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The paper considers problems of developing stochastic models consistent with results of character image recognition in video stream. A set of assumptions that dene the models structure and properties is stated. A class of distributions, namely the Dirichlet distribution and its generalizations, that set a description of the model components is pointed out; and methods for statistical estimation of the distribution parameters are given. To rank the models, the Akaike information criterion is used. The proposed theoretical distributions are veried vs sample data.

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The paper proposes an approach to training a convolutional neural network using information on the level of distortion of input data. The learning process is modified with an additional layer, which is subsequently deleted, so the architecture of the original network does not change. As an example, the LeNet5 architecture network with training data based on the MNIST symbols and a distortion model as Gaussian blur with a variable level of distortion is considered. This approach does not have quality loss of the network and has a significant error-free zone in responses on the test data which is absent in the traditional approach to training. The responses are statistically dependent on the level of input image's distortions and there is a presence of a strong relationship between them.

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