Cindy Grimm

Modeling surfaces of arbitrary topology using manifolds

Manifolds describe complicated objects that are locally

Curvature maps for local shape comparison

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ESTIMATING CURVATURE ON TRIANGULAR MESHES

by defining a set of overlapping maps from the object to

Interactive decal compositing with discrete exponential maps

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Subtle gaze direction

. In this thesis we present a general technique for inverting that process: we define a complicated object from a set of overlapping subsets of

Three-dimensional panoramic imaging of cardiac arrhythmias in rabbit heart.

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Say cheese! Experiences with a robot photographer

. We first present a constructive definition that describes how to perform such a construction in general. We then apply this construction to the particular problem of defining surfaces of arbitrary topology. The surface is built in two steps: we build a manifold with the correct topology then embed the manifold into

Local shape descriptors, a survey and evaluation

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The IBar: a perspective-based camera widget

using traditional spline techniques. The surface inherits many of the properties of B-splines: local control, a compact representation, and guaranteed continuity of arbitrary degree. The surface is specified using a polyhedral control mesh instead of a rectangular one; the resulting surface approximates the polyhedral mesh much as a B-spline approximates its rectangular control mesh. Like a B-spline, the surface is a single, continuous object.

Simple manifolds for surface modeling and parameterization

The ability to identify similarities between shapes is important for applications such as medical diagnosis, object registration and alignment, and shape retrieval. In this paper we present a method, the curvature map that uses surface curvature properties in a region around a point to create a unique signature for that point. These signatures can then be compared to determine the similarity of one point to another. To gather curvature information around a point we explore two techniques, rings (which use the local topology of the mesh) and geodesic fans (which trace geodesies along the mesh from the point). We explore a variety of comparison functions and provide experimental evidence for which ones provide the best discriminatory power. We show that curvature maps are both more robust and provide better discrimination than simply comparing the curvature at individual points.