
Manifolds of Projective Shapes
The projective shape of a configuration of k points or "landmarks" in RP...
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Topologically Robust 3D Shape Matching via Gradual Deflation and Inflation
Despite being vastly ignored in the literature, coping with topological ...
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Printable Aggregate Elements
Aggregating base elements into rigid objects such as furniture or sculpt...
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Efficient TopologyControlled Sampling of Implicit Shapes
Sampling from distributions of implicitly defined shapes enables analysi...
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Fillings of skew shapes avoiding diagonal patterns
A skew shape is the difference of two topleft justified Ferrers shapes ...
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Connecting the Dots: Discovering the "Shape" of Data
Scientists use a mathematical subject called 'topology' to study the sha...
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Partial Matching in the Space of Varifolds
In computer vision and medical imaging, the problem of matching structur...
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The Topology of Shapes Made with Points
In architecture, city planning, visual arts, and other design areas, shapes are often made with points, or with structural representations based on pointsets. Shapes made with points can be understood more generally as finite arrangements formed with elements (i.e. points) of the algebra of shapes U_i, for i = 0. This paper examines the kind of topology that is applicable to such shapes. From a mathematical standpoint, any "shape made with points" is equivalent to a finite space, so that topology on a shape made with points is no different than topology on a finite space: the study of topological structure naturally coincides with the study of preorder relations on the points of the shape. After establishing this fact, some connections between the topology of shapes made with points and the topology of "pointfree" pictorial shapes (when i > 0) are discussed and the main differences between the two are summarized.
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