In recent years there has been a considerable growth in the prevalence of digital 3D content. With applications in medical imaging, architecture, industrial design, entertainment and education, to mention just a few, there is a growing need for methodologies for scientific analysis of 3D data. In this project we will focus on an important problem which facilitates such analysis – creating informative, structure-preserving maps between 3D shapes. In many applications we are presented with a collection of related shapes, such as humans, animals, etc., and we need a way to map the shapes to each other. Such maps take all shapes to the same “common ground”, allowing the use of standard mathematical machinery for further analysis. Mapping between 3D shapes has been an active research area recently, however two aspects of this problem have not been thoroughly addressed. First, many existing methods assume little variability between the mapped shapes, an assumption which is not valid for most shape collections and might yield erroneous mappings. Second, almost all methods consider only maps between two shapes, disregarding the contextual information one can gain from investigating the collection of shapes as a whole. To address these shortcomings, we propose to design and investigate alternative map representations, namely generalized maps, which broaden the definition of maps between shapes. Our main objectives are to formulate the required design goals for generalized maps which address the shortcomings of existing methods, and to investigate one such specific representation based on a probabilistic formulation of the mapping problem. Combining the experience gained by the applicant during her postdoctoral period with the expertise in related fields provided by the host institution, will allow to advance the current state-of-the art in the shape mapping problem, as well as nurture collaboration with the applicant’s postdoctoral institution.
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