Analysis and Synthesis of Image Patterns by Spatial Interaction Models

Abstract We will consider various types of spatial interaction models for representing images. Some of the models considered are the recursive models, simultaneous and conditional Markov models over infinite lattices and finite lattice models. Every model is characterized by a set of neighbors, the corresponding coefficients and an independent random sequence with prespecified probability density. We analyze the models and evaluate their second order properties like covariance function, spectral density etc. in terms of the model parameters. Procedures are given for synthesizing an image of each type starting from a set of random variates obtained from a random number generator. Statistical procedures have been developed for determining the appropriate type of model for each image and for estimating the unknown parameters in the model from the given image. Numerical results regarding the synthesis and estimation algorithms are also given. We also compare these models with the random mosaic models.

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