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Analysis of Global Properties of Shapes

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Doctoral thesis

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With increasing amounts of data describing 3D geometry at scales small and large, shape analysis is becoming increasingly important in fields ranging from computer graphics to robotics to computational biology. While a great deal of research exists on local shape analysis, less work has been done on global shape analysis. This thesis aims to advance global shape analysis in three directions symmetry-aware mesh processing, part decomposition of 3D models, and analysis of 3D scenes. First, we propose a pipeline for making mesh processing algorithms symmetry-aware, using large-scale symmetries to aid the processing of 3D meshes. Our pipeline can be used to emphasize the symmetries of a mesh, establish correspondences between symmetric features of a mesh, and decompose a mesh into symmetric parts and asymmetric residuals. We make technical contributions towards two of the main steps in this pipeline a method for symmetrizing the geometry of an object, and a method for remeshing an object to have a symmetric triangulation. We offer several applications of this pipeline modeling, beautification, attribute transfer, and simplification of approximately symmetric surfaces. Second, we conduct several investigations into part decomposition of 3D meshes. We propose a hierarchical mesh segmentation method as a basis for consistently segmenting a set of meshes. We show how our method of consistent segmentation can be used for the more specific applications of symmetric segmentation and segmentation transfer. Then, we propose a probabilistic version of mesh segmentation, which we call a partition function,that aims to estimate the likelihood that a given mesh edge is on a segmentation boundary. We describe several methods of computing this structure, and demonstrate its robustness to noise, tessellation, and pose and intra-class shape variation. We demonstrate the utility of the partition function for mesh visualization, segmentation deformation, and registration.

Subject Categories:

  • Computer Programming and Software
  • Cybernetics

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