Contextual Variance Clustering

This work was supported by a fellowship from the Belgium National Council at the Laboratory for Medical Imaging Research ESAT-Radiology

From a set of monodimensionnal data (grey levels of pixels), we want to define clusters without any supervision.

This leads to search modes in the histogram. However, when two underlying distributions are too strongly mixed, they result in one single mode. As we work on images we add a contextual hypothesis to improve the discrimination between mixed distributions.

Hyp. : A pixel belong to the same class as its neighbors

This hypothesis is obviously true except along edges. Consider the grey level set. Some intervals correspond to well defined classes and between these intervals, we have some transition areas . If a grey value corresponds to a well defined class, the set of neighbors of pixels having this grey value are samples of the underlying distribution. The variance of this set is then an estimator of the distribution variance. Consider now a grey value corresponding to a transition areas between two classes. The set of neighbors of pixels having this grey value are samples of a mixture between the two classes. Then the variance of this set is greater than the variance of both classes. We compute the variance of this set for each grey level and detect the picks corresponding to the "frontiers" between the classes using a Scale Space Analysis.

As an exemple, consider the histogram of two strongly mixed Gaussians :