Abstract
This paper proposes a new method to split images into regions. It consists of two subsystems: cluster detection and cluster fusion. A competitive neural network or the k-means algorithm, followed by an algorithm, which obtains connected clusters, performs the cluster detection. The cluster fusion involves a procedure that is based on the theory of equivalence relations. Proofs are given for the significant properties that we have found. It is not necessary to specify the number of regions in advance, which is a significant improvement over the standard competitive-style strategies. Finally, simulation results are given to demonstrate the performance of this method for some images.