Scale-Based Fuzzy Connected Image Segmentation: Theory, Algorithms, and Validation

This paper extends a previously reported theory and algorithms for object definition based on fuzzy connectedness. In this approach, a strength of connectedness is determined between every pair of image elements. This is done by considering all possible connecting paths between the two elements in each pair. The strength assigned to a particular path is defined as the weakest affinity between successive pairs of elements along the path. Affinity specifies the degree to which elements hang together locally in the image. Although the theory allowed any neighborhood size for affinity definition, it did not indicate how this was to be selected. By bringing object scale into the framework in this paper, not only the size of the neighborhood is specified but also it is allowed to change in different parts of the image. This paper argues that scale-based affinity, and hence connectedness, is natural in object definition and demonstrates that this leads to more effective object segmentation. The approach presented here considers affinity to consist of two components. The homogeneity-based component indicates the degree of affinity between image elements based on the homogeneity of their intensity properties. The object-feature-based component captures the degree of closeness of their intensity properties to some expected values of those properties for the object. A family of non-scale-based and scale-based affinity relations are constructed dictated by how we envisage the two components to characterize objects. A simple and 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. The method has been tested in several applications qualitatively. A quantitative statistical comparison between the non-scale-based and the scale-based methods was made based on 250 phantom images. These were generated from 10 patient MR brain studies by first segmenting the objects, then setting up appropriate intensity levels for the object and the background, and then by adding five different levels for each of noise and blurring and a fixed slow varying background component. Both the statistical and the subjective tests clearly indicate that the scale-based method is superior to the non-scale-based method in capturing details and in robustness to noise. It is also shown, based on these phantom images, that any (global) optimum threshold selection method will perform inferior to the fuzzy connectedness methods described in this paper.