Reconstructing occlusal surfaces of teeth using a genetic algorithm with simulated annealing type selection

In this paper, we present an application of numerical optimization for surface reconstruction (more precisely: reconstruction of missing parts of a real geometric object represented by volume data) by employing a specially designed genetic algorithm to solve a problem concerning computer-aided design in dentistry. Using a space mapping technique the surface of a given model tooth is fitted by a shape transformation to extrapolate (or reconstruct) the remaining surface of a patient's tooth with occurring damage such as a “drill hole.” Thereby, the genetic algorithm minimizes the error of the approximation by optimizing a set of control points that determine the coefficients for spline functions, which in turn define a space transformation. The fitness function to be minimized by the genetic algorithm is the error between the transformed occlusal surface of the model tooth and the remaining occlusal surface of the damaged (drilled) tooth. The algorithm, that is used, is based upon a proposal by Mahfoud and Goldberg. It uses a simulated-annealing type selection scheme, which is applied sequentially (pair-wise, or one-by-one) to the members in the parent generation and their respective offspring generated by mutation-crossover. We outline a proof of convergence for this algorithm. The algorithm is parallel in regard to computing the fitness-values of creatures.