## 1 Introduction
This approach allows users to feel more comfortable and natural when browsing and interacting, optimizes information communication, enhances interface aesthetics, improves user experience and satisfaction, and ultimately promotes the sustainability of public service interfaces. Scholars have explored the technical optimization, interactive experience, and interface evaluation of virtual museums. However, there is a notable lack of evaluation research from the perspectives of both human aesthetic experience and visual behavioral habits. Furthermore, quantitative studies on the correlation between these two aspects are even scarcer. [PERSON] et al. [12] focused on optimizing virtual museum systems using extended reality (XR) technology, aiming to enhance platform stability. [PERSON] et al. [13] utilized virtual reality to restore and expand exhibit content, thereby optimizing the user experience when viewing artwork. In terms of interactive experience optimization, [PERSON] et al. [14] advocated for a \"user-centered\" approach, emphasizing how users engage with virtual museums and their resources. Regarding the evaluation of virtual museum interfaces, [PERSON] et al. [15] proposed a VRID design model for interactive interfaces, categorizing interface design into graphical elements, interactive feedback, and behavioral performance. [PERSON] et al. [16] provided seven guidelines for interface design, focusing on layout positioning and interaction feedback, using methods such as heuristic evaluation, interviews, and usability testing. [PERSON] et al. [17] conducted a case study revealing that icon visual design significantly enhances user experience in navigating and searching for information. The gray model effectively elucidates the mapping relationship between interface layout aesthetics and users' visual cognitive features. Additionally, the gray H-convex correlation model offers significant advantages over other gray models [18]. We provide a comparative analysis in the subsequent sections. However, it is important to note that the gray H-convex correlation model has a limitation in that it ignores the influence of indicator weights. To address this, our study employs the ICRITIC (improved criteria importance through intercriteria correlation) method to optimize the model. The ICRITIC method is superior to the original CRITIC (criteria importance through intercriteria correlation) method due to its more reasonable weight acquisition process. Therefore, this paper proposes an improved gray H-convex correlation model based on the ICRITIC method to solve the correlation problem between aesthetic features and visual cognitive features of interface layouts, which represents a pioneering attempt in this area. The remainder of this paper is arranged as follows. Section 2 reviews related studies on interface layout aesthetics and visual perception, delineates our motivation and methodology, and presents the overall framework of this study. In Section 3, we establish an evaluation index system for interface layout, focusing on both aesthetics and visual cognition. Section 4 details the construction of an improved gray H-convex correlation model to determine the mapping relationship between layout aesthetics and visual cognition. Section 5 validates our proposed method by applying it to virtual museum interfaces from various provinces in China, thereby assessing its suitability as a standard for future interface design. Finally, Section 6 summarizes the study's findings, discusses its limitations, and proposes directions for future research.