Luc J. Van Gool, Theo Moons, Eric Pauwels and André Oosterlinck,
Semi-Differential Invariants,
In Joseph Mundy and Andrew Zisserman eds., Geometric Invariance in Computer Vision,
Cambridge, MA, USA, Series: Artificial intelligence, pp. 157-192, The MIT Press, 1992.We describe algorithms for the detection of similarities between planar contours. Perspective projection is assumed, which implies that the 3D similarity transformations between the original contours take the form of 2D projective transformations in the image. Examples of tasks envisaged are object recognition and symmetry detection. The problems are tackled by generating contour descriptions which remain invariant under the projective transformations. Traditional approaches to this problem are briefly reviewed. We argue that a compromise between correspondence search and numerical differentiation leads to a compelling class of invariants, which we call ``semi-differential''. They are situated in what we regard as a vast wasteland between algebraic and differential geometry, and which seems highly promising for vision applications in general.