Descending Variance Graphs for Segmenting Neurological Structures

We present a novel and relatively simple method for clustering pixels into homogeneous patches using a directed graph of edges between neighboring pixels. For a 2D image, the mean and variance of image intensity is computed within a circular region centered at each pixel. Each pixel stores its circle's mean and variance, and forms the node in a graph, with possible edges to its 4 immediate neighbors. If at least one of those neighbors has a lower variance than itself, a directed edge is formed, pointing to the neighbor with the lowest variance. Local minima in variance thus form the roots of disjoint trees, representing patches of relative homogeneity. The method works in n-dimensions and requires only a single parameter: the radius of the circular (spherical, or hyper spherical) regions used to compute variance around each pixel. Setting the intensity of all pixels within a given patch to the mean at its root pixel significantly reduces image noise while preserving anatomical structure, including location of boundaries. The patches may themselves be clustered using techniques that would be computationally too expensive if applied to the raw pixels. We demonstrate such clustering to identify fascicles in the median nerve in high-resolution 2D ultrasound images, as well as white matter hyper intensities in 3D magnetic resonance images.