Segmenting Homogeneous Regions in Images using Variance Wells

Abstract

We present a method to identify small regions of relative homogeneity in an N-dimensional image based on local variance. We call these regions “variance wells” or “vWells,” because they surround and separate local minima in the variance of image intensity. VWells fall into a class of entities in computer vision known as “super-pixels,” generally irregularly shaped small homogenous regions that can be combined to segment ob-jects in the image while preserving sharp boundaries. Computing vWells requires no parameters and is not iterative, having a computation time proportional to the total number of pixels. The vWells in an image can form the nodes of a graph whose edges connect adjacent pairs of vWells. When using such a graph to cluster vWells for segmentation, similarity between adjacent vWells can be computed using well established statistical methods based on the mean and variance of the pixels within each vWell. We use such a graph of vWells to segment arteries in 2D MRI images of the brain by finding the optimal path between two manu-ally placed starting points, and then performing a region-growing algorithm to include adjacent vWells up to the vessel boundary. In this way, we demonstrate that vWells may form a useful preprocessing step to simplify data for further analysis by reducing noise and reducing the number of primitives compared to in-dividual pixels, while preserving boundaries. Our software implementation is available (see Appendix 1).