Abstract

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.

中文翻译：

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用随机计数的最优格子分区表示图像

摘要

该论文基于与采样随机（照片）计数的最佳分区相关的特殊元数据，对图像的新表示进行了研究。基于图像点阵模型的分区的使用提供了可扩展性的建议表示属性。由于尺度的控制仅与晶格参数的选择有关，因此尺寸/精度特性的平衡问题成为表征形成过程中的一个容易控制的因素。与这些特征相关的表示的灵活性意味着它们在与大数据问题相关的一系列任务中的广泛应用：图像分类、对象识别、特征特征提取等。 从数学的角度来看，所提出的方法的一个主要特点是初始图像数据的统计描述的特异性，随机计数。这种描述与机器学习领域的朴素贝叶斯和其他方法的形式主义非常吻合。特别是，通过类比众所周知的钾-均值分割方法，可以合成一个循环过程，用于采样计数的分区最大化，以便找到表示元数据的最大合理参数。这里的一个新元素是引入了计数格环境的概念，这使得有效控制计算量成为可能。讨论了晶格环境与当今在卷积神经网络 (CNN) 领域广泛使用的概念、感受野的概念之间的关系。该论文详细讨论了所获得过程的算法实现，并详细讨论了其许多特征，包括收敛性、渐近效率等问题。