Conformal-affine point-pattern matching

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This section contains an implementation of the algorithm given in the paper

A Fast Expected-Time 2d Point-Pattern Matching Algorithm, P.B. Van Wamelen et al., Pattern Recognition 37 (2004), 1699-1711.

This is an efficient randomized algorithm for point-pattern matching under the class of conformal affine transformations in `RR^2`. It is based on examining local neighborhoods of the points of `Q in RR^2` and the points of `P in RR^2`. Only if the local neighborhoods match, it is checked if the match is also global. Such a technique is a fast way to reject transformation candidates. However, it has certain drawbacks:

• It might reject a valid transformation.
• If the point-patterns are highly self-similar (e.g. a grid of points), then lots of local neighborhoods match and the algorithm slows down remarkably.

The first drawback is taken care by probabilistic arguments: it is accepted provided that it does not happen often. This is taken care by choosing the local neighborhood sizes carefully. The second drawback is a general problem in point-pattern matching.

Remark 1.7.5 - Page generated 16.06.2017 01:36.