Geometric invariance in computer vision
Differential and Numerically Invariant Signature Curves Applied to Object Recognition
International Journal of Computer Vision
Numerically Invariant Signature Curves
International Journal of Computer Vision
Proceedings of the Second Joint European - US Workshop on Applications of Invariance in Computer Vision
3D-2D projective registration of free-form curves and surfaces
ICCV '95 Proceedings of the Fifth International Conference on Computer Vision
Multiple View Geometry in Computer Vision
Multiple View Geometry in Computer Vision
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We present a novel algorithm for deciding whether a given planar curve is an image of a given spatial curve, obtained by a central or a parallel projection with unknown parameters. A straightforward approach to this problem consists of setting up a system of conditions on the projection parameters and then checking whether or not this system has a solution. The computational advantage of the algorithm presented here, in comparison to algorithms based on the straightforward approach, lies in a significant reduction of a number of real parameters that need to be eliminated in order to establish existence or non-existence of a projection that maps a given spatial curve to a given planar curve. Our algorithm is based on projection criteria that reduce the projection problem to a certain modification of the equivalence problem of planar curves under affine and projective transformations. The latter problem is then solved using a separating set of rational differential invariants. A similar approach can be used to solve the projection problem for finite lists of points. The motivation comes from the problem of establishing a correspondence between an object and an image, taken by a camera with unknown position and parameters.