On Genuine Connectivity Relations Based on Logical Predicates

This paper introduces a framework for the generation of genuine connectivity relations whose equivalent classes (called connected components) define unique partitions of the definition domain of a given grey tone image. This framework exploits the total ordering relation between the alpha-connected components of a pixel (two pixels are alpha-connected if there exists at least one path joining them such that the intensity differences between successive pixels of this path does not exceed a threshold value equal to alpha). Genuine connectivity relations are then obtained by considering the largest alpha-connected components satisfying one or more logical predicates such as the variance of the intensity values of the alpha-connected components not exceeding a given threshold value. Fine to coarse hierarchy partitions are generated by carefully varying the input threshold values. The proposed framework has the striking property of uniqueness. That is, the results do not depend on pixel processing order and are fully defined by the values of the threshold values, in contrast to most region growing procedures.