Our goal is to develop automated methods for the segmentation of thr- dimensional biomedical images. Here, we describe the segmentation of c- focal microscopy images of bee brains (20 individuals) by registration to one or several atlas images. Registration is performed by a highly parallel imp- mentation of an entropy-based nonrigid registration algorithm using B-spline transformations. We present and evaluate different methods to solve the cor- spondence problem in atlas based registration. An image can be segmented by registering it to an individual atlas, an average atlas, or multiple atlases. When registering to multiple atlases, combining the individual segmentations into a ?nalsegmentationcanbeachievedbyatlasselection,ormulticlassi?erdecision fusion. Wedescribeallthesemethodsandevaluatethesegmentationaccuracies that they achieve by performing experiments with electronic phantoms as well as by comparing their outputs to a manual gold standard. The present work is focused on the mathematical and computational t- ory behind a technique for deformable image registration termed Hyperelastic Warping, and demonstration of the technique via applications in image regist- tion and strain measurement. The approach combines well-established prin- ples of nonlinear continuum mechanics with forces derived directly from thr- dimensional image data to achieve registration. The general approach does not require the de?nition of landmarks, ?ducials, or surfaces, although it can - commodate these if available. Representative problems demonstrate the robust and ?exible nature of the approach. Three-dimensional registration methods are introduced for registering MRI volumes of the pelvis and prostate. The chapter ?rst reviews the applications, xi xii Preface challenges, and previous methods of image registration in the prostate.

The Handbook of Mathematical Methods in Imaging provides a comprehensive treatment of the mathematical techniques used in imaging science. The material is grouped into two central themes, namely, Inverse Problems (Algorithmic Reconstruction) and Signal and Image Processing. Each section within the themes covers applications (modeling), mathematics, numerical methods (using a case example) and open questions. Written by experts in the area, the presentation is mathematically rigorous. The entries are cross-referenced for easy navigation through connected topics. Available in both print and electronic forms, the handbook is enhanced by more than 150 illustrations and an extended bibliography. It will benefit students, scientists and researchers in applied mathematics. Engineers and computer scientists working in imaging will also find this handbook useful.

Whenever images taken at different times, from different viewpoints, and/or by different sensors need to be compared, merged, or integrated, image registration is required. Registration, also known as alignment, fusion, or warping, is the process of transforming data into a common reference frame. This book provides an overview of state-of-the-art registration techniques from theory to practice, numerous exercises, and via a supplementary Web page, free access to FAIR.m, a package that is based on the MATLAB software environment.

This book constitutes the refereed proceedings of the 4th International Conference on Functional Imaging and Modeling of the Heart, FIMH 2007, held in Salt Lake City, UT, USA in June 2007. The contributions describe both experimental and computational studies and cover topics such as imaging and image analysis, cardiac electrophysiology, electro- and magnetocardiography, cardiac mechanics and clinical application, imaging and anatomical modeling.

This book contains eleven original and survey scientific research articles arose from presentations given by invited speakers at International Workshop on Image Processing and Inverse Problems, held in Beijing Computational Science Research Center, Beijing, China, April 21–24, 2018. The book was dedicated to Professor Raymond Chan on the occasion of his 60th birthday. The contents of the book cover topics including image reconstruction, image segmentation, image registration, inverse problems and so on. Deep learning, PDE, statistical theory based research methods and techniques were discussed. The state-of-the-art developments on mathematical analysis, advanced modeling, efficient algorithm and applications were presented. The collected papers in this book also give new research trends in deep learning and optimization for imaging science. It should be a good reference for researchers working on related problems, as well as for researchers working on computer vision and visualization, inverse problems, image processing and medical imaging.

This book constitutes the refereed proceedings of the 6th International Workshop on Biomedical Image Registration, WBIR 2014, held in London, UK, in July 2014. The 16 full papers and 8 poster papers included in this volume were carefully reviewed and selected from numerous submitted papers. The full papers are organized in the following topical sections: computational efficiency, model based regularisation, optimisation, reconstruction, interventional application and application specific measures of similarity.

This book constitutes the refereed proceedings of the 4th International Workshop on Biomedical Image Registration, WBIR 2010, held in Lübeck, Germany, in July 2010. The 17 revised full papers and 7 revised poster papers presented were carefully reviewed and selected for inclusion in the book. The papers cover all areas of biomedical image registration and are organized in topical sections on biomedical applications, evaluation, methods of registration, and model based registration.

Processing, Analyzing and Learning of Images, Shapes, and Forms: Part 2, Volume 20, surveys the contemporary developments relating to the analysis and learning of images, shapes and forms, covering mathematical models and quick computational techniques. Chapter cover Alternating Diffusion: A Geometric Approach for Sensor Fusion, Generating Structured TV-based Priors and Associated Primal-dual Methods, Graph-based Optimization Approaches for Machine Learning, Uncertainty Quantification and Networks, Extrinsic Shape Analysis from Boundary Representations, Efficient Numerical Methods for Gradient Flows and Phase-field Models, Recent Advances in Denoising of Manifold-Valued Images, Optimal Registration of Images, Surfaces and Shapes, and much more. Covers contemporary developments relating to the analysis and learning of images, shapes and forms Presents mathematical models and quick computational techniques relating to the topic Provides broad coverage, with sample chapters presenting content on Alternating Diffusion and Generating Structured TV-based Priors and Associated Primal-dual Methods

This book constitutes the refereed proceedings of the 5th International Workshop on Biomedical Image Registration, WBIR 2012, held in Nashville, Tennessee, USA, in July 2012. The 20 full papers and 11 poster papers included in this volume were carefully reviewed and selected from 44 submitted papers. They full papers are organized in the following topical sections: multiple image sets; brain; non-rigid anatomy; and frameworks and similarity measures.