On reliably inferring differential structure from three-dimensional images

• Main Author: Sander, Peter T.
• Format: Others
• Language: en
• Published: McGill University 1988
• Subjects: Pattern recognition systems > Mathematical models; Magnetic resonance imaging; Three-dimensional display systems
• Online Access: http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=75752

Early image understanding seeks to derive analytic representations from image data. This thesis presents steps towards this goal for three-dimensional imagery by focusing on the inference of trace points (points belonging to surfaces), and the estimation of associated differential structure given by the principal curvature and direction fields over smooth surfaces. Computation of these fields is posed as the determination of a cross section through the bundle of curvature frames over the estimated trace. Algorithm robustness and the stability of results are essential for analysis of real images; to this end, I present a functional minimization algorithm where the principal direction cross section meets appropriate criteria for a minimum, and develop an implementation as an iterative constraint satisfaction procedure based on local surface smoothness properties. For shape description and eventual object recognition, the exact recovery of local structure everywhere is less important than the identification of singular surface points which prove stable to noise and small surface perturbations, in particular, the umbilic points of surfaces. Such points are computed naturally from the estimated local surface structure embodied in the principal direction cross section of the frame bundle. Examples of the recovery of local structure are presented for synthetic images degraded by noise and for clinical magnetic resonance images.