This article surveys deformable models, a promising and vigorously researched computer-assisted medical image analysis technique. Among model-based techniques, deformable models offer a unique and powerful approach to image analysis that combines geometry, physics, and approximation theory. They have proven to be effective in segmenting, matching, and tracking anatomic structures by exploiting (bottom-up) constraints derived from the image data together with (top-down) a priori knowledge about the location, size, and shape of these structures. Deformable models are capable of accommodating the significant variability of biological structures over time and across different individuals. Furthermore, they support highly intuitive interaction mechanisms that, when necessary, allow medical scientists and practitioners to bring their expertise to bear on the model-based image interpretation task. This article reviews the rapidly expanding body of work on the development and application of deformable models to problems of fundamental importance in medical image analysis, includingsegmentation, shape representation, matching, and motion tracking.

The purpose of this chapter is to present a survey of recent publications concerning medical image registration techniques. These publications will be classified according to a model based on nine salient criteria, the main dichotomy of which is extrinsic versus intrinsic methods The statistics of the classification show definite trends in the evolving registration techniques, which will be discussed. At this moment, the bulk of interesting intrinsic methods is either based on segmented points or surfaces, or on techniques endeavoring to use the full information content of the images involved. Keywords: registration, matching Received May 25, 1997

The development of algorithms for the spatial transformation and registration of tomographic brain images is a key issue in several clinical and basic science medical applications, including computer aided neurosurgery, functional image analysis, and morphometrics. This paper describes a technique for the spatial transformation of brain images, which is based on elastically deformable models. A deformable surface algorithm is used to find a parametric representation of the outer cortical surface and then and then to define a map between corresponding cortical regions in two brain images. Based on the resulting map, a three-dimensional elastic warping transformation is then determined, which brings two images into register. This transformation models images as inhomogeneous elastic objects which are deformed into registration with each other by external force fields. The elastic properties of the images can vary from one region to the other, allowing more variable brain regions, such as...

Abstract. In this paper we introduce the concept of statistical deformation models (SDM) which allow the construction of average models of the anatomy and their variability. SDMs are build by performing a statistical analysis of the deformations required to map anatomical features in one subject into the corresponding features in another subject. The concept of SDMs is similar to active shape models (ASM) which capture statistical information about shapes across a population but offers several new advantages: Firstly, SDMs can be constructed directly from images such as MR or CT without the need for segmentation which is usually a prerequisite for the construction of active shape models. Instead a non-rigid registration algorithm is used to compute the deformations required to establish correspondences between the reference subject and the subjects in the population class under investigation. Secondly, SDMs allow the construction of an atlas of the average anatomy as well as its variability across a population of subjects. Finally, SDMs take the 3D nature of the underlying anatomy into account by analysing dense 3D deformation fields rather than only the 2D surface shape of anatomical structures. We demonstrate the applicability of this new framework to MR images of the brain and show results for the construction of anatomical models from 25 different subjects. 1

Objective. The spatial normalization and registration of tomographic images from different subjects is a major problem in several medical imaging areas, including functional image analysis, morphometrics, and computer aided neurosurgery. The focus of this paper is the development of a computerized methodology for the spatial normalization of 3D images. Materials and Methods. We propose a technique which is based on geometric deformable models. In particular, we first describe a deformable surface algorithm which finds a mathematical representation of the outer cortical surface. Based on this representation, a procedure for obtaining a map between corresponding regions of the outer cortex in two different images is established. This map is subsequently used to derive a three-dimensional elastic warping transformation, which brings two images in register. Results. The performance of our algorithm is demonstrated on several datasets. In particular, we first test our deformable surface a...

Statistical analysis of anatomical maps in a stereotaxic space has been shown to be a useful tool in population-based studies for quantifying local anatomical differences or changes, without a priori assumptions about the location and extent of the regions of interest. This paper presents an extension and validation of a previously published methodology, referred to as RAVENS, for characterizing regional atrophy in the brain. A new method for elastic, volume-preserving spatial normalization, which allows for accurate quantification of very localized atrophy, is used. The RAVENS methodology was tested on images with simulated atrophy within two gyri: precentral and superior temporal. It was found to accurately determine the regions of atrophy, despite their localized nature and the interindividual variability of cortical structures. Moreover, it was found to perform substantially better than the voxel-based morphology method of SPM’99. Improved sensitivity was achieved at the expense of human effort involved in defining a number of sulcal curves that serve as constraints on the 3D elastic warping. © 2001 Academic Press

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This manuscript tackles the registration of 2D biological images (histological sections or autoradiographs) to 2D images from the same or di#erent modalities (e.g., histology or MRI). The process of acquiring these images typically induces composite transformations that can be modeled as a number of rigid or a#ne local transformations embedded in an elastic one. We propose a registration approach closely derived from this model. Given a pair of input images, we first compute a dense similarity field between them with a block matching algorithm. A hierarchical clustering algorithm then automatically partitions this field into a number of classes from which we extract independent pairs of sub-images. Finally, the pairs of sub-images are, independently, a#nely registered and a hybrid a#ne/non-linear interpolation scheme is used to compose the output registered image. We investigate the behavior of our approach under a variety of conditions, and discuss examples using real biomedical images, including MRI, histology and cryosection data.

A key issue in several brain imaging applications, including computer aided neurosurgery, functional image analysis, and morphometrics, is the spatial normalization and registration of tomographic images from different subjects. This paper proposes a technique for spatial normalization of brain images based on elastically deformable models. In our approach we use a deformable surface algorithm to find a parametric representation of the outer cortical surface and then use this representation to obtain a map between corresponding regions of the outer cortex in two different images. Based on the resulting map we then derive a three-dimensional elastic warping transformation which brings two images in register. This transformation models images as inhomogeneous elastic objects which are deformed into registration with each other by external force fields. The elastic properties of the images can vary from one region to the other, allowing more variable brain regions, such as the ventricles,...

Nonrigid registration of medical images is important for a number of applications such as the creation of population averages, atlas-based segmentation, or geometric correction of functional magnetic resonance imaging (fMRI) images to name a few. In recent years, a number of methods have been proposed to solve this problem, one class of which involves maximizing a mutual information (MI)-based objective function over a regular grid of splines. This approach has produced good results but its computational complexity is proportional to the compliance of the transformation required to register the smallest structures in the image. Here, we propose a method that permits the spatial adaptation of the transformation’s compliance. This spatial adaptation allows us to reduce the number of degrees of freedom in the overall transformation, thus speeding up the process and improving its convergence properties. To develop this method, we introduce several novelties: 1) we rely on radially symmetric basis functions rather than B-splines traditionally used to model the deformation field; 2) we propose a metric to identify regions that are poorly registered and over which the transformation needs to be improved; 3) we partition the global registration problem into several smaller ones; and 4) we introduce a new constraint scheme that allows us to produce transformations that are topologically correct. We compare the approach we propose to more traditional ones and show that our new algorithm compares favorably to those in current use.