Quick Simulation Random Field Properties

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  • A real-time algorithm to produce correlated random fields on general undirected graphs has been used in CAPTCHA generation and optical character recognition. This algorithm can not simulate all possible joint graph distributions but does match all marginal vertex distributions as well as specified covariance between vertices. Herein, a modified algorithm is given by completing the graph and setting the non-specified covariances to zero. The modifiedalgorithm graph distribution is derived and the following questions are studied: 1) For which marginal pmfs and covariances will this algorithm work? Are there collections consistent with a random field that this algorithm can not handle? 2) When does the marginal property hold, where the subgraph distribution of a algorithm-simulated field matches the distribution of the algorithm-simulated field on the subgraph? 3) When does the permutation property hold, where the vertex simulation order does not affect the joint distribution?

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    Research Material
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    © 2015 Michael Kouritzin. This version of this article is open access and can be downloaded and shared. The original authors and source must be cited.