Journal Article10.1023/A:1007992709392
Differential and Numerically Invariant Signature Curves Applied to Object Recognition
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TL;DR: It is shown how a new approach to the numerical approximation of differential invariants, based on suitable combination of joint invariants of the underlying group action, allows one to numerically compute differential invariant signatures in a fully group-invariant manner.
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Abstract: We introduce a new paradigm, the differential invariant signature curve or manifold, for the invariant recognition of visual objects A general theorem of E Cartan implies that two curves are related by a group transformation if and only if their signature curves are identical The important examples of the Euclidean and equi-affine groups are discussed in detail Secondly, we show how a new approach to the numerical approximation of differential invariants, based on suitable combination of joint invariants of the underlying group action, allows one to numerically compute differential invariant signatures in a fully group-invariant manner Applications to a variety of fundamental issues in vision, including detection of symmetries, visual tracking, and reconstruction of occlusions, are discussed
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Invariant signatures for planar shape recognition under partial occlusion
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