Deformable Medical Image Registration: A Survey <s> D <s> The quantitative evaluation of optical flow algorithms by Barron et al. led to significant advances in the performance of optical flow methods. The challenges for optical flow today go beyond the datasets and evaluation methods proposed in that paper and center on problems associated with nonrigid motion, real sensor noise, complex natural scenes, and motion discontinuities. Our goal is to establish a new set of benchmarks and evaluation methods for the next generation of optical flow algorithms. To that end, we contribute four types of data to test different aspects of optical flow algorithms: sequences with nonrigid motion where the ground-truth flow is determined by tracking hidden fluorescent texture; realistic synthetic sequences; high frame-rate video used to study interpolation error; and modified stereo sequences of static scenes. In addition to the average angular error used in Barron et al., we compute the absolute flow endpoint error, measures for frame interpolation error, improved statistics, and flow accuracy at motion boundaries and in textureless regions. We evaluate the performance of several well-known methods on this data to establish the current state of the art. Our database is freely available on the Web together with scripts for scoring and publication of the results at http://vision.middlebury.edu/flow/. <s> BIB001 </s> Deformable Medical Image Registration: A Survey <s> D <s> 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, plus numerous exercises designed to enhance readers understanding of the principles and mechanisms of the described techniques. It also provides, via a supplementary Web page, free access to FAIR.m, a package that is based on the MATLAB software environment, which enables readers to experiment with the proposed algorithms and explore the presented examples in more depth. Written from an interdisciplinary point of view, this book will appeal to mathematicians who want to learn more about image registration, medical imaging professionals who want to know more about and explore available imaging techniques, and computer scientists and engineers who want to understand the numerical schemes behind the techniques. The book is also appropriate for use as a course text at the advanced graduate level. Contents: FAIR Listings; FAIR Examples; List of Figures; List of Tables; Preface; Chapter 1: Introduction; Chapter 2: FAIR Concepts; Chapter 3: Image Interpolation; Chapter 4: Transforming Images by Parameterized Transformations; Chapter 5: Landmark-Based Registration; Chapter 6: Parametric Image Registration; Chapter 7: Distance Measures; Chapter 8: Regularization; Chapter 9: Nonparametric Image Registration; Chapter 10: Outlook; Bibliography; Symbols, Acronyms, Index. <s> BIB002 </s> Deformable Medical Image Registration: A Survey <s> D <s> This book presents a thorough and detailed guide to image registration, outlining the principles and reviewing state-of-the-art tools and methods. The book begins by identifying the components of a general image registration system, and then describes the design of each component using various image analysis tools. The text reviews a vast array of tools and methods, not only describing the principles behind each tool and method, but also measuring and comparing their performances using synthetic and real data. Features: discusses similarity/dissimilarity measures, point detectors, feature extraction/selection and homogeneous/heterogeneous descriptors; examines robust estimators, point pattern matching algorithms, transformation functions, and image resampling and blending; covers principal axes methods, hierarchical methods, optimization-based methods, edge-based methods, model-based methods, and adaptive methods; includes a glossary, an extensive list of references, and an appendix on PCA. <s> BIB003
EFORMABLE registration  - BIB003 has been, along with organ segmentation, one of the main challenges in modern medical image analysis. The process consists of establishing spatial correspondences between different image acquisitions. The term deformable (as opposed to linear or global) is used to denote the fact that the observed signals are associated through a nonlinear dense transformation, or a spatially varying deformation model. In general, registration can be performed on two or more images. In this paper, we focus on registration methods that involve two images. One is usually referred to as the source or moving image, while the other is referred to as the target or fixed image. In this paper, the source image is denoted by , while the target image is denoted by . The two images are defined in the image domain and are related by a transformation . The goal of registration is to estimate the optimal transformation that optimizes an energy of the form  The previous objective function (1) comprises two terms. The first term, , quantifies the level of alignment between a target image and a source image . Throughout this paper, we interchangeably refer to this term as matching criterion, (dis)similarity criterion or distance measure. The optimization problem consists of either maximizing or minimizing the objective function depending on how the matching term is chosen. The images get aligned under the influence of transformation . The transformation is a mapping function of the domain to itself, that maps point locations to other locations. In general, the transformation is assumed to map homologous locations from the target physiology to the source physiology. The transformation at every position is given as the addition of an identity transformation with the displacement field , or . The second term, , regularizes the transformation aiming to favor any specific properties in the solution that the user requires, and seeks to tackle the difficulty associated with the ill-posedness of the problem. Regularization and deformation models are closely related. Two main aspects of this relation may be distinguished. First, in the case that the transformation is parametrized by a small number of variables and is inherently smooth, regularization may serve to introduce prior knowledge regarding the solution that we seek by imposing task-specific constraints on the transformation. Second, in the case that we seek the displacement of every image element (i.e., nonparametric deformation model), regularization dictates the nature of the transformation. Thus, an image registration algorithm involves three main components: 1) a deformation model, 2) an objective function, and 3) an optimization method. The result of the registration algorithm naturally depends on the deformation model and the objective function. The dependency of the registration result on the optimization strategy follows from the fact that image registration is inherently ill-posed. Devising each component so that the requirements of the registration algorithm are met is a demanding process. Depending on the deformation model and the input data, the problem may be ill-posed according to Hadamard's definition of well-posed problems  . In probably all realistic scenarios, registration is ill-posed. To further elaborate, let us consider some specific cases. In a deformable registration scenario, one seeks to estimate a vector for every position given, in general, scalar information conveyed by image intensity. In this case, the number of unknowns is greater than the number of constraints. In a rigid setting, let us consider a consider a scenario where two images of a disk (white background, gray foreground) are registered. Despite the fact that the number of parameters is only 6, the problem is ill-posed. The problem has no unique solution since a translation that aligns the centers of the disks followed by any rotation results in a meaningful solution. Given nonlinear and nonconvex objective functions, in general, no closed-form solutions exist to estimate the registration parameters. In this setting, the search methods reach only a local minimum in the parameter space. Moreover, the problem itself has an enormous number of different facets. The approach that one should take depends on the anatomical properties of the organ (for example, the heart and liver do not adhere to the same degree of deformation), the nature of observations to be registered (same modality versus multi-modal fusion), the clinical setting in which registration is to be used (e.g., offline interpretation versus computer assisted surgery). An enormous amount of research has been dedicated to deformable registration towards tackling these challenges due to its potential clinical impact. During the past few decades, many innovative ideas regarding the three main algorithmic registration aspects have been proposed. General reviews of the field may be found in  -  , BIB002 . However due to the rapid progress of the field such reviews are to a certain extent outdated. The aim of this paper is to provide a thorough overview of the advances of the past decade in deformable registration. Nevertheless, some classic papers that have greatly advanced the ideas in the field are mentioned. Even though our primary interest is deformable registration, for the completeness of the presentation, references to linear methods are included as many problems have been treated in this low-degree-of-freedom setting before being extended to the deformable case. The main scope of this paper is focused on applications that seek to establish spatial correspondences between medical images. Nonetheless, we have extended the scope to cover applications where the interest is to recover the apparent motion of objects between sequences of successive images (optical flow estimation)  , BIB001 . Deformable registration and optical flow estimation are closely related problems. Both problems aim to establish correspondences between images. In the deformable registration case, spatial correspondences are sought, while in the optical flow case, spatial correspondences, that are associated with different time points, are looked for. Given data with a good temporal resolution, one may assume that the magnitude of the motion is limited and that image intensity is preserved in time, optical flow estimation can be regarded as a small deformation mono-modal deformable registration problem. The remainder of the paper is organized by loosely following the structural separation of registration algorithms to three components: 1) deformation model, 2) matching criteria, and 3) optimization method. In Section II, different approaches regarding the deformation model are presented. Moreover, we also chose to cover in this section the second term of the objective function, the regularization term. This choice was motivated by the close relation between the two parts. In Section III, the first term of the objective function, the matching term, is discussed. The optimization methods are presented in Section IV. In every section, particular emphasis was put on further deepening the taxonomy of registration method by grouping the presented methods in a systematic manner. Section V concludes the paper.