Representation of Images by the Optimal Lattice Partitions of Random Counts

The paper presents a study of new representations of images based on special metadata related to the optimal partitioning of sampled random (photo) counts. The use of partitions based on the lattice model of image provides the proposed representations property of scalability. Since the control of the scale is connected only with the choice of the lattice parameters, the question of the balance of dimension/precision characteristics turns out to be an easily controllable factor in the procedure for representations formation. The flexibility of representations in relation to these characteristics implies their widespread application in a whole range of tasks related to the big data problem: image classification, object identification, characteristic features extraction, etc. From a mathematical point of view, a main feature of the proposed approach is the specificity of the statistical description of initial image data, random counts. This description is in good agreement with the formalism of naive Bayesian and other approaches in the field of machine learning. In particular, by analogy with the well-known K-mean segmentation method, it is possible to synthesize a recurrent procedure for partitioning–maximization of sampled counts in order to find the maximal plausible parameters of the metadata of the representations. A new element here is the introduction of the concept of a lattice environment of counts, which makes it possible to effectively control the amount of computations. The relationship of the lattice environment with the concept that is widely used today in the field of convolutional neural networks (CNNs), the concept of receptive fields, is discussed. The paper discusses in detail the algorithmic implementation of the procedure obtained and provides a detailed discussion of a number of its features, including questions of convergence, asymptotic efficiency, etc. All questions of applying the procedure to the formation of representations of real images are illustrated by computer simulations.