This dissertation presents a technique for comparing local shape properties for similar three-dimensional objects represented by meshes. We develop a shape representation that is sensitive to subtle shape differences but relatively insensitive to noise, and use this representation to detect features of the objects. The features are used, along with a measure for shape similarity, to compute a correspondence between the objects, which then allows shape comparison based on the shape properties at corresponding points. An advantage of this approach is that the final comparisons depend on the similarity-based correspondence and not on a physical three-dimensional alignment.; Our novel shape representation, the curvature map, describes shape as a function of surface curvature in the region around a point. A multi-pass approach is applied to the curvature map to detect features at different scales. The feature detection step does not require user input or parameter tuning. We use features ordered by strength, the similarity of pairs of features, and pruning based on geometric consistency to efficiently determine key corresponding locations on the objects. For genus zero objects, the corresponding locations are used to generate a consistent spherical parameterization that defines the point-to-point correspondence used for the final shape comparison.
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