Abstract

This article is the fourth in a series of publications devoted to the state of the art and prospects for developing Descriptive Image Analysis, one of the leading and intensively developing fields of modern mathematical image analysis theory. The fundamental problem discussed in the article is to automate information extraction from images necessary for making intelligent decisions. This study is devoted to regularizing the generation of descriptive algorithmic image analysis and recognition schemes. The main result is the definition of a new mathematical structure with the following functional capabilities: 1) solution of an image recognition problem in a given formulation, with given initial data and a scenario that determines the sequence of application of information processing procedures and their iterative loops; 2) construction of descriptive algorithmic schemes for solving a problem with given initial data in the absence of a given scenario; in the case of a successful solution, the fixation of the sequence of procedures and information processing loops that yielded its solution governs the corresponding descriptive algorithmic schemes and scenarios that can be further used to solve the corresponding class of image recognition problems; 3) comparative analysis and optimization of methods for solving image recognition problems via their realization as descriptive algorithmic schemes and scenarios allowed by the structure. The introduced structure is a tool for representing and implementing information processing while solving an image recognition problem for arbitrary formulations, scenarios, models, and solution methods; it can also emulate any descriptive algorithmic scheme and combinations thereof, which are used and generated when solving an image recognition problem. The introduced structure is interpreted as a fundamental model for generating and emulating image recognition procedures. A type characteristic of the introduced information structure for generating descriptive algorithmic schemes is as follows: 1) the set of structure elements consists of two subsets: a) a subset of functional blocks that perform mathematical operations of information processing necessary to implement the used of processing, analysis, and image recognition methods; b) a subset of control blocks for information processing procedures, which verify the logical conditions for branching of processing procedures, whether the rules for stopping information processing are met, etc.; 2) relations given over the elements of the set of the structure, mainly, the partial ordering relations that determine the sequence of execution and methods for combining the functional and control blocks of the structure; 3) these relations, by definition, must satisfy the axioms of the Descriptive Approach to Image Analysis and Understanding. The paper presents the basic definitions associated with the introduction of a new information structure and describes the information processing procedures implemented therein, as well as the main blocks and loops. Block diagrams of the information structure and iteration loops are given. The fundamental importance of the results of the described studies for developing the mathematical theory of image analysis and their scientific novelty are related to formulation of problems and development of methods for modeling the processes for automating image analysis when the input data are poorly formalized representations of images, including spatial data—images and their fragments, image models, incompletely formalized representations, and subsets of combinations thereof. Introduction of a new information structure as a standard structure for a) representation of algorithms for analysis and recognition of 2-dimensional information and representation of procedures for constructing dual representations of images as descriptive algorithmic schemes; b) generation of descriptive algorithmic schemes indicated in (a) will make it possible to generalize and substantiate the known heuristic recognition algorithms, to comparatively analysis them, and to assess their mathematical properties and applied usefulness. The problem of automating the construction and analysis of descriptive algorithmic image recognition schemes is formulated for the first time.

中文翻译：

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描述性图像分析：第四部分。用于生成图像识别描述性算法方案的信息结构

摘要

本文是系列出版物中的第四篇，该系列出版物致力于描述性图像分析的发展和发展，这是现代数学图像分析理论的主要领域之一。本文讨论的基本问题是自动从图像中提取信息，以做出明智的决策。这项研究致力于规范化描述性算法图像分析和识别方案的生成。主要结果是定义具有以下功能的新数学结构：1）以给定的公式，给定的初始数据和确定信息处理程序及其迭代应用顺序的方案来解决图像识别问题循环; 2）构造描述性算法方案，以在没有给定场景的情况下解决给定初始数据的问题；在成功的解决方案的情况下，产生解决方案的过程序列和信息处理循环的固定将控制相应的描述性算法方案和方案，这些方案和方案可进一步用于解决相应类别的图像识别问题；3）比较分析和优化方法，通过将其实现为结构允许的描述性算法方案和方案来解决图像识别问题。引入的结构是一种工具，用于表示和实现信息处理，同时解决任意公式，方案，模型和求解方法的图像识别问题；它还可以模拟解决图像识别问题时使用和生成的任何描述性算法方案及其组合。引入的结构被解释为用于生成和仿真图像识别过程的基本模型。引入的用于生成描述性算法方案的信息结构的类型特征如下：1）结构元素集由两个子集组成：a）功能块的子集，这些子集执行信息处理的数学运算，以实现处理所使用的信息，分析和图像识别方法；b）信息处理程序的控制块的子集，它验证处理程序分支的逻辑条件，是否满足停止信息处理的规则等；2）与结构集合的元素有关的关系，主要是确定执行顺序的局部排序关系以及将结构的功能块和控制块组合在一起的方法；3）根据定义，这些关系必须满足图像分析和理解描述方法的公理。本文介绍了与引入新信息结构相关的基本定义，并描述了其中实现的信息处理过程以及主要的块和循环。给出了信息结构和迭代循环的框图。所描述的研究结果对于发展图像分析的数学理论及其科学新颖性的根本重要性与问题的提出和模型开发有关，当输入数据的形式化表示形式不佳时，图像分析的自动化过程将得以建立。 ，包括空间数据-图像及其片段，图像模型，不完全形式化的表示及其组合的子集。引入一种新的信息结构作为标准结构，用于：a）用于分析和识别二维信息的算法表示，以及用于将图像的双重表示构造为描述性算法方案的过程的表示；b）（a）中指示的描述性算法方案的生成将有可能归纳和证实已知的启发式识别算法，对其进行比较分析，并评估其数学性质和应用实用性。首次提出了描述性算法图像识别方案的自动构建和分析问题。