Automated System for Evaluating 2D-Image Compositional Characteristics: Mathematical Model

Abstract

Mathematical model creation was presented in a previous publication of the authors. It is the concept of an automated system for estimating the compositional characteristics of 2D images. Rudolf Arnheim's experiment to determine the visual weight of objects using the structural plan of a square and a dark disk is repeated using a mathematical representation of the concepts given in the book "Art and Visual Perception". The structural plan is used as a frame of reference, which has key points, lines and coordinates. The parameters of objects and formulas for calculating the magnitude of the perceptual forces influence are described. A method for estimating the balance of a visual scene is proposed. The mathematical model of Arnheim’s experiment is represented in different stages, with a different position of the object in the visual scene relative to the source of perceptual force being investigated. The factors that affect object’s perception within the structural plan, and the features of the key positions of the objects are explained. An experimentally constructed function to determine the visual weight of an object is proposed depending on the distance to source of the perceptual forces. Akima spline interpolation method was used for obtaining a qualitative graph of the function, devoid of "oscillations" near extremes and with sharp changes in values. The alternative graphs of functions for various sources of influence of perceptive forces are offered, and the difference in the principles of the action of different sources is explained. The coefficients for different perceptive factors and sources of influence are introduced, which will ensure accurate tuning of the system. A method for adjusting the coefficients of the system is proposed. The obtained mathematical model confirms the possibility of program realization of the methods proposed by Arnheim.