Three-Dimensional Model Reconstruction and Layout Optimization in Virtual Museums Using Spatial Intelligence Algorithms: An Analysis of User Visual Impact

Abstract

Digital technology has facilitated substantial progress in the development and implementation of virtual museums. Despite these advancements, current virtual museums continue to face challenges in spatial layout and information presentation, including limited exhibit hierarchy, inefficient spatial organization, low information display efficiency, and sub-optimal visual experiences. To address these challenges, spatial intelligence algorithms are utilized to reconstruct three-dimensional models of selected cultural relics for scene creation and to optimize the spatial layout of virtual museum exhibits. The layout optimization approach considers both symmetrical and asymmetrical arrangements, as well as visual hierarchy and information density. This approach aims to establish a more complex exhibit hierarchy, rational spatial organization, and enhanced visual information display. Comparative experiments and analyses of the visual impact from symmetrical layout optimization, along with other spatial layout optimizations, are conducted. User evaluations and eye-tracking experiments indicate that spatial intelligence-optimized algorithms improve both spatial layout and information display in virtual museums, leading to a more positive user visual experience.

1. Introduction

The integration of virtual reality technology into museums has become increasingly widespread due to ongoing technological advancements. Virtual museums, which utilize digital transformation technologies such as virtual reality, artificial intelligence, and interaction engines [1], play a significant role in the preservation of cultural heritage [2]. These platforms provide enhanced flexibility in scene–space layout, personalized navigation, 3D model construction, and display methods, as evidenced by the China Sanxingdui bronze virtual museum [3], the virtual exhibition hall of the China Museum [4], and the virtual experience space of the China Grand Canal Museum [5]. The combination of visual interaction, perceptual feedback, and related technologies creates an immersive and interactive browsing experience. Virtual museums facilitate deeper engagement with cultural heritage by offering immersive visual art experiences, which have emerged as a prominent research focus in recent years [6,7]. Moreover, artificial intelligence [8] and data-driven approaches are critical for optimizing the spatial layout and information architecture of virtual museums. For example, Wang examines the application of artificial intelligence in digital museum space design to achieve high-quality spatial, visual, and esthetic outcomes [9]. Vasic et al. employ artificial intelligence to automatically analyze and predict user behavior patterns to enhance user experience [10]. Puspasari et al. [11] evaluate the use of intelligent algorithms based on machine learning classifiers for exhibition recommendation and virtual touring. Aliyev et al. [12] apply data-driven optimization to dynamically adjust exhibition layouts based on visitor movements and interactions. Spatial intelligence algorithms are particularly important for optimizing virtual museum environments.

Despite advancements, virtual museums continue to encounter challenges related to spatial layout and user experience, including monotonous exhibition arrangements, insufficient spatial hierarchy, and exhibition modules that operate independently from panoramic roaming systems [13]. The authentic experience of museum visitors depends on cultural relics, the surrounding environment, and activities, which correspond to exhibits, spatial layout, and information interaction in virtual museums [14]. These elements collectively shape users’ perceived authenticity in virtual museum settings. Visitor engagement in virtual museums is primarily influenced by visual effects, interactivity, the quantity and content of exhibits, technological features, and environmental factors [15]. Spatial layout is particularly significant for the visual experience, yet manual exhibit positioning is both labor-intensive and inefficient. Consequently, automatic positioning algorithms and systems have been developed for virtual museums. For instance, Kim et al. [16] introduced a virtual exhibition system capable of clustering and locating artworks based on key attributes such as theme, color, material, and artist. Research further demonstrates that exhibition space, guided tour routes, and information interaction are critical determinants of user satisfaction in virtual museums [17]. To evaluate user experience, questionnaire-based assessments are frequently employed to measure functionality and usability [18,19]. In addition, scientific experimental methods such as eye tracking [20] and electroencephalography (EEG) [21] are utilized to investigate visual perception and psychological responses. Notably, visual attention patterns identified through eye-tracking experiments offer valuable guidance for optimizing the layout and interaction of visual elements in virtual museums [22]. Some researchers have used eye-tracking datasets to enhance the visual experience of virtual museums based on these attention patterns [23,24]. Other studies combine questionnaire evaluations with eye-tracking or EEG methods to provide a more comprehensive analysis of users’ visual and emotional experiences in virtual museums [25,26].

Existing research has primarily addressed technical implementation, such as 3D modeling and interaction design, while offering limited systematic analysis of the impact of spatial layout on users’ visual experience and perceived authenticity. Most studies concentrate on specific aspects, including 3D reconstruction or user evaluation, and do not present a comprehensive methodological framework that integrates model reconstruction, layout optimization, and user experience feedback. In particular, research on leveraging user behavior data to adjust spatial layout in real time remains underdeveloped. To advance research in this field, we have developed a methodological framework that combines 3D model reconstruction, layout optimization algorithms, and user experience feedback, including Likert-scale questionnaires and eye-tracking experiments. This framework enables a comprehensive analysis of how spatial layout optimization influences users’ visual experience and perceived authenticity, and provides an objective evaluation using eye-tracking data. This study explores intelligent algorithms for 3D model reconstruction and layout optimization in virtual museums. It assesses their accuracy and efficiency through technical applications and evaluates their impact on user visual experience through experiments. The goal is to address challenges such as low efficiency, subjective bias, and difficulty adapting to dynamic requirements in manual positioning. This article uses the virtual museum of “Five Kilns of the Song Dynasty” as a case study to present research findings that guide virtual reconstruction and spatial layout design for cultural relics museums. These findings highlight the scientific contribution of this study to the field.

2. Overview of Spatial Intelligence Algorithms Applied in Virtual Museum

Spatial intelligence algorithms process and interpret spatial data to extract valuable information, including location, object shape, and topological relationships [27]. These algorithms integrate principles from computer science, mathematics, and geography, employing mathematical models and computational logic to address challenges related to spatial location, such as spatial construction, layout, and structure optimization. These applications depend on core technologies such as spatial relationship reasoning, three-dimensional spatial computing, image generation, and data fusion. By leveraging spatial intelligence algorithms and digital technologies, virtual museums can replicate physical exhibitions, creating cultural experience spaces that are familiar, perceptible, and interactive for visitors. This study introduces and applies a novel set of algorithms for the layout and optimization of virtual museum spaces, as presented in

Table 1. The proposed spatial intelligence algorithms set.

Spatial intelligence algorithms set	Model construction algorithm set	Neural surface reconstruction (NeuS): MLP + CNN	Geometric model generation
		Intelligent material mapping algorithms: GAN	Model material generation
		LOD simplification algorithm	Model display accuracy optimization
	Layout optimization algorithm set	PSO	Exhibition positioning
		symmetry quantification formula	Symmetrical layout optimization
		Color visual weight formula	Color tone optimization
		local density uniformity formula	Layout density optimization

.

Several key methods exist for optimizing the spatial layout of virtual museums through spatial intelligence algorithms. First, these algorithms enable theme partitioning, layout planning, and automatic positioning of exhibits. For instance, exhibits may be categorized into areas such as ancient cultural relics and modern art, with the spatial configuration of each area analyzed prior to exhibit placement. While traditional exhibition halls often employ symmetrical layouts, art and technology exhibition spaces may utilize asymmetrical designs. Second, spatial intelligence algorithms optimize exhibit placement by simulating audience paths and visual focal points, thereby aligning with users’ visual habits. Key exhibits are positioned in locations that naturally attract attention, such as the center of the virtual museum or prominent nodes along the viewing route. Third, these algorithms facilitate dynamic adjustment of spatial layout, display density, or color tone within the user’s line of sight, responding to real-time changes in browsing routes and user location. This dynamic adaptation enhances the efficiency and engagement of visual information presentation. The present study introduces a novel set of intelligent layout strategies. In comparison to existing research, the proposed layout algorithm is more systematic and comprehensive, integrating rationality, balance, and visual esthetics, with a heightened emphasis on user visual experience, as demonstrated in

Table 2. Comparison between this study and existing cutting-edge spatial layout research.

Literature	Key Tools and Algorithms	Method	Function
Chen et al. [28]	conceptual prototype of VirtuNarrator	Propose a layout framework that includes three distinct narrative levels	Multi-perspective experience and perception
Kim et al. [16]	Genetic optimization algorithm	Cluster analysis and automatic localization	Theme clustering layout and optimization
Li [29]	Monte Carlo sampling method	Using constraint functions and density functions	Quick positioning and balanced layout of exhibits
Li and Wu [30]	Interactive Genetic Algorithm	Scene information extraction and coordinate transformation	Accurate layout that matches the layout nodes
This study	Space Layout Optimization Algorithm	Symmetrical layout, layout density, and color tone optimization	Automatic positioning and layout with visually balanced and esthetically pleasing

.

Guided by the technology framework of spatial intelligence algorithms, the “Five Kilns of the Song Dynasty” virtual museum was used as a case study to conduct a comprehensive process encompassing scene construction, model reconstruction, layout optimization, and experimental evaluation, as shown in Figure 1.

3. Three-Dimensional Model Reconstruction

Spatial intelligence algorithms enable high-precision 3D modeling of cultural relics in virtual museums, facilitating the restoration and reconstruction of damaged artifacts over time and providing high-definition visualization of their details.

3.1. Algorithm

The process of virtually reconstructing cultural relics in a virtual exhibition hall involves the application of spatial intelligence algorithms. Neural surface reconstruction (NeuS) is employed to generate geometric models of the virtual cultural relics. Intelligent material mapping algorithms are then used to produce model materials. ZBrush refines material details, and a level of detail (LOD) simplification algorithm is applied to simplify the model in layers [31]. Figure 2 illustrates the specific network models, tools, and methods used in this process.

The neural surface reconstruction algorithm [32,33,34] for 3D model generation implicitly represents the geometry and appearance of a 3D model using neural networks. This approach utilizes a Multilayer Perceptron (MLP) [35], a fully connected neural network with multiple hidden layers, to convert 2D image point vectors into 3D spatial coordinates. A Convolutional Neural Network (CNN) [36] extracts features from the input image and key feature points, which are subsequently passed to the MLP. The key feature point $x_i$ in the 2D image is transformed into a corresponding query point $o_i$ in 3D space, and a global neural network integrates these features to generate a 3D spatial model. The 3D transformation process for 2D key feature points using the MLP can be described as follows:

$$o_i=MLP\left(x_i,I,\theta \right)$$

(1)

where $I$ denotes the input image; $\theta$ is the weight parameter of the CNN. The weight parameter is obtained from prior network model training and encapsulates the image features learned by the CNN from the training dataset. The primary objective of neural surface reconstruction is to accurately reconstruct three-dimensional geometric shapes by extracting and analyzing geometric features from images of cultural relics using a CNN. These features include shape, structure, contour, and surface undulations. The resulting ‘white mold’ is a purely geometric model that omits color and material information.

The subsequent stage involves material generation, which employs intelligent material mapping algorithms to assign materials to the generated geometric models. The algorithm automatically identifies and segments distinct regions, such as porcelain glaze and metal patterns, and analyzes geometric features including surface curvature and normal direction. Materials are then assigned based on these features. Following feature matching, relevant material parameters—such as base color, metallicity, roughness, and other physical properties—are retrieved from the physically based rendering (PBR) material library. These parameters are input into generative adversarial networks (GANs) [37] for material generation and matching, resulting in the integration of materials into a unified model. This process transforms the geometric white mold into a virtual artifact with realistic textures and dynamic light and shadow effects. The material matching and generation algorithm can be described as follows.

$$\mathit{Material}\left(a\right)=G\left(z,\mathit{Geometry}\left(a\right),T\right)$$

(2)

where $G$ denotes the generative adversarial network employed for material generation. $a$ indicates distinct material regions; $\mathit{Geometry}\left(a\right)$ refers to the geometric features of each region; $z$ is a material random variable; $T$ represents the material parameter retrieved from the physically based rendering (PBR) material library based on the matching outcome. The cultural relic models produced by these methods may require further refinement. Detailed adjustments can be made using the design software ZBrush 2023.2. Modifying the material texture and shape details enables the generated 3D model to more accurately replicate the original appearance of the cultural relic.

Model optimization is performed to ensure that the generated 3D model can be efficiently rendered and interacted with across various terminal devices. A multi-level detail (LOD) optimization algorithm dynamically adjusts model complexity according to the user’s viewing distance and system performance. For example, a simplified model is used to maintain performance when viewed from a distance, while a high-precision model is employed to display details at close range. The algorithm further refines the model’s multi-level detail $LO{D}_{\mathit{level}}$ based on the visual error $E$ between the user’s perspective and the actual model size under specific display conditions. The following outlines the specific method.

$$LO{D}_{\mathit{level}}=\left\{\begin{array}{ll}0& \mathit{if} E\le E_0\\ 1& \mathit{if}{ E}_0<E\le E_1\\ 2& \mathit{otherwise}\end{array}\right.$$

(3)

where the values 0, 1, and 2 correspond to the highest-quality, medium-quality, and low-quality model displays, respectively. The high-quality and medium-quality visual error thresholds, denoted as $E_0$ and $E_1$ respectively, vary by display device. For example, these thresholds are set to 2 and 8 for computer screens, and 1 and 4 for VR device terminals. When the current visual error $E$ of the device is less than the high-quality visual error threshold $E_0$, the virtual scene displays a high-quality 3D model. If the current visual error exceeds the low-quality visual error threshold $E_1$, a low-quality 3D model is displayed. Values between these thresholds result in a medium-quality model display. Device visual error is calculated as the ratio of the model’s display size within the user’s current line of sight to the screen space ratio. The specific calculation method is as follows:

$$E={\displaystyle \frac{S·R·W}{D·tan\left(\frac{\mathit{FOV}}{2}\right)}}$$

(4)

where $S$ denotes the object modeling dimensions; $R$ refers to the resolution coefficient that indicates the device’s pixel density; and $W$ represents the visual importance weight, which quantifies the visual attention allocated to cultural relic models in the current scene. $S·R·W$ is used to calculate the display size of the model within the user’s current line of sight on a specific device. $D$ indicates the straight-line distance from the user’s viewpoint to the center of the cultural relic. $\mathit{FOV}$ specifies the angle of the vertical field of view; for instance, the value for a computer screen is π/3, corresponding to 60 degrees, while for a VR device it is π/2, corresponding to 90 degrees. $D·tan\left({\displaystyle \frac{\mathit{FOV}}{2}}\right)$ is applied to convert the visual distance into a screen-space ratio. This comprehensive parameter system allows virtual museum displays to optimize the balance between computational resources and user visual experience, thereby ensuring both authenticity and smoothness in the presentation of cultural relic models.

3.2. Implement

To evaluate the effectiveness of the proposed algorithm, we developed a virtual museum themed on the “Five Kilns of the Song Dynasty”. Spatial intelligence algorithms were employed to generate three-dimensional models of selected cultural relics for scene construction. First, 3D scenes are constructed in the Unity Engine according to the architectural floor plan to establish a virtual museum environment. And then, 3D models of selected cultural relics are generated and positioned within the scene. Neural surface reconstruction algorithms are employed to produce the base models, and intelligent material-mapping algorithms are applied to generate realistic surface materials.

3.2.1. Three-Dimensional Scene Creation

The process begins by generating a virtual museum scene to establish a foundation for the placement of cultural relic models and the overall spatial layout. A floor plan of the virtual museum is created (see Figure 3a), and a basic color palette is selected. The primary color tones of the virtual museum are dark gray and blue, with dark gray dominating the overall scene environment. Strategic lighting is employed to enhance the visual impact of the cultural relics. Based on the floor plan, a virtual museum scene is constructed (see Figure 3b), and the layout is refined to ensure coordination and meet visual requirements throughout the creation process. The Unity engine is utilized for scene construction, which includes the development of walls, display cabinets, guide posters, and lighting arrangements.

3.2.2. Three-Dimensional Model Reconstruction and Visual Optimization Experiment

We conducted a three-dimensional reconstruction experiment using the Blue Glazed Fish Ear Furnace from the Ge Kiln of the Song Dynasty as a case study. The resulting cultural relic model demonstrates accurate appearance and decorative details, and the visual effect is realistic, as shown in Figure 4.

The experimental procedure and algorithmic workflow for 3D model reconstruction and material generation for cultural relics can be described as follows. First, the neural surface reconstruction algorithm for 3D model generation employs a convolutional neural network (CNN) to analyze geometric features of the image, such as normal lines, shapes, and object sizes, to extract the 2D points of the image. The 2D image point $x_i$ is subsequently processed by a multilayer perceptron (MLP), which transforms the 2D image point $x_i$ into the corresponding 3D model point $o_i$. This transformation incrementally generates the required white model, as described by Equation (1). Second, the intelligent material mapping algorithm creates materials for the geometric white mold by using a CNN for image material segmentation. Physically based rendering (PBR) is then used to retrieve material parameters that match the image, such as those for rusted bronze ware. The retrieved material parameters are imported into a generative adversarial network (GAN), which, in combination with an image fusion module, generates a complete model material based on image feature matching. This process is governed by Equation (2). Third, after refining the appearance and texture details using the ZBrush tool, the model is imported into a virtual scene. The level of detail (LOD) simplification algorithm is applied to perform layered visual optimization of objects, adjusting model quality according to user visual error across different device scenarios. For instance, on the PC platform, visual error thresholds are set at 2 and 8 pixels. The relevant algorithms are described in Equations (3) and (4). When the visual error $E\le 2$, the model is displayed in high quality; when the visual error $2<E\le 8$, the model is displayed at medium quality; and when the visual error $E>8$, the model is displayed in low quality.

4. Spatial Layout Optimization for Virtual Museum

To investigate the mechanisms and effects of spatial intelligence algorithms in optimizing virtual museum layouts, these algorithms are applied to improve exhibition arrangements and enhance the visual experience of users.

4.1. Spatial Layout Optimization Algorithm

The particle swarm optimization algorithm (PSO) [38] is employed to optimize the spatial layout of virtual museums, with each particle representing the specific location of an exhibit. PSO serves as an efficient tool for automatic decision-making and optimization in virtual museum layouts, converting complex, experience-dependent processes such as exhibition arrangement, visitor guidance, and photography planning into quantifiable mathematical optimization problems. The layout of exhibits is initially described as a collection of multiple exhibit locations, such as

$$P\left(X\right)=(p_1,p,\dots ,p_N)$$

(5)

where $P\left(X\right)$ indicates the overall layout of the exhibits collection $X$, represented as an array containing the position coordinates of $N$ exhibits. $p_i$ refers to the position coordinates of each individual exhibit, which may be expressed as one-dimensional data in a linear layout, two-dimensional data in a matrix layout, or three-dimensional data in a spatial three-dimensional layout. The positioning method for virtual museum exhibits is determined by the specific requirements of layout planning, and subsequent layout optimization is performed as needed. Common optimization strategies focus on enhancing the uniformity, symmetry, and density of the exhibit arrangement.

4.1.1. Symmetrical Layout Optimization Algorithm

The symmetry layout optimization algorithm quantitatively evaluates the degree of symmetry in exhibit layouts, resulting in a harmonious and balanced visual effect. The symmetry quantification formula produces

$$F_{\mathit{symmetry}}(X)={\sum }_{i=1}^N{||\mathit{reflect}(p_i,\mathit{axis})-p_j||}^2$$

(6)

where $\mathit{reflect}(p_i,\mathit{axis})$ denotes the mirror position coordinates of the $i$-th exhibit, and $p_j$ indicates the position of the exhibit closest to the mirror position that can be identified. The formula calculates the total symmetry error, $F_{\mathit{symmetry}}\left(X\right)$, between the mirror positions of each exhibit and their respective nearest actual positions, thereby quantifying the degree of asymmetry in the overall layout. A smaller value indicates greater symmetry. The mirror function is defined as follows:

$$\mathit{reflect}(p_i,\mathit{axis})=p_i+2\times (p_o-p_i)·\overrightarrow{n}$$

(7)

where $p_o$ denotes the coordinate of the axis point. $\overrightarrow{n}$ represents the normal vector of the axis of symmetry, which specifies the direction of symmetry.

4.1.2. Layout Density Optimization Algorithm

Exhibit density significantly influences the efficiency of users’ visual information search and their cognitive load. A local density adjustment algorithm is employed to determine the optimal exhibit layout density. The method for calculating the density value is as follows.

$${\mu }_d=2R/N$$

(8)

where $R$ denotes the radius of the exhibition hall layout. The virtual museum predominantly employs a linear layout across multiple exhibition halls. Within the exhibition hall layout space defined by radius $R$, the exhibit layout density is controlled by adjusting the independent variable $N$. Furthermore, the local density uniformity formula is applied to regulate the uniformity of the exhibit layout, resulting in

$${\mathit{Var}}_{\mathit{density}}={\sum }_{i=1}^N{\left(D_i-{\mu }_d\right)}^2/N$$

(9)

where $D_i$ represents the density value of the $i$-th sample. The variance of the density values ${\mathit{Var}}_{\mathit{density}}$ is calculated using this method. A higher variance indicates a more uneven distribution, while a lower variance suggests a more uniform density distribution. The specific calculation method for $D_i$ is as follows.

$$D_i=(\left|p_{i+1}-p_i\right|+\left|p_{i-1}-p_i\right|)/2$$

(10)

where $p_{i+1}$ and $p_{i-1}$ denote the linear coordinates of the adjacent exhibits located on the left and right sides of the exhibit, respectively.

4.1.3. Spacing Uniformity Optimization Algorithm

The exhibit layout is optimized using the spacing uniformity function to ensure consistent spacing between exhibits, reduce cognitive load, enhance user immersion, and achieve a visually uniform and balanced presentation. The spacing uniformity function for the layout of the exhibits collection $X$ is defined as follows:

$$F_{\mathit{spacing}}(X)={\sum }_{i=1}^{N-1}{\left(\right|p_{i+1}-p_i|-d_{\mathit{optimal}})}^2$$

(11)

where $|p_{i+1}-p_i|$ denotes the actual distance between the $i$-th exhibit and the ($i$-th)th exhibit. $d_{\mathit{optimal}}$ represents the optimal spacing, which defines the ideal viewing distance between two exhibits and serves as a core variable in virtual museum layout design. This parameter addresses both physical collision prevention and, more importantly, the enhancement of the viewing experience, thereby improving the layout’s esthetic quality and logical coherence. The formula for the optimal spacing parameter is as follows:

$$d_{\mathit{optimal}}=k_{\mathit{safety}}\times \left({\mathit{max}}_{\mathit{dim}}\right(i)+{\mathit{max}}_{\mathit{dim}}(i+1\left)\right)/2+\delta$$

(12)

where $k_{\mathit{safety}}$ denotes a safety factor, typically ranging from 1.2 to 2, which prevents visual overlap of exhibits and maintains a minimum safety distance. ${\mathit{max}}_{\mathit{dim}}\left(i\right)$ represents the maximum size of the $i$-th exhibit. Larger exhibits necessitate greater spacing, whereas smaller exhibits may be positioned more closely. The parameter $\delta$ refers to the basic margin, generally between 0.2 and 1 m, to ensure a comfortable visual distance.

4.2. Spatial Layout Optimization Practice

The visual experience of users in virtual museums is shaped by several factors, such as spatial layout, color, and information density. Spatial layout determines the positional relationships and the pathways for visiting exhibits. Color differences influence the visual hierarchy within the exhibition, while information density reflects the richness of the content presented. These factors directly impact user visual guidance, information acquisition, and immersion. This study applies spatial intelligence algorithms to optimize the primary spatial layout elements of virtual museums—exhibit arrangement, visual hierarchy, and information density—to improve the overall user visual experience.

4.2.1. Symmetrical Layout Optimization

The primary approach to layout optimization is the use of symmetrical layout strategies, which employ axisymmetric forms to organize exhibits within a single exhibition hall. Axis symmetry relies on the arrangement of objects along the central axis, with exhibits of similar shape, size, and theme positioned on either side. Symmetrical layouts, characterized by lower complexity and a heightened sense of order compared to asymmetric layouts, improve users’ visual esthetics and comfort. The selection between symmetrical and asymmetrical layouts significantly influences the perceived order and dynamism within virtual spaces. In the symmetrical layout optimization algorithm, the geometric center of the virtual exhibition area serves as the origin for constructing axisymmetric or centrosymmetric models, thereby ensuring the symmetrical distribution of exhibits in both size and position.

Symmetrical layout optimization is employed in a virtual exhibition hall, which utilizes a linear layout with the central axis serving as the axis of symmetry. The symmetry quantification algorithm, as defined in Equations (6) and (7), is applied. The position coordinates $p_j$ of exhibits are adjusted near their respective mirror positions, and the symmetry error $F_{\mathit{symmetry}}\left(X\right)$ is iteratively minimized to optimize the symmetry of the museum exhibit layout. This process establishes regularity and order, as illustrated in Figure 5, thereby enhancing information acquisition efficiency, visual esthetics, and user comfort.

4.2.2. Color Tone Optimization

The visual hierarchy of a virtual exhibition hall can be optimized by adjusting color tone, a critical factor influencing the perception of virtual spaces. This study applies a color visual weight formula to improve both color tone and visual hierarchy, which yields

$$W_{{\mathit{color}}_i}={\mathit{Saturation}}_i\ast {\mathit{Value}}_i\ast \left(1+\left|{\mathit{Warmness}}_i\right|\right)$$

(13)

where ${\mathit{Saturation}}_i$ denotes the overall color saturation of the $i$-th exhibit, ${\mathit{Value}}_i$ indicates its overall brightness, and ${\mathit{Warmness}}_i$ refers to the color tone temperature. The system adjusts the color temperature of cultural relics by modifying the comprehensive visual weight ${\mathit{Warmness}}_i$ according to this method. This approach accommodates variations in lighting within the virtual exhibition hall and enhances users’ color perception, as illustrated in Figure 6.

4.2.3. Exhibit Layout Density Optimization

The exhibit layout density for a virtual exhibition hall, which employs a linear layout, can be optimized using a density optimization algorithm based on Equations (8)–(10). This algorithm adjusts the exhibit layout density by varying the number of exhibits $N$ within a specified radius of the exhibition hall ($R=2$). Subsequently, a distance uniformity algorithm based on Equations (11) and (12) is applied to achieve a uniform distribution by adjusting the positions of each exhibit, as illustrated in Figure 7. According to the algorithm, increasing the value of $N$ results in a tighter layout, while decreasing $N$ produces a sparser arrangement. Adjusting $N$ allows for control over the density of the exhibition hall layout to enhance the user’s visual experience. Consequently, eye tracking experiments can be conducted to determine the optimal value of $N$ for a fixed-radius exhibition hall. Although intelligent algorithms produce an optimized layout, the result may appear overly uniform and mechanical. Therefore, incorporating manual positioning adjustments can enhance the diversity and engagement of the exhibition layout.

5. User Evaluation of Visual Experience in Virtual Museums Through Intelligent Space Layout Optimization

Layout optimization is applied to specific exhibition halls within the virtual museum using the aforementioned algorithm. The optimization process includes: (1) enhancing the symmetry of exhibition hall O in Figure 3 by applying the symmetry quantification formula; (2) improving the visual hierarchy of exhibition hall O by utilizing a color tone enhancement algorithm to increase the warm color tones of the exhibits; and (3) optimizing the exhibit layout density in exhibition hall O by integrating a density optimization algorithm with a spacing uniformity formula. Subsequently, subjective user evaluations are conducted to assess the overall visual experience resulting from intelligent spatial layout optimization in the virtual museum.

5.1. User Experience Evaluation Methods and Indicators

The subjective assessment questionnaire was administered to 30 graduate and undergraduate students, none of whom had prior experience with virtual museums. The valid sample comprised 24 participants, including 10 males and 14 females. Participants experienced the virtual museum both before and after optimization. Subsequently, they rated seven user experience indicators on a 1–5 scale, with ratings recorded to two decimal places. The Likert scale used was defined as follows: 1 indicated an inferior experience, 2 indicated a poor experience, 3 indicated an average experience, 4 indicated a good experience, and 5 indicated an excellent experience. Higher scores reflected a more positive overall user experience. The seven subjective evaluation indicators and their definitions are presented below.

(1)

Visual attractiveness (VA) denotes the quality of visual design in digital exhibition interfaces and the presentation of cultural relics. It encompasses multidimensional sensory effects, including color coordination, esthetic appeal, and material detail, which rapidly capture users’ attention and foster positive initial impressions.

(2)

Esthetic fun (AF) refers to the esthetic pleasure and cognitive interest experienced by users when viewing cultural relics. It reflects the extent to which the presentation of exhibits is engaging, stimulates imagination and emotional resonance, and sustains a high level of interest and participation in the aesthetic experience.

(3)

User immersion (UI) refers to a profound state of engagement within a virtual environment, marked by intense attentional focus, diminished awareness of time, and a comprehensive emotional and cognitive experience that culminates in a state of “flow”.

(4)

Layout rationality (LR) assesses whether the arrangement of elements, including exhibits, signage, and interactive controls, within a virtual exhibition space is logically precise, coordinated, and unified. It also considers whether users can easily comprehend the spatial structure and navigate or interact with the environment efficiently.

(5)

Exhibit richness (ER) denotes the quantity, variety, and depth of information regarding cultural relics and related content presented in an exhibition. It also assesses the extent to which this information fulfills users’ needs for learning and exploration concerning cultural background, artifact details, and multidimensional content.

(6)

Experience Smoothness (ES) evaluates system technical performance by assessing interactive response, scene switching, and content loading. This metric ensures the absence of visible graphics lag, delays, or operational barriers, thereby providing a seamless and natural user experience.

(7)

Overall satisfaction (OS) represents a comprehensive subjective assessment of the user experience across multiple dimensions of the virtual exhibition system. It indicates whether the system meets or surpasses user expectations and contributes to a positive perception and overall acceptance.

5.2. User Experience Evaluation Data and Result Analysis

Statistical analysis was performed on the maximum, minimum, and average user ratings of various indicators before and after the optimization of the virtual museum, as illustrated in Figure 8.

Maximum-value statistical analysis indicates that, prior to intelligent optimization of the virtual museum’s space layout, none of the user experience indicators achieved high ratings (≥4.5, representing excellent experience). After optimization, four indicators—UI, ER, ES, and OS—attained high ratings. The greatest improvement occurred in overall user satisfaction (OS), which increased by 0.7 points.

Minimum-value statistical analysis shows that, prior to intelligent optimization of the space layout, the scores for seven indicators of virtual museum user experience were relatively low (≤2.5, indicating average experience). Following optimization, only three indicators—visual attractiveness (VA), learning relevance (LR), and emotional response (ER)—remained low (≤2.5, indicating poor experience). The greatest improvement was observed in esthetic fun (AF), which increased by 0.6 points, while the smallest improvement occurred in visual attractiveness (VA), which increased by 0.2 points.

Mean-value statistical analysis shows that, after intelligent optimization of the spatial layout, multiple user experience indicators for the virtual museum increased by 0.2 to 0.6 points. Overall user satisfaction (OS) improved by 0.6 points, while the other six indicators showed only modest gains. Visual appeal (VA) exhibited the smallest improvement, increasing by 0.2 points.

Combined with the specific distribution of user experience ratings before and after intelligent optimization of virtual museum spatial layout, as shown in Table 1. According to the headcount statistics by rating range, the proportion of persons with common experience (2–3 points) has decreased overall, while the proportion of persons with good user experience rate (3–5 points) and the proportion of persons with excellent user experience rate (4–5 points) have both improved. The rates of excellent user experience for three indicators, including user immersion UI, layout rationality LR, and overall user satisfaction OS, have reached over 15%, while these rates for these three indicators before optimization are all below 10%, reflecting the comprehensive improvement effect of spatial layout intelligent optimization on user visual experience of virtual museum.

Table 3. Distribution of user experience ratings before and after intelligent optimization of the virtual museum spatial layout (The data in the table represents the number and proportion of people).

	Before Spatial Layout Optimization				After Spatial Layout Optimization
Rating Range	1–2 Points /Poor	2–3 Points /Common	3–4 Points /Good	4–5 Points /Excellent	1–2 Points /Poor	2–3 Points /Common	3–4 Points /Good	4–5 Points /Excellent
VA	0 (0%)	18 (75%)	6 (25%)	0 (0%)	0 (0%)	13 (54.2%)	9 (37.5%)	2 (8.3%)
AF	0 (0%)	21 (87.5%)	2 (8.3%)	1 (4.2%)	0 (0%)	16 (66.7%)	6 (25%)	2 (8.3%)
UI	0 (0%)	18 (75%)	4 (16.7%)	2 (8.3%)	0 (0%)	11 (45.8%)	8 (33.3%)	5 (20.8%)
LR	0 (0%)	18 (75%)	5 (20.8%)	1 (4.2%)	0 (0%)	10 (41.7%)	10 (41.7%)	4 (16.7%)
ER	0 (0%)	20 (83.3%)	4 (16.7%)	0 (0%)	0 (0%)	12 (50%)	9 (37.5%)	3 (12.5%)
ES	0 (0%)	16 (66.7%)	6 (25%)	2 (8.3%)	0 (0%)	13 (54.2%)	8 (33.3%)	3 (12.5%)
OS	0 (0%)	18 (75%)	5 (20.8%)	1 (4.2%)	0 (0%)	8 (33.3%)	11 (45.8%)	5 (20.8%)

presents the distribution of user experience ratings before and after the intelligent optimization of the virtual museum spatial layout. The proportion of users reporting a common experience (2–3 points) decreased, while the proportions of users with good (3–5 points) and excellent (4–5 points) user experience ratings increased. The rates of excellent user experience for user immersion (UI), layout rationality (LR), and overall user satisfaction (OS) each exceeded 15% following optimization, compared to rates below 10% for these indicators prior to optimization. These results demonstrate the comprehensive improvement in user visual experience resulting from the intelligent optimization of spatial layout in the virtual museum.

The above research demonstrates significant improvements in the visual experience of virtual museum users through intelligent spatial layout optimization, thereby positively influencing immersion and user satisfaction.

6. An Eye-Tracking Investigation of the Visual Impact of Intelligent Spatial Layout Optimization in Virtual Museums

Visual perception, which serves as the primary channel for acquiring sensory information, can be evaluated using eye-tracking data to measure information extraction efficiency, visual processing level, and visual emotional arousal.

6.1. Eye-Tracking Experiment Research

The influence of intelligent spatial layout optimization on user visual perception within a virtual museum was examined using eye-tracking experiments. Statistical analyses were performed on the eye-tracking data to assess group differences. Spatial intelligence algorithms were employed to optimize layout methods, emphasizing symmetry and asymmetry, visual hierarchy through increased contrast between cool and warm tones, and information density in selected exhibition halls. Participants observed visual stimuli from the virtual museum before and after layout optimization, and the corresponding eye-tracking data were collected and analyzed.

6.1.1. Experimental Procedure

The experimental instrument utilized is a Tobii Pro ErgoLAB 3.0 desktop telemetry eye tracker. Participants consist of 35 students from the first to fourth year at the institution, including 20 males and 15 females, with an average age of 21. All participants are right-handed and possess normal or corrected vision. To evaluate different layout methods for the virtual museum, comparative visual stimuli materials before and after optimization are employed. This approach facilitates a series of eye movement experiments designed to examine the specific impact of spatially intelligent visual optimization algorithms on users’ visual perception within the virtual museum. To ensure objectivity and accuracy in the research conclusions, a single-variable method is implemented, whereby only one algorithm is varied during optimization while all other elements remain constant.

Experiment 1 examined the visual impact of symmetrical layout optimization. The comparative study employed visual stimuli from a scene with symmetrical layout optimization (SLO) in virtual exhibition hall A (see Figure 3) and a non-optimized scene (NSLO). Participants explored the virtual exhibition hall in both conditions, and eye-tracking data were collected for subsequent analysis.

Experiment 2 investigated the visual impact of visual hierarchy optimization. A comparative study utilized visual stimuli from scenes featuring color tone optimized exhibition layouts in virtual exhibition hall B (see Figure 3) (CTO) and from non-optimized scenes (NCTO). Participants viewed and interacted with the virtual exhibition hall before and after visual hierarchy optimization, and corresponding eye-tracking data were collected for subsequent analysis.

Experiment 3 examined the visual impact of layout density optimization. In virtual exhibition hall C (see Figure 3), exhibit layout density was optimized at six distinct levels by varying specific parameters. Exhibit positions were manually adjusted according to these settings to improve layout differentiation and visitor engagement. Comparative experiments utilized visual stimuli materials with varying density layouts, and relevant eye-tracking data were collected for analysis.

6.1.2. Data Statistics and Analysis

Table 4. Eye-tracking data statistics of comparative experiments on layout methods.

Indicators	First Entry Fixation Time FF(s)	Total Gaze Duration TG /Total Duration TD	Average Fixation Duration AF (s)	Mean Pupil Diameter MP (mm)
NSLO	0.02	2.31/3 = 0.77	0.37	3.95
SLO	0.03	2.35/3 = 0.783333	0.39	3.94

presents the eye movement data statistics for the comparative experiments on symmetry layout optimization in Experiment 1;

Table 5. Eye-tracking data statistics of comparative experiments on color tone optimization.

Indicators	First Entry Fixation Time FF(s)	Total Gaze Duration TG /Total Duration TD	Average Fixation Duration AF (s)	Mean Pupil Diameter MP (mm)
NCTO	0.01	2.40/3 = 0.8	0.35	3.57
CTO	0.01	2.41/3 = 0.803333	0.37	3.92

presents the eye movement data statistics for the comparative experiments on color tone optimization in Experiment 2; and

Table 6. Eye-tracking data statistics of comparative experiments on layout density optimization.

Indicators	Total Gaze Duration TG /Total Duration TD	Average Fixation Duration AF (s)	Average Number of Eye Twitches AT (N/s)	Mean Pupil Diameter MP (mm)
LD (N = 4)	3.17/4 = 0.7925	0.47	2.14	4.01
LD (N = 6)	3.19/4 = 0.7975	0.49	1.99	4.05
LD (N = 8)	3.21/4 = 0.8025	0.44	2.12	3.91
LD (N = 10)	4.19/5 = 0.838	0.64	1.83	3.76
LD (N = 12)	4.07/5 = 0.814	0.48	2.07	3.8
LD (N = 14)	4.07/5 = 0.814	0.39	2.11	3.5

displays the eye movement data statistics for the layout density optimization comparison conducted in Experiment 3.

Based on the guiding explanation of eye-tracking indicators provided in reference [39], as well as the relationship between eye-tracking indicators and cognitive processes identified in reference [40], and in conjunction with visual perception principles, effective fixation duration typically reflects the efficiency of visual information extraction. First-entry fixation time measures the visual attractiveness of stimuli, while average fixation duration indicates the depth of visual information processing. The average number of saccades represents the degree of visual focus, and changes in pupil diameter serve as indicators of visual emotional arousal in eye-tracking research within virtual museums. Based on the eye movement data presented above, we perform the following analyses.

• The impact of symmetrical layout optimization on visual perception is evident in the experimental data presented in Table 4. Users in virtual exhibitions with symmetrical layout optimization demonstrate higher visual information extraction efficiency, as indicated by TG/TD, and greater visual information processing depth, as indicated by AF. In contrast, the asymmetrical layout more effectively attracts user attention, as indicated by a higher FF. The trajectory maps of subjects’ viewpoints in

  Table 7. Trajectory charts of the comparative experiment for layout method and visual hierarchy optimization.

  Stimulus Subjects	Subject 1	Subject 2	Subject 3
  Symmetrical optimization (SO)
  Non-symmetrical optimization (NSO)

  show that gaze points in the symmetrical layout exhibition space are more uniformly distributed and concentrated than in the unoptimized layout. This distribution guides users to focus more effectively on the main exhibition areas.
• Visual perception impact of visual hierarchy optimization: Analysis of the experimental data in Table 5 demonstrates that user visual attractiveness (measured by FF), information extraction efficiency (measured by TG/TD), and visual information processing depth (measured by AF) in the virtual exhibition space optimized through increased contrast between cool and warm tones do not differ significantly from those in the unoptimized virtual exhibition space. In contrast, the user’s visual emotional arousal level is higher in the optimized virtual exhibition space, as indicated by a greater MP.
• Visual perception impact of layout density optimization: Experimental data presented in Table 6 demonstrate that variations in the layout density of virtual exhibition halls result in corresponding changes in user visual perception indicators. When the number of exhibits in a 2 m radius exhibition hall with a linear layout reaches ten, user visual extraction efficiency (measured by TG/TD) and processing degree (measured by FF) are optimal. Furthermore, increased density leads to a decline in visual emotional arousal (as indicated by MP), suggesting that sparsely arranged exhibits more effectively stimulate individualized emotional responses. This finding may explain why valuable exhibits in museums are often displayed independently.

  Table 8. Trajectory charts of the comparative experiment for layout destiny optimization.

  Subjects Density	$\mathbf{Low} \mathbf{Density} (\mathit{N}$ = 6)	$\mathbf{Density} \mathbf{Optimization} (\mathit{N}$ = 10)	$\mathbf{High} \mathbf{Density} (\mathit{N}$ = 14)
  Subject 1
  Subject 2

  presents viewpoint trajectory maps for two randomly selected subjects, offering a more intuitive reference.

6.2. Significance Analysis of User Visual Impact by Intelligent Spatial Layout Optimization in Virtual Museums

6.2.1. Statistical Differences and Effect Size Analysis

The ratio of inter-group variance to intra-group variance (F-value) and the statistical probability (p-value) for various indicators significantly affecting the visual perception of virtual museum users in eye tracking experiments are calculated and analyzed. It is usually considered that the analysis results show statistical difference when $p<0.05$, no statistical difference when $p\ge 0.05$, significant statistical differences when $p<0.01$, and extremely significant statistical differences when $p<0.001$. The F-value is used to measure whether the intergroup differences are significantly greater than the intra-group differences; generally, the larger the F-value, the smaller the p-value. A statistical difference analysis was conducted on the data presented in Table 4 and Table 5. Further data testing, calibration, and effect size reporting resulted in

Table 9. Visual impact significance analysis of symmetrical layout optimization.

SLO/NSLO	Visual information extraction efficiency: TG/TD					Visual information processing depth: AF
	F	p	Corrected p-value	Effect size (η2)	Significance	F	p	Corrected p-value	Effect size (η2)	Significance
	0.872	0.354	1.000	0.028	Not significant	0.165	0.874	1.000	0.005	Not significant

and

Table 10. Visual impact significance analysis of color tone optimization.

CTO/NCTO	Visual emotional arousal level: MP
	F	p	Corrected p-value	Effect size (η2)	Significance
	2.06	0.005	0.016	0.27	Significant

, which, respectively, present the specific effects of symmetry layout optimization and color tone optimization in virtual museums on various user visual perception indicators.

Then a statistical difference analysis was conducted on the data presented in Table 6. Further data testing, calibration, and effect size reporting resulted in

Table 11. Visual impact significance analysis of layout density optimization.

	$\mathbf{Layout} \mathbf{Destiney}: (\mathit{N}$$= 10)/(\mathit{N}$ = 6)					$\mathbf{Layout} \mathbf{Destiney}: (\mathit{N}$$=10)/(\mathit{N}$ = 14)
	F	p	Corrected p-Value	Effect Size (η2)	Significance	F	p	Corrected p-Value	Effect Size (η2)	Significance
TG/TD	0.004	0.000	0.000	0.45	Extremely significant	0.418	0.000	0.000	0.32	Significant
AF	1.998	0.333	0.333	0.08	Not significant	8.427	0.126	0.189	0.12	Not significant
MP	1.115	0.078	0.156	0.18	Edge significant	3.733	0.000	0.000	0.25	Significant

, which demonstrates the specific impact of optimizing virtual museum layout density on various user visual perception indicators.

6.2.2. Results and Discussion

Integrating the eye-tracking experiment results from Table 4 with the difference-significance analyses in Table 9 indicates that symmetrical layout optimization increases the efficiency of user visual information extraction and the depth of visual information processing, although this improvement is not significant.

Integrating the eye-tracking experiment results from Table 5 with the difference-significance analyses in Table 10 indicates that color tone optimization within the visual hierarchy elevates users’ visual emotional arousal levels and exhibits a significant effect.

Integrating the eye-tracking experiment results from Table 6 with the difference-significance analyses in Table 11 indicates that the application of spatial intelligence algorithms to layout density optimization in virtual museums produces several notable outcomes. First, layout density optimization effectively improves the efficiency of visual information extraction for users and has a significant or Extremely significant impact. Second, information density optimization can enhance users’ depth of visual information processing to some extent, though this effect is not significant. Third, information density optimization can enhance users’ visual emotional arousal, with a significant or edge-significant impact.

The experimental results demonstrate the effectiveness of spatial intelligence algorithms in optimizing the spatial layout of virtual museums and improving user visual perception. In comparison to previous research on visual perception, including studies employing eye movement experiments, [41] demonstrated through eye tracking experiments that indicators such as gaze duration, scanning patterns, and pupil responses are highly sensitive to changes in color perception. The conclusion of this literature, indicating that pupil response is highly sensitive to color changes, aligns with the experimental findings of significant differences in pupil diameter resulting from variations in color tone presented in this article. Several studies have examined the use of eye-tracking experiments to investigate visual perception of cultural relics. For instance, [42] identified, through eye-tracking experiments, the specific areas of cultural relics that attracted the greatest attention from tourists. Ref. [43] analyzed visual perception patterns in prehistoric pottery using eye movement experiments and found that early Neolithic pottery encouraged horizontal scanning, while pottery from the Bronze and Iron Ages promoted vertical scanning. Furthermore, the position, direction, and style of decoration were shown to significantly influence eye movement patterns. In contrast to previous studies, this article investigates the specific impact of virtual museum cultural relic layout on key indicators of user visual perception and reports the effect size. These findings offer more precise guidance for optimizing museum cultural relic layouts.

7. Conclusions

This study examines the application of spatial intelligence algorithms in virtual museums, specifically through the development of the “Song Dynasty Five Kilns” virtual museum. The spatial intelligence algorithm set facilitated the reconstruction of three-dimensional models of selected cultural relics for scene creation and enabled the optimization of spatial layouts using symmetry, visual hierarchy, and density optimization. Subjective user evaluations demonstrate that applying spatial intelligence algorithms for reconstruction and layout optimization positively influences visual attractiveness, user immersion, exhibition richness, and overall satisfaction among virtual museum users. Eye-tracking experiments demonstrate that intelligent layout optimization influences user visual information extraction efficiency, visual processing level, and visual emotional arousal to varying degrees. Specifically, symmetrical layout optimization improves the efficiency of visual information extraction and increases the depth of visual information processing, and color tone optimization significantly affects visual emotional arousal. Layout density optimization enhances the depth of visual information processing and has a notable impact on both information extraction efficiency and emotional arousal; a linear layout with approximately 10 exhibits within a 2 m range yielded optimal results.

However, these findings are case-specific, as the current results are based on a virtual museum environment featuring ceramic cultural relics with consistent stylistic attributes and a controlled exhibition layout. The extent to which these outcomes generalize to other exhibition designs remains uncertain. Variations in exhibition hall design, object types, and narrative contexts may influence the effectiveness or optimal parameters of these algorithms, particularly regarding layout density thresholds and emotional arousal triggers.

Additionally, due to limitations in the experimental environment and sample size, the preliminary findings of this study provide guidance for the development of virtual museums. These results primarily reflect the responses of specific test groups within controlled settings. Caution is warranted when generalizing these findings to a broader and more diverse population of museum users, including individuals with varying cultural backgrounds, ages, and levels of digital literacy. Future work will focus on more extensive algorithm optimization and visual impact studies, including path and information perception interaction, to provide broader references for intelligent algorithm optimization and user experience research in virtual museums.