Statistical and structural methods are two major approaches commonly used in image analysis and have demonstrated considerable success. The former is based on statistical properties and stochastic models of the image and the latter utilizes geometric and topological models. In this study, Markov random field (MRF) theory/model based image segmentation and Fuzzy Connectedness (FC) theory/Fuzzy connected objeect delineation are chosen as the representatives for these two approaches, respectively. The comparative study is focused on their theoretical foundations and main operative procedures.
The MRF is defined on a lattice and the associated neighborhood system and is based on the Markov property. The FC method is defined on a fuzzy digital space and is based on fuzzy relations. Locally, MRF is characterized by potentials of cliques, and FC is described by fuzzy adjacency and affinity relations. Globally, MRF is characterized by Gibbs distribution, and FC is described by fuzzy connectedness. The task of MRF model based image segmentation is toe seek a realization of the embedded MRF through a two-level operation: partitioning and labeling. The task of FC object delineation is to extract a fuzzy object from a given scene, through a two-step operation: recognition and delineation.
Theoretical foundations which underly statistical and structural approaches and the principles of the main operative procedures in image segmentation by these two approaches demonstrate more similarities than differences between them. Two approaches can also complement each other, particularly in seed selection, scale formation, affinity and object membership function design for FC and neighbor set selection and clique potential design for MRF.