Regression based Bandwidth Selection for Segmentation using Parzen Windows

We consider the problem of segmentation of images that can be modelled as piecewise continuous signals having unknown, non-stationary statistics. We propose a solution to this problem which first uses a regression framework to estimate the image PDF, and then mean-shift to find the modes of this PDF. The segmentation follows from mode identification wherein pixel clusters or image segments are identified with unique modes of the multi-modal PDF. Each pixel is mapped to a mode using a convergent, iterative process. The effectiveness of the approach depends upon the accuracy of the (implicit) estimate of the underlying multi-modal density function and thus on the bandwidth parameters used for its estimate using Parzen windows. Automatic selection of bandwidth parameters is a desired feature of the algorithm. We show that the proposed regression-based model admits a realistic framework to automatically choose bandwidth parameters which minimizes a global error criterion. We validate the theory presented with results on real images.