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

This paper tackles the problem of the in situ extraction of specific geometrical primitives from a three‐dimensional (3D) biomedical data set. This task involves two main problems: segmentation of major structures and extraction of the features of interest. The segmentation algorithm studied focuses on cortical bone structures. It proceeds through an analysis of a 3D watershed transform applied to the contrast image and outputs numerical surfaces as basin borders. The feature extraction task focuses on the identification of smooth regions exhibiting homogeneous curvatures, i.e., articular surfaces. We hypothesize that such surfaces can be accurately modeled through the zero set of a second‐order polynomial surface. Tracking the set of optimal parameters makes use of global and local optimization procedures, both working in the same encoding framework. The latter is a minimal subset encoding scheme. In this scheme, a model under test is indirectly described through the minimal set of data points that it interpolates, i.e., nine points in the quadratic model case. Optimization is reached by maximizing an objective function accounting for the point‐matching score of a fuzzy representation of the geometrical model vs. data points of the numerical surfaces. As such, a huge search space does not enable exhaustive exploration (e.g., the Hough transform) and the global search step makes use of a canonical genetic algorithm (i.e., a stochastic process). The latter outputs a fitness‐ordered set of solutions, which is not the best one. The subsequent local search 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.© 2000 John Wiley & Sons, Inc. Int J Imaging Syst Technol, 11, 30–43, 2000