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, nonstationary 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 multimodal 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 multimodal 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.