Type of Document	Dissertation
Author	Joshi, Shantanu H
Author's Email Address	joshi@eng.fsu.edu
URN	etd-01252008-124830
Title	Inferences in Shape Spaces with Applications to Image Analysis and Computer Vision
Degree	Doctor of Philosophy
Department	Electrical and Computer Engineering, Department of
Advisory Committee	Advisor Name Title Anuj Srivastava Committee Chair Anke Meyer-Baese Committee Co-Chair Eric Klassen Committee Member John W. Fisher III Committee Member Rodney Roberts Committee Member Simon Y. Foo Committee Member
Keywords	Statistical Shape Bayesian Extraction Shape Analysis Computer Vision Shape Image Analysis
Date of Defense	2007-07-25
Availability	unrestricted
Abstract Shapes of boundaries can play an important role in characterizing objects in images. Shape analysis involves choosing mathematical representations of shapes, deriving tools for quantifying shape differences, and characterizing imaged objects according to the shapes of their boundaries. We describe an approach for statistical analysis of shapes of closed curves using ideas from differential geometry. In this thesis, we initially focus on characterizing shapes of continuous curves, both open and closed, in R^2 and then propose extensions to more general elastic curves in R^n. Under appropriate constraints that remove shape-preserving transformations, these curves form infinite-dimensional, non-linear spaces, called shape spaces. We impose a Riemannian structure on the shape space and construct geodesic paths under different metrics. Geodesic paths are used to accomplish a variety of tasks, including the definition of a metric to compare shapes, the computation of intrinsic statistics for a set of shapes, and the definition of intrinsic probability models on shape spaces. Riemannian metrics allow for the development of a set of tools for computing intrinsic statistics for a set of shapes and clustering them hierarchically for efficient retrieval. Pursuing this idea, we also present algorithms to compute simple shape statistics --- means and covariances, --- and derive probability models on shape spaces using local principal component analysis (PCA), called tangent PCA (TPCA). These concepts are demonstrated using a number of applications: (i) unsupervised clustering of imaged objects according to their shapes, (ii) developing statistical shape models of human silhouettes in infrared surveillance images, (iii) interpolation of endo- and epicardial boundaries in echocardiographic image sequences, and (iv) using shape statistics to test phylogenetic hypotheses. Finally, we present a framework for incorporating prior information about high-probability shapes in the process of contour extraction and object recognition in images. Here one studies shapes as elements of an infinite-dimensional, non-linear quotient space, and statistics of shapes are defined and computed intrinsically using differential geometry of this shape space. Prior models on shapes are constructed using probability distributions on tangent bundles of shape spaces. Similar to the past work on active contours, where curves are driven by vector fields based on image gradients and roughness penalties, we incorporate prior shape knowledge also in form of gradient fields on curves. Through experimental results, we demonstrate the use of prior shape models in estimation of object boundaries, and their success in handling partial obscuration and missing data. Furthermore, we describe the use of this framework in shape-based object recognition or classification. This Bayesian shape extraction approach is found to yield a significant improvement in detection of objects in presence of occlusions or obscurations.
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