Image segmentation and robust estimation using Parzen windows

This thesis explores the use of Parzen windows for modeling image data. The validity of such a model is shown to follow naturally from the elementary Gestalt laws of vicinity, similarity, and continuity of direction. Consistency results are derived for Parzen window estimators, both for continuous-time and discrete-time images. The problem of scale is addressed; A novel plug-in estimator is proposed for the bandwidth (scale) of the window kernels. Asymptotic optimality of the proposed bandwidth is proved. The bandwidth selection scheme is validated for segmentation of real images. The density estimation framework is extended to model more structured images, e.g., those containing structures representable using local or global linear parametric models. Algorithms for robust parameter estimation and segmentation are given. Convergence results are derived for these algorithms. The robust parameter estimation framework is then extended to the problem of registering images of an object undergoing 2-D motion, overall image alignment (camera motion), and partial image alignment (2-D object tracking). For this purpose, novel estimation measures have been proposed. Algorithms have been proposed for the above tasks, and convergence of these algorithms have been proved. All proposed algorithms have been validated on real data.