Region Merging with Topological Control

Abstract: This paper presents a region merging process controlled by topological features on regions in 3D images. Betti numbers, a well-known topological invariant, are used as criteria. Classical and incremental algorithms to compute Betti numbers using information represented by the topological map of an image are provided. The region merging algorithm, which allows the merge of any number of connected components of regions together, is explained and its complexity is studied. A topological control of the merging process is implemented using Betti numbers to control the topology of an evolving 3D image partition. The interest of incremental approaches of Betti numbers computation is established by providing processing times comparison. A visual example showing the result of the algorithm and the impact of topological control is also given.

Keywords: Topological constraint; Betti numbers; Region merging; Topological map; Image processing