Descriptive Image Analysis: Part II. Descriptive Image Models

Abstract

The article is the second in a series on the current state and prospects of Descriptive Image Analysis, which is the leading branch of the modern mathematical theory of image analysis. Descriptive image analysis is a logically organized set of descriptive methods and models for analyzing and evaluating information in the form of images and for automating knowledge and data extraction from images necessary for making intelligent decisions about real-world scenes displayed and represented in an analyzed image. Problems on making intelligent decisions based on data analysis require formal representation of the source information, ideally, a mathematical model. Image modeling has a long, but not very productive history. Therefore, in the Descriptive Approach to image analysis and understanding (DA), the primary problem is bringing an image to a form suitable for recognition. The DA interprets the sought representation in the form of a descriptive image model (DIM). Due to the extremely complex informational nature and technical features involved in the digital representation of an image, it is impossible to construct a classical mathematical model of an image as an information object. To overcome this complexity and regularize the problem of bringing an image to a form convenient for recognition, a new mathematical object, a DIM is introduced and used in the DA. Models of recognition objects—images—and definitions of transformations over image models are considered. A formalized concept of descriptive image models is proposed. The results can be used to create a basis for methods of transforming and understanding an image as a mathematical object. The article’s main contribution to developing the mathematical theory of image analysis is understanding of an image as an information object and mathematical object.