Abstract
We recently used a Monte Carlo method for eliminating double counting. The same idea is useful for characterizing the "state" of an image automatically, which is particularly interesting because photographs and digital images have become so commonplace. Automatic detection of change of state is suddenly desirable. What we do is compute a multiplicative factor p, which we use to tighten the Bonferroni bound on the size of a union of sets, assuming we already know the individual sizes of the sets. We then obtain a new bound that is more accurate and useful. We explain how to use this new bound to estimate the number of edges in a triangulation if we are given the tetrahedra (in 3D). We also explain how to eliminate duplication in complicated data sets. Finally, we explain how to use the same idea to characterize images.
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