Book excerpt: A companion to the Insight Toolkit An introduction to the theory of modern medical image processing, including the analysis of data from - X-ray computer tomography, - magnetic resonance imaging, - nuclear medicine, - and ultrasound. Using an algorithmic approach, and providing the mathematical, statistical, or signal processing as needed for background, the authors describe the principles of all methods implemented in the Insight Toolkit (ITK), a freely available, open- source, object-oriented library. The emphasis is on providing intuitive descriptions of the principles and illustrative examples of results from the leading filtering, segmentation, and registration methods. This book covers the mathematical foundations of important techniques such as: - Statistical pattern recognition, - PDE-based nonlinear image filtering, - Markov random fields, - Level set methods, - Deformable models, - Mutual information, image-based registration - Non-rigid image data fusion With contributions from: Elsa Angelini, Brian Avants, Stephen Aylward, Ting Chen, Jeffrey Duda, Jim Gee, Luis Ibanez, Celina Imielinska, Yinpeng Jin, Jisung Kim, Bill Lorensen, Dimitris Metaxas, Lydia Ng, Punam Saha, George Stetten, Tessa Sundaram, Jay Udupa, Ross Whitaker, Terry Yoo, and Ying Zhuge. The Insight Toolkit is part of the Visible Human Project from the National Library of Medicine, with support from NIDCR, NINDS, NIMH, NEI, NSF, TATRC, NCI, and NIDCD.