This paper presents a region merging process controlled by topological features on regions in three-dimensional (3D) images. Betti numbers, a well-known topological invariant, are used as criteria. Classical and incremental algorithms to compute the Betti numbers using information represented by the topological map of an image are provided. The region merging algorithm, which merges any number of connected components of regions together, is explained. A topological control of the merging process is implemented using Betti numbers to control the topology of an evolving 3D image partition. The interest in incremental approaches of the computation of Betti numbers is established by providing a processing time comparison. A visual example showing the result of the algorithm and the impact of topological control is also given. © 2009 Elsevier B.V. All rights reserved.
Dupas, A., & Damiand, G. (2009). Region merging with topological control. Discrete Applied Mathematics, 157(16), 3435–3446. https://doi.org/10.1016/j.dam.2009.04.005