Scale-based fuzzy connectivity: a novel image segmentation methodology and its validation

This paper extends a previously reported theory and algorithms for fuzzy connected object definition. It introduces "object scale" for determining the neighborhood size for defining affinity, the degree of local hanging togetherness between image elements. Object scale allows us to use a varying neighborhood size in different parts of the image. This paper argues that scale-based fuzzy connectivity is natural in object definition and demonstrates that this leads to a more effective object segmentation than without using scale in fuzzy connectedness. Affinity is described as consisting of a homogeneity-based and an object-feature-based component. Families of non scale-based and scale-based affinity relations are constructed. An effective method for giving a rough estimate of scale at different locations in the image is presented. The original theoretical and algorithmic framework remains more-or-less the same but considerably improved segmentations result. A quantitative statistical comparison between the non scale-based and the scale-based methods was made based on phantom images generated from patient MR brain studies by first segmenting the objects, and then by adding noise and blurring, and background component. Both the statistical and the subjective tests clearly indicate the superiority of scale-based method in capturing details and in robustness to noise.