Reconstruction of functions and digital images using sign representations

Abstract

The paper deals with the reconstruction of implicitly defined functions or digital images. Functions are defined using observations, each of which is the result of a pairwise comparison of the function values for two random arguments. The analysis of the current state of research for particular statements of this problem is presented: the method of pairwise comparisons used in decision-making for a finite set of alternatives; reconstruction of preference/utility function in multicriteria tasks; sign representations of images used for the description and analysis of digital images. A unified approach to reconstructing functions and images according to their sign representations is proposed, based on mapping in a high-dimensional space and constructing a linear (when reconstructing a function and images) or non-linear (including non-parametric) classifier (when reconstructing preferences). For a number of classification algorithms, experimental studies have been conducted to evaluate the effectiveness of the proposed approach using the example of the reconstruction of the utility function in problems of decision theory and reconstruction of the brightness function of real images.