The Hausdorff distance between two sets of curves is a measure for the similarity of these objects and therefore an interesting feature in shape recognition. If the curves are algebraic computing the Hausdorff distance involves computing the intersection points of the Voronoi edges of the one set with the curves in the other. Since computing the Voronoi diagram of curves is quite difficult we characterize those points algebraically and compute them using the computer algebra system SYNAPS. This paper describes in detail which points have to be considered, by what algebraic equations they are characterized, and how they actually are computed.

In this ongoing work, we propose a Bayesian model that can be used to detect targets in multispectral images when the signals from the materials in the image mix linearly, the noise is Gaussian, and abundance parameters are nonnegative. By using efficient implementations of the Gibbs sampler, the expectation of any measurable functional of the abundance parameters, relative to the posterior distribution, can be computed easily. This general approach can be used to include additional constraints.

No abstract

We analyze a probabilistic algorithm for matching shapes modeled by planar regions under translations and rigid motions (rotation and translation). Given shapes A and B, the algorithm computes a transformation t such that with high probability the area of overlap of t(A) and B is close to maximal. In the case of polygons, we give a time bound that does not depend significantly on the number of vertices.

No abstract