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In an earlier question I inquired about contour lines reflecting probability values in a Bivariate Gaussian Distribution. I have spent some time thinking and playing around with a Mathematica manipulate, but I have been unable to find a model that suits my needs.

In my computer-vision problem, a blob can move either forward or backwards (with a slight chance of moving sideways) along its directional axis. I am seeking a bivariate model because I need to determine whether a blob's new position (with respect to its old one) is "feasible," or "likely." However, the blob can not move extreme distances very quickly.

Thus, there is a high probability that the blob will not move very far if it does move (but still a sufficient amount such that the probability distribution will be elongated along one axis [not the orthogonal]).

I am searching for a model that has high probability values within a smaller region, but has a larger encompassing region with small (and distinctly different) probability values.

Thank you for your help!

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There can be many such distributions. A Gaussian distribution with high excess kurtosis might be what you're looking for -- i.e., a very narrow "bell curve". Gaussian distributions are convenient because they are related to Gaussian convolution kernels, which are used in image processing quite often. However, I suspect that this particular question might be better suited for the Signal Processing StackExchange. There are many, many probability distributions that may or may not suit your needs; chances are you need one that better relates to your specific application, which is off-topic here. –  Arkamis Jul 17 '12 at 20:38
Thank you for the redirect. I was not aware of the Signal Processing StackExchange's existence, and will post my question there. –  JT Cho Jul 17 '12 at 20:42

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