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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References
Geometry-Driven Diffusion in Computer Vision
Bart M. ter Haar Romeny
- 01 Sep 1994
TL;DR: This paper presents a meta-analyses of differential Invariant Signatures and Flows in Computer Vision: a Symmetry Group approach P. Sapiro, A. Tannenbaum, and a Differential Geometric Approach to Anisotropic Diffusion.
853
Theorie der Transformationsgruppen
TL;DR: In this paper, the authors present a general theory of the Beruhrungstransformationen and the Gruppen von Beruhrasformationen (GBSs) in the context of continuirlichen Transformationsgruppen.
688
Geometric invariants and object recognition
TL;DR: The role of the general invariance concept in object recognition is discussed, the classical and recent literature on projective invariance is reviewed, and shape descriptors, computed from the geometry of the shape, that remain unchanged under geometric transformations such as changing the viewpoint are reviewed.
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