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

Abstract. This paper presents a new method for determining the minimal non-rigid deformation between two 3-D surfaces, such as those which describe anatomical structures in 3-D medical images. Although we match surfaces, we represent the deformation as a volumetric transformation. Our method performs a least squares minimization of the distance between the two surfaces of interest. To quickly and accurately compute distances between points on the two surfaces, we use a precomputed distance map represented using an octree spline whose resolution increases near the surface. To quickly and robustly compute the deformation, we use a second octree spline to model the deformation function. The coarsest level of the deformation encodes the global (e.g., affine) transformation between the two surfaces, while finer levels encode smooth local displacements which bring the two surfaces into closer registration. We present experimental results on both synthetic and real 3-D surfaces. 1.

There is a need for frameless guidance systems to help surgeons plan the exact location for incisions, to define the margins of tumors and to precisely identify locations of neighboring critical structures. We have developed an automatic technique for registering clinical data, such as segmented MRI or CT reconstructions, with any view of the patient on the operating table, using a series of registration algorithms, which we demonstrate on the specific example of neurosurgery. The method enables a visual mix of live video of the patient with the segmented 3D MRI or CT model, supporting enhanced reality techniques for planning and guiding neurosurgical procedures, and to interactively view extracranial or intracranial structures non-intrusively. Extensions of the method include image guided biopsies, focused therapeutic procedures and clinical studies involving change detection over time sequences of images. 1 Artificial Intelligence Laboratory, Massachusetts Institute of Tech...

In this paper, we propose and analyze several methods to estimate a rigid transformation from a set of 3-D matched points or matched frames, which are important features in geometric algorithms. We also develop tools to predict and verify the accuracy of these estimations. The theoretical contributions are: an intrinsic model of noise for transformations based on composition rather than addition; a unified formalism for the estimation of both the rigid transformation and its covariance matrix for points or frames correspondences, and a statistical validation method to verify the error estimation, which applies even when no "ground truth" is available. We analyze and demonstrate on synthetic data that our scheme is well behaved. The practical contribution of the paper is the validation of our transformation estimation method in the case of 3-D medical images, which shows that an accuracy of the registration far below the size of a voxel can be achieved, and in the case of protein substructure matching, where frame features drastically improve both selectivity and complexity. 1.

We consider elastic registration of medical image data based on thin-plate splines using a set of corresponding anatomical point landmarks. Previous work on this topic has concentrated on using interpolation schemes. Such schemes force the corresponding landmarks to exactly match each other and assume that the landmark positions are known exactly. However, in real applications the localization of landmarks is always prone to some error. Therefore, to take into account these localization errors, we have investigated the application of an approximation scheme which is based on regularization theory. This approach generally leads to a more accurate and robust registration result. In particular, outliers do not disturb the registration result as much as is the case with an interpolation scheme. Also, it is possible to individually weight the landmarks according to their localization uncertainty. In addition to this study, we report on investigations into semi-automatic extraction of anat...

This paper presents a literature survey of automatic 3D surface registration techniques emphasizing the mathematical and algorithmic underpinnings of the subject. The relevance of surface registration to medical imaging is that there is much useful anatomical information in the form of collected surface points which originate from complimentary modalities and which must be reconciled. Surface registration

This paper describes a method to automatically generate the mapping between a completely labeled reference image and the 3D medical image of a patient. Toachieve this, we combined three techniques: the extraction of 3D feature lines, their matching using 3D deformable line models, the extension of the deformation to the whole image space using warping techniques. We present experimental results for the segmentation of structures in Magnetic Resonance images of the brain of different patients; the segmentation of the cortical and ventricle structures. We emphasize the advantages of using crest lines deformable models prior to surface based models. This gives a sparser representation of the data, easier to manipulate, and which makes the convergence of the model much less sensitive to initial positionning. In the future, we hope to use this method to generate anatomical atlases, by the automatic interpretation of large sets of 3D medical images.

This paper introduces a new free-form surface representation scheme for the purpose of fast and accurate registration and matching. Accurate registration of surfaces is a common task in computer vision. The proposed representation scheme captures the surface curvature information, seen from certain points and produces images, called surface signatures, at these points. Matching signatures of di#erent surfaces enables the recovery of the transformation parameters between these surfaces. We propose to use template matching to compare the signature images. To enable partial matching, another criterion, the overlap ratio, is used. This representation scheme can beusedasa global representation of the surface as well as a local one and performs near real-time registration. We show that the signaturerepresentation can beusedtomatch objects in 3-D scenes in the presence of clutter and occlusion. Applications presented include free-form object matching, multimodal medical volumes registration and dental teeth reconstruction from intra-oral images. I

this paper we present an approach to localize semi-automatically landmarks characterized by extremal isocontour curvature. The semi-automatic approach implies that a rough estimate of the landmark position centered at a volume-of-interest is interactively provided by the user as an input. The algorithm then refines this position [10]. Monga and Benayoun [4] presented an approach to compute locally the curvature characteristics of isosurfaces. The gradient direction is used to define locally the tangent plane of the isosurface. Then a local parametrization is defined by setting up two arbitrary orthogonal vectors within this tangent plane. Given this parametrization they show how the principal curvatures of the isosurface and the associated principal directions can be computed. Additionally, they derive an extremality criterion based on the spatial derivative of the principal curvature in direction of the corresponding principal direction. Application of this extremality criterion in maximum curvature direction yields a 1D subset of points on the isosurface which they call ridge (or crest) lines. Thirion [6] proposed an algorithm to extract automatically isocontour curvature extrema, which he denoted extremal points, from 3D images and which then serve as input for a rigid registration algorithm. His algorithm basically uses the extremality criterion of Monga and Benayoun [4] in both principal curvature directions.