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Abstract
Correspondence determination between different objects plays a pivotal rolein a wide range of applications in computer vision and computer graphics. Inthis dissertation, we address some key problems in computer vision and computergraphics that are dependent on accurate correspondence determination betweenthe underlying objects under consideration. Following a general introduction tothe correspondence problem in Chapter 1, in Chapter 2, we introduce a pairwisegeodesic distance-based global shape representation for 3D shapes and exploit thespectrum of this representation to address correspondence determination between3D shapes and, self-symmetry detection and detection of stable regions within 3Dshapes. A surface differential-oriented global shape representation is introducedin Chapter 3 that is shown to encode the local surface geometry. We successfullyexploit the spectrum of this representation for symmetry detection within a 3Dshape and correspondence determination between 3D shapes. Furthermore, a novelcriterion is introduced to measure the compatibility of the representation spectrumin the context of an important application such as deformation transfer. All theshapes under consideration are isometric transformation pairs (i.e., related via anisometric transformation).In Chapter 4, we present a comparative study of the performance of the shaperepresentations introduced in Chapters 2 and 3 in the presence of noise. In addition,we introduce in Chapter 4 a biharmonic density-based surface point featurethat is computed by exploiting the eigenspectra of the shape representations thatare quintessential for establishing correspondence between shapes. Furthermore,we successfully apply the shape representation to address deformation transferfrom a given source shape to a target shape.In Chapter 5, we address non-rigid structure from motion, a very importantproblem in computer vision, to extract 3D information from a 2D image sequence.To address this problem we impose a constraint on the distribution of the 2D correspondencesbetween consecutive frames of the temporal image sequence. Finally,we conclude in Chapter 6 by giving an outline of some possible direction towardsfuture extensions of the works presented.All the problems and applications considered in this dissertation either directlyaddress or indirectly depend upon accurate correspondence determination betweenthe different objects under consideration. In computer graphics these objects arethe 3D shapes, whereas in computer vision the objects are the regions within theimages. The results of the proposed framework in each chapter are comparedto those from other relevant state-of-the-art schemes. It is shown that the proposedschemes perform competitively when compared with their state-of-the-artcounterparts.