer input cross-sections, hence reducing the manual time needed to extract the desired shape.

No abstract

Figure 1: A curve network (misc2) representing a genus-7 mechanical part (left), cycles found by our algorithm (middle), and surface patches generated from the cycles (right). The curve network contains 410 curves. Our algorithm completed in half a second. AbstractGenerating surfaces from 3D curve networks has been a longstanding problem in computer graphics. Recent attention to this area has resurfaced as a result of new sketch based modeling systems. In this work we present a new algorithm for finding cycles that bound surface patches. Unlike prior art in this area, the output of our technique is unrestricted, generating both manifold and nonmanifold geometry with arbitrary genus. The novel insight behind our method is to formulate our problem as finding local mappings at the vertices and curves of our network, where each mapping describes how incident curves are grouped into cycles. This approach lends us the efficiency necessary to present our system in an interactive design modeler, whereby the user can adjust patch constraints and change the manifold properties of curves while the system automatically re-optimizes the solution.

in St. Louis for sampling distinct topologies in this space. Besides specifying topological constraints, the user can steer the algorithm interactively, such as by scribbling. We demonstrate, on synthetic and biological shapes, how our algorithm opens up new opportunities for topology-aware modeling in the multi-labeled context.

No abstract