Y.F. Lam, D.F. Gillies, D. Rueckert, P. Charters, P. Groom, and S. Roughley (UK)

Generic Anatomical Modelling, Corresponding landmarks

Statistical shape models of bones are useful for a number of tasks, which include the study of anatomy and preoperative planning. In order to build statistical shape models of bones, it is necessary to have volumetric data sets in which the correspondence of the points on the surfaces of the bones is known. Anatomical landmarks can be chosen, and identified manually, but there are too few of them to define the geometry of the shape accurately. Previous work in modelling bony structures often uses feature-based registration. This paper presents a different approach, which uses non-rigid registration, based solely on the image intensity, to determine corresponding points on the surface. This is, as far as we know, the first use of the technique in building generic anatomical models of bone structures. Difficulties are caused by parts of the bone structures where there is no proper correspondence, such as the teeth in the mandible. The results show that, using a low resolution deformation grid it is feasible to use non-rigid registration for determining correspondences in human mandibles. However to obtain greater accuracy it is necessary to preprocess the image sets to remove those parts for which there is no equivalence between specimens. is slow and cannot feasibly identify enough points to represent the full 3D geometry accurately. Anatomical landmarks that are easy to identify are few in number. Consequently considerable effort has been put into constructing corresponding landmarks automatically. This is equivalent to establishing the biological homology and then identifying the locations that represent the equivalence without ambiguity. Subsol et al. [1] proposed a scheme for automatically extracting corresponding landmarks from a training set in order to build an anatomical atlas. They used the iterative closet-point (ICP) algorithm introduced by Besl and McKay [2]. ICP iterates the nearest-neighbor relationship with a spatial transformation to determine the correspondences. Since ICP can be trapped by local minima, and does not guarantee the correct one-to-one mapping, Subsol and his colleagues used a heuristic algorithm to reinforce the "injectivity" and "monotonicity" constraints. ICP is usually classified as a feature-based method. For example, Andresen et al. extracted feature lines from Gaussian smoothed mandibles [3]. Crest lines corresponding to the maximum Gaussian curvature are used as the inputs of the registration. However, there is no guarantee that the crest lines are in proper anatomical correspondence even though they are extracted from areas that are anatomically equivalent. Recently, Frangi et al. [4] proposed a system to establish correspondences automatically using B-spline based nonrigid registration. In this system, a mean shape was defined from the training set and was landmarked using the vertices of a triangulated iso-surface. Every shape in the set was registered toward the mean shape by free form deformation. Then the landmarks were propagated from the mean shape to each individual shape by inverting the deformation. The method was validated by using several landmarks that were picked both manually and automatically by the system. An average error of 2.2mm was reported. The advantage of this method over other methods is that no geometrical constraints are enforced and there is no topological limitation resulting from surface parameterisation. It can be applied to any shapes represented by intensity data.

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