Vectorial scale-based fuzzy-connected image segmentation

This paper presents an extension of previously published theory and algorithms for fuzzy-connected image segmentation. In this approach, a strength of connectedness is assigned to every pair of image elements. This is done by finding the strongest among 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. A scale is determined at every element in the image that indicates the size of the largest homogeneous hyperball region centered at the element. In determining affinity between any two elements, all elements within their scale regions are considered. This method has been effectively utilized in several medical applications. In this paper, we generalize this method from scalar images to vectorial images. In a vectorial image, scale is defined as the radius of the largest hyperball contained in the same homogeneous region under a predefined condition of homogeneity of the image vector field. Two different components of affinity, namely homogeneity-based affinity and object-feature-based affinity, are devised in a fully vectorial manner. The original relative fuzzy connectedness algorithm is utilized to delineate a specified object via a competing strategy among multiple objects. We have presented several studies to evaluate the performance of this method based on simulated MR images, 20 clinical MR images, and 250 mathematical phantom images. These studies indicate that the fully vectorial fuzzy connectedness formulation has generally overall better accuracy than the method using some intermediate ad hoc steps to fit the vectorial image to a scalar fuzzy connectedness formulation, and precision and efficiency are similar for these two methods.