Mathematical model and method for generating the perceptual state of web pages based on rendering

Source abstract

The subject of this study is the process of formalizing and generating a perceptual representation of web pages as a reflection of their state in user perception within a dynamic web environment. The aim of the work is to formalize the perceptual state of a web page and to develop a reproducible method for its generation based on rendering results. To achieve this goal, the study addresses the following tasks: defining sufficient requirements for perceptual web page representation that account not only for document structure but also for rendered output in the execution environment; developing a model of the perceptual state of a web page capable of integrating geometric, stylistic, and structural characteristics of interface elements as well as relationships between them; developing a similarity metric for perceptual representations that combines geometric and textual components to assess correspondence between different page states; developing a method for generating perceptual representations based on web page rendering while considering visibility, spatial arrangement, and inter-element relationships; and experimentally evaluating the proposed approach by determining its invariance to technical modifications and sensitivity to perceptual transformations of web interfaces. The study employs methods from graph theory, geometric analysis, text processing, similarity metrics, elements of set and relation theory, and experimental data analysis in a temporal environment. Results. A model of the perceptual state of a web page is proposed as an attributed graph integrating the geometric, stylistic, and structural characteristics of interface elements. A method for generating this representation based on page rendering is developed, accounting for visibility, spatial composition, and the mutual arrangement of elements. A similarity metric that combines geometric and textual components is proposed to assess the proximity of page states. An experimental evaluation on a temporal dataset demonstrated that perceptual representation is more robust to HTML markup changes and more sensitive to layout transformations than text-based, visual, and DOM-oriented approaches. Conclusions. The proposed approach enables a shift from analyzing the technical structure of web pages to analyzing their perceptual state as a formalized object. The developed model provides a foundation for building interpretable and robust data extraction systems, analyzing web content changes, and developing agent-based systems for interaction with web environments. Practical application of the results can improve the stability and explainability of methods for processing dynamic web pages.