AN ALGEBRAIC TOPOLOGICAL METHOD FOR FEATURE IDENTIFICATION
2006 ◽
Vol 16
(04)
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pp. 291-314
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We develop a mathematical framework for describing local features of a geometric object—such as the edges of a square or the apex of a cone—in terms of algebraic topological invariants. The main tool is the construction of a "tangent complex" for an arbitrary geometrical object, generalising the usual tangent bundle of a manifold. This framework can be used to develop algorithms for automatic feature location. We give several examples of applying such algorithms to geometric objects represented by point-cloud data sets.
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2013 ◽
Vol 34
(22)
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pp. 8215-8234
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2019 ◽
Vol XLII-2/W17
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pp. 53-60
2021 ◽
Vol 87
(7)
◽
pp. 479-484
2019 ◽
Vol 16
(4)
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pp. 172988141985753
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