Computing skeleton-based handle/tunnel loops

Abstract

Finding surface loops around narrow sections of a surface is widely used as a prepossessing step in various applications such as segmentation, shape analysis, path planning, and robotics. A common approach to locating such loops is based on surface topology. However, such geodesic loops also exist on topologically trivial genus-0 surfaces, where all such loops can continuously deform to a point. While a few existing 3D geometry-aware topological approaches may succeed in detecting such additional narrow loops, their construction can be cumbersome. To extend beyond the limitations of topologically nontrivial independent loops while remaining efficient, we propose a novel approach that leverages the shape’s skeleton for computing surface loops of handle or tunnel type. Given a closed surface mesh, our algorithm produces a practically comprehensive set of loops encircling narrow regions of the volume inside or outside the surface. Notably, our approach streamlines and expedites computations by accepting a skeleton, a 1D representation of the shape, as part of the input. Specifically, handle-type loops are discovered by examining a small subset of the skeleton points as candidate loop centers, while tunnel-type loops are identified by examining only the high-valence skeleton points.