Peer group image enhancement.

Peer group image processing identifies a "peer group" for each pixel and then replaces the pixel intensity with the average over the peer group. Two parameters provide direct control over which image features are selectively enhanced: area (number of pixels in the feature) and window diameter (window size needed to enclose the feature). A discussion is given of how these parameters determine which features in the image are smoothed or preserved. We show that the Fisher discriminant can be used to automatically adjust the peer group averaging (PGA) parameters at each point in the image. This local parameter selection allows smoothing over uniform regions while preserving features like corners and edges. This adaptive procedure extends to multilevel and color forms of PGA. Comparisons are made with a variety of standard filtering techniques and an analysis is given of computational complexity and convergence issues.

Variational image segmentation using boundary functions.

A general variational framework for image approximation and segmentation is introduced. By using a continuous "line-process" to represent edge boundaries, it is possible to formulate a variational theory of image segmentation and approximation in which the boundary function has a simple explicit form in terms of the approximation function. At the same time, this variational framework is general enough to include the most commonly used objective functions. Application is made to Mumford-Shah type functionals as well as those considered by Geman and others. Employing arbitrary Lp norms to measure smoothness and approximation allows the user to alternate between a least squares approach and one based on total variation, depending on the needs of a particular image. Since the optimal boundary function that minimizes the associated objective functional for a given approximation function can be found explicitly, the objective functional can be expressed in a reduced form that depends only on the approximating function. From this a partial differential equation (PDE) descent method, aimed at minimizing the objective functional, is derived. The method is fast and produces excellent results as illustrated by a number of real and synthetic image problems.