Christopher Brown,
Numerical Evaluation of Differential and Semi-Differential
Invariants,
In Joseph Mundy and Andrew Zisserman eds., Geometric Invariance in Computer Vision,
Cambridge, MA, USA, Series: Artificial intelligence, pp. 215-227, The MIT Press, 1992.The goal of this chapter is to illuminate to some extent the behaviour of some of the differential invariants and semi-invariants that are mentioned elsewhere in this volume. A straightforward implementation of Wilczynski's differential projective invariants Theta 3 and Theta 8, Weiss's differential semi-invariants P2 and P3, and Van Gool's semi-differential invariants tau 1(t) and tau 2(t) is used to give a qualitative idea of the behaviour of these invariants as a function of curve sampling rates and numerical precision in positional measurements. The results also give a qualitative feeling for how useful these invariant representations might be for matching and recognition.