Development and comparison of strategies for the reconstruction of full and partial skull geometries

Abstract

This thesis presents the development and comparison of strategies for the reconstruction of full and partial surface mesh based skull geometries. The intended application is to aid the South African Police Service Victim Identification Centre (SAPS VIC) with forensics, specifically prediction of a mandible when only the cranium is available. Various methods for the registration of surface meshes are outlined. A new non-rigid iterative closest point (NR-ICP) algorithm based on an adaptively refined least square Radial Basis Function (RBF) approximation of the forward and backward nearest neighbour correspondence is developed. The newly developed non-rigid registration strategy is demonstrated and characterised for various parameters using an artificial mandible dataset constructed through Monte-Carlo (MC) sampling of a quadratic displacement field. Various suitable parameters are shown to result in imperceptible visual registration differences, with the correspondence error mainly distributed in-surface. Multivariate regression techniques suited to the application of geometry prediction are considered, specifically for cases where the data is expected to be multi-collinear and the number of variables are far greater than the number of observations. Two regression approaches based on spatial information are considered. The first is the classical use of Procrustes Analysis where the Cartesian coordinates are used directly for regression. The second is a new Euclidean distance based approach utilizing pair-wise distances to consistent reference points. The proposed regression methods’ time-space scaling is investigated to limit system sizes that result in time tractable cross-validation and model comparison. Pre- and post-processing required for tractability considerations are also developed for both approaches. Proof of concept of the registration based prediction strategies are demonstrated. This is accomplished through the use of an artificial dataset with embedded covariance and the use of registration targets without point-wise correspondence. The registration based prediction strategy is shown to be capable of accurate predictions for data with strong underlying structure/covariance. The proposed registration based prediction strategy is demonstrated on a real cranium and mandible dataset, where the mandible geometry is predicted from the cranium geometry. Marginal improvement over the geometric mean is obtained. Observation scaling suggests that model accuracy is improved for increased observations, which merits expanding the dataset. The proposed registration strategy has the limitation that it is not capable of registration of significant partial/incomplete geometries. A new regression-registration hybrid strategy is developed for use with partial geometries, when a full dataset of the given geometry is available. The regression-registration hybrid strategy is demonstrated on a real mandible dataset and mandible fossil.