Statistical Shape Modeling for Custom Design and Analysi

The goal of this dissertation research is to use pre-existing shape data to improve efficiency and quality of custom design and analysis.;The rapid advancement of sensor miniaturization and growing sensor networks and computer power has lead to wide availability of massive shape data from populations of objects. Such massive shape data range from human body shapes to longitudinal knee observations of osteoarthritis patients. Populations of shape data also include shapes of man-made objects, such as part shapes of the same model due to manufacturing process variation as well as part shapes due to shape degradation after deployment. Mining and analysis of such massive population-based shape data can result in knowledge of shape variability of the population and lead to the construction of faithful subject-specific 3D shape models from sparse measurements. It is then possible to predict shape-specific functional performance and population-wide structural performance variation. Such an ability brings about unprecedented capabilities and tantalizing opportunities for mass customization, part-specific failure prediction and just-in-time part maintenance, and patient-specific biomedical intervention and treatment.;This work aims at developing efficient approaches that can: 1) construct faithful subject-specific shape models from sparse measurements; 2) predict shape-specific structural performance from a given subject-specific shape model; and 3) predict structural performance variation over a shape population. Toward this end, we present a statistical atlas based approach that incorporates statistical shape modeling in subject-specific shape reconstruction, finite element (FE) modeling and analysis.;The statistical atlas contains three parts: the mean shape and the variation modes of the shape population which span a linear shape space, the FE mesh of the mean shape, and the selected feature points and sizing dimensions. The feature points and sizing dimensions are selected by maximizing the total variance they capture of the shape population. Given a subject (e.g. a person), the corresponding dimensions are measured and the subject specific shape model is synthesized. The FE mesh of the mean shape serves as the template mesh which can be morphed to the subject shape to conduct subject-specific FE analysis. The FE solution on the template mesh can also be extrapolated to the subject shape through Taylor expansion. The shape variances along the variation modes are obtained by the principal component analysis. These variances tell the amount of shape variabilities in the population and are combined with the Taylor expansion of the FE solution to obtain the structural performance variation across the population. The numerical testings with various 2D and 3D shape databases demonstrate the efficiency and effectiveness of the proposed approach for custom design and analysis.;In this dissertation a statistical atlas based framework is developed for custom design and analysis. The main contributions of this work are: 1) An approach that selects feature points and sizing dimensions based on the total variance captured of the shape population. 2) Automated subject-specific FE modeling through mesh morphing based on the shape correspondence obtained by searching in the shape space. A multi-correlation based metric is developed to evaluate the quality of the obtained shape correspondences. 3) A Taylor expansion approach for predicting subject-specific structural performance and computing structural performance variation over a shape population. Multi-point Taylor expansion approach is developed for the cases that the structural performance is highly nonlinear with respect to the shape parameters.