The Insight Toolkit is an open source library of software tools, created as part of the Visible Human Project from the National Library of Medicine, to expedite the tasks of filtering, segmenting, and registering medical images. This companion to the Insight Toolkit provides an introduction to the theory of medical image processing, including analysis of data from X-ray computer tomography, magnetic resonance imaging, nuclear medicine, and ultrsound. The focus is on principles, leaving the source code to be learned from the companion volume ITK Software Guide. Coverage includes the mathematical foundations of techniques such as statistical pattern recognition, PDE-based nonlinear image filtering, and Markov random fields, among others. Color plates are included