Building optimal 3D shape models

Allan Reinhold Kildeby

AbstractThis thesis presents a general approach towards automated 3D statistical shape model building through the utilization of spherical mapping and Minimum Description Length, based on algorithms proposed by Angenent et al. and Davies et al.

A thorough treatment and discussion of the theoretic foundation involved in conformally mapping 3D surfaces to the unit sphere is given. The basic algorithm is extended through the imposing of an area-preservation criteria.

The theoretical foundation behind Minimum Description Length shape modelling is presented and discussed, followed by several extensions to the basic algorithm. Extensions include employment of the spherical map derived, robust landmark positioning and simplification of objective function, all of which have been included in a high performance C++ framework.

Experimental results on both synthetical and biological training data reveal the potential of and difficulties in composing unique spherical maps as well as in building a fully automated shape model, while retaining specificity, generality and compactness.

It is concluded that automated statistical shape learning successfully can accomplish compact and general shape models, through the use of spherical maps, though this approach to automated 3D model building is still fairly unexplored.
KeywordsDeformable Template Models, Point Distribution, Principal Component Analysis, Shape Analysis, Shape Alignment, Finite Elements Models, Spherical Mapping, Conformal Mapping, Area-preserving Mapping, Minimum Description Length Automated Shape Learning
TypeMaster's thesis [Academic thesis]
PublisherInformatics and Mathematical Modelling, Technical University of Denmark, DTU
AddressRichard Petersens Plads, Building 321, DK-2800 Kgs. Lyngby
NoteSupervisor: Rasmus Larsen
Electronic version(s)[pdf]
BibTeX data [bibtex]
IMM Group(s)Image Analysis & Computer Graphics