Nonrigid Image Registration

Image registration is the process of determining correspondence between all points in two images of the same scene. Image analysis applications that involve two or more images of a scene often require registration of the images. Nonrigid image registration refers to a class of methods where the images to be registered have nonlinear geometric differences. Image registration has a long history. One of the first examples of image registration appeared in the work of Roberts [33]. By aligning projections of edges of polyhedral solids with image edges, he was able to locate and recognize predefined polyhedral objects in images. Registration of entire images first appeared in the remote sensing literature. Anuta [1, 2] and Barnea and Silverman [8] developed automatic methods for registering satellite images using the sum of absolute differences as the similarity measure. Leese et al. [20] and Pratt [31] did the same using cross-correlation coefficient as the similarity measure. Use of image registration in computation of depth was initially pursued by Julesz [19], and then by Bakis and Langley [7], Mori et al. [27], Levine et al. [22], and Nevatia [28]. Image registration found its way to biomedical image analysis as data from various scanners that measure anatomy and function became digitally available [6, 37, 39]. Fischler and Elschlager [15] were among the first to use nonrigid registration to locate deformable objects such as human faces in images. Burr [11] later recognized handwritten characters by nonrigid registration. Bajcsy and Broit [4] developed a nonrigid registration method that could align deformed images in their entirety. In medical imaging, nonrigid registration was initially used to standardize MR and CT brain images with respect to an atlas [5, 9]. Most nonrigid image registration methods are iterative and minimize a cost or an energy function, defined in terms of the geometric and/or intensity difference between images. A smaller number of methods are based on matched feature points and use nonlinear transformation functions to align the images. The paper by Cachier et al. [12] in this issue classifies various nonrigid image registration methods. Further surveys and classifications of image registration methods can be found in papers by Gerlot and Bizais [18], Brown [10], van den Elsen et al. [38], Maurer and Fitzpatrick [26], Maintz and Viergever [25], and Lester and Arridge [21]. Most work on nonrigid registration has used medical images, and in particular brain images. The brain is of tremendous interest because of many applications in neuroscience and neurosurgery, presenting many unique challenges. Nonrigid registration of the brain is a difficult task but has many important applications including comparison of shape and function between individuals or groups [17], development of probabilistic models and atlases [23], measurement of change within an individual, and determination of location with respect to a preacquired image during stereotactic surgery [34]. The detailed nonrigid registration and comparison of brain images requires the determination of correspondence throughout the brain and the transformation of one image space with respect to another according to the correspondences. There are three types of deformation which need to be accounted for in nonrigid brain image registration: 1) change within an individual’s brain due to growth, surgery, or disease; 2) differences between individuals; and 3) warping due to image distortion, such as in echo-planar magnetic resonance imaging. Deformations of type 1 represent an individual’s brain changes during development, surgery, or degenerative process such as Alzheimer’s disease, multiple sclerosis, or malignant disease. In the cases of growth and degenerative disease, the deformation is incremental and likely to be representable in terms of relatively small and smooth transformations. During