Analytical surface recognition in three-dimensional (3D) medical images using genetic matching: Application to the extraction of spheroidal articularsurfaces in 3D computed tomography data sets

This paper tackles the problem of the in situ extraction of specific geomet rical primitives from a three-dimensional (3D) biomedical data set, This ta sk involves two main problems: segmentation of major structures and extract ion of the features of interest. The segmentation algorithm studied focuses on cortical bone structures. It proceeds through an analysis of a 3D water shed transform applied to the contrast image and outputs numerical surfaces as basin borders. The feature extraction task focuses on the identificatio n of smooth regions exhibiting homogeneous curvatures, i.e., articular surf aces, We hypothesize that such surfaces can be accurately modeled through t he zero set of a second-order polynomial surface. Tracking the set of optim al parameters makes use of global and local optimization procedures, both w orking in the same encoding frame-work. The latter is a minimal subset enco ding scheme. In this scheme, a model under test is indirectly described thr ough the minimal set of data points that it interpolates, i.e., nine points in the quadratic model case. Optimization is reached by maximizing an obje ctive function accounting for the point-matching score of a fuzzy represent ation of the geometrical model vs, data points of the numerical surfaces, A s such, a huge search space does not enable exhaustive exploration (e.g., t he Hough transform) and the global search step makes use of a canonical gen etic algorithm (i.e., a stochastic process). The latter outputs a fitness-o rdered set of solutions, which is not the best one. The subsequent local se arch acts as a refinement step; it performs an iterative approximation that merges some suboptimal solutions of the final-ordered set coming from the global search. This search process is applied to the in situ extraction of spheroidal joint surfaces with the help of an ellipsoidal model. The whole algorithm is shown to be accurate and time efficient. (C) 2000 John Wiley & Sons, Inc.