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.
