We present a new method for simplifying the topology of a 3D shape. Unlike existing methods that either remove all topological features or offer indirect control over the target topology, our method aims at exactly preserving the user-prescribed numbers of topological features of each type (e.g., components, handles, and voids), while making minimal geometric changes. Guided by persistent homology , our method removes features with low persistence by performing either cutting or filling. This is achieved by an algorithm for computing candidate cuts and fills that remove only low-persistence features, an efficient algorithm for selecting an optimal subset of candidates by computing a weighted independent set, and an iterative framework that alternates between candidate computation and selection. Our method is shown to be highly successful in achieving the prescribed topology on a large test suite involving many complex 3D shapes and target topologies.

Abstract Medial axis (MA) is a classical shape descriptor in graphics and vision. The practical utility of MA, however, is hampered by its sensitivity to boundary noise. To prune unwanted branches from MA, many definitions of significance measures over MA have been proposed. However, pruning MA using these measures often comes at the cost of shrinking desirable MA branches and losing shape features at fine scales. We propose a novel significance measure that addresses these shortcomings. Our measure is derived from a variational pruning process, where the goal is to find a connected subset of MA that includes as many points that are as parallel to the shape boundary as possible. We formulate our measure both in the continuous and discrete settings, and present an efficient algorithm on a discrete MA. We demonstrate on many examples that our measure is not only resistant to boundary noise but also excels over existing measures in preventing MA shrinking and recovering features across scales.