Gaze graphs in spatial navigation: visual behavior during free exploration explains individual differences in navigation performance

1 Introduction

The ability to orient and navigate within a new environment is an essential skill in everyday life. As such, people typically navigate in noisy and complex environments, especially in cities and other urban spaces. However, despite spatial navigation having been studied for many decades, only more recently has the focus shifted to more naturalistic and complex settings (Ishikawa and Montello, 2006; Ishikawa et al., 2008; Kiefer et al., 2014; Ohm et al., 2014; 2017; Delaux et al., 2021; Bae et al., 2024). Especially the advancement in virtual reality (VR) technology over the last few years has offered new opportunities to combine complex and more naturalistic conditions with experimental control (Delaux et al., 2021; König et al., 2021; Wunderlich and Gramann, 2021; He et al., 2023; Schinazi et al., 2023; Varshney et al., 2024).

However, even with the rise in the use of more naturalistic and immersive experimental setups, reliably assessing and measuring active spatial learning and navigation remains challenging. For example, while more naturalistic setups might be utilized for participants’ spatial learning and exploration of an environment, they are often followed by tests and assessments conducted in less immersive modalities, such as questionnaires or 2D desktop screens, which require a shift away from the original immersive experience, e.g., (Ishikawa and Montello, 2006; König et al., 2021). Similarly, classical self-report questionnaires are often applied to identify differences in spatial strategy preferences and spatial navigation ability, but their associations with spatial navigation performance have been inconsistent across studies (Credé et al., 2019; König et al., 2019; 2021; Wunderlich and Gramann, 2021). In addition, while movement patterns during spatial navigation have recently started to receive more attention (Brunec et al., 2023; Sánchez Pacheco et al., 2025), our understanding of the participants’ continuous behavior during spatial learning, active orientation, and navigation remains severely limited. Overall, despite the methodological advances, current approaches remain limited in their ability to capture the continuous behavioral processes underlying spatial knowledge acquisition and linking them to navigation performance.

In addition, we know little about human visual behavior during spatial learning and navigation, despite the importance of vision for spatial navigation (Foo et al., 2005; Chan et al., 2012; Ekstrom, 2015; Ekstrom and Isham, 2017). For example, most landmark definitions are based on visible properties (Foo et al., 2005; Chan et al., 2012; Ekstrom, 2015; Ekstrom and Isham, 2017), yet we know little about active visual behavior with respect to landmarks during both spatial learning and navigation. While there is a broad consensus that landmarks are crucial for the formation of spatial knowledge (Siegel and White, 1975; Presson and Montello, 1988) and spatial navigation (Steck, 2000; Foo et al., 2005; Chan et al., 2012; Richter and Winter 2014; Yesiltepe et al., 2021), their functional role during spatial knowledge acquisition is still under discussion. Additionally, it remains unclear why certain buildings are utilized as landmarks and not others. Also, we know little about the role of other environmental cues and city features beyond landmarks for spatial knowledge formation. Therefore, investigating visual behavior during spatial exploration with respect to environmental cues and landmarks would be an important step towards determining the functional role of landmarks and gaining new insights into active spatial learning.

As an initial step to address these challenges, we investigated free visual behavior during spatial learning in a complex immersive setting in our earlier work (Walter et al., 2022). Specifically, we focused on eye-tracking data collected during free exploration of a virtual city using virtual reality. Since traditional eye-tracking methods couldn't capture participants’ freedom of movement in this dynamic setting, we developed a new analysis approach using graph theory. This allowed us to transform eye-tracking data into gaze graphs, enabling us to analyze general visual behavior patterns across participants while accounting for the variability introduced by individual movement choices. Our graph-theoretical analysis offered new insights into vision during spatial knowledge acquisition, identifying a subgroup of buildings that consistently emerged as outstanding buildings within participants’ visual networks. These buildings, classified as gaze-graph-defined landmarks, were preferentially connected, suggesting they may serve as reference points for the formation of spatial memory. However, while this approach revealed novel insights, it remains unclear how stable these gaze graphs and landmarks are across different contexts. Additionally, to fully understand the role of visual behavior in spatial knowledge formation, we must connect these visual patterns to actual spatial navigation performance. Therefore, to extend our previous findings and address these unresolved questions, a new experimental approach is necessary to directly link visual behavior during spatial learning to navigation outcomes.

One particularly promising avenue to explore visual behavior in relation to spatial navigation performance is examining individual differences, which are consistently observed in spatial navigation performance. These differences are not only widespread but can be also observed in a variety of tasks (Ishikawa and Montello, 2006; Gramann, 2013; Weisberg and Newcombe, 2014; 2016; 2018; Weisberg et al., 2014; Ekstrom and Isham, 2017; Hegarty et al., 2018; 2023; Newcombe, 2018; Boone et al., 2019; Zanchi et al., 2022; He et al., 2023; Ishikawa, 2023; Maxim and Brown, 2023; Newcombe et al., 2023; Schinazi et al., 2023; Spiers et al., 2023). Individual differences are especially prevalent in people’s ability to learn a new environment and form a map-like knowledge (also referred to as survey knowledge or allocentric representation) (Ishikawa and Montello, 2006; Weisberg et al., 2014; Weisberg and Newcombe, 2016; 2018; Hegarty et al., 2018; Ishikawa, 2023; Newcombe et al., 2023), therefore investigating how differences in visual behavior relate to individual performance differences could offer a new perspective to spatial learning and navigation. In general, a multitude of factors have been found to contribute to the observed individual differences, including differing levels of spatial (navigation) capabilities (Hegarty et al., 2018), the size of brain regions (Maguire et al., 2000), gender (Lawton, 1996; Brunyé et al., 2018; Coutrot et al., 2018; Boone et al., 2019; Nazareth et al., 2019; Schinazi et al., 2023; Spiers et al., 2023), and environmental factors like the spatial entropy of the city participants grew up in (Coutrot et al., 2022), cultural and language differences (Haun et al., 2011; Hund et al., 2012; Coutrot et al., 2018; Spiers et al., 2023). Importantly, some of the observed differences can be influenced or reduced through instructions (Boone et al., 2019) and motivation (Schinazi et al., 2023), suggesting that factors unrelated to spatial navigation itself may also play a role. Nevertheless, individual differences appear to be rooted in multiple developmental and environmental factors (Gramann, 2013; Newcombe et al., 2023). This highlights the potential of visual behavior to both shape and reflect navigation differences. Therefore, investigating the relationship between visual behavior during spatial learning and individual differences in navigation performance promises valuable insights into the mechanisms underlying spatial navigation and the role of visual behavior in shaping individual differences.

In this study, we combine a long free exploration period of the virtual city of Westbrook with immersive pointing tasks conducted in the same environment using an immersive virtual reality setup with eye tracking functionality (Schmidt et al., 2023b). This experimental design allows us to link participants’ active exploration behavior with their spatial navigation performance, extending and improving the approach from our earlier work (Walter et al., 2022). The current study is part of a larger experiment framework and focuses on the analysis of the visual behavior and linking it to participants’ task performance. An analysis of the behavioral and qualitative self-reported changes related to spatial learning and a comparison to a participant group trained in an augmented condition is published in (Schmidt et al., 2023b). The eye-tracking data collected during free spatial exploration is transformed into gaze graphs before applying the graph-theoretical analysis approach from our earlier work (Walter et al., 2022). Specifically, we investigate the architecture of gaze graphs, examine the characteristics of gaze-graph-defined landmarks in comparison to other buildings, and assess differences in spatial task performance. We further model individual differences using three conceptually distinct approaches: a questionnaire-based model, a gaze metrics-based model, and a gaze graph-based model.

2 Results

In the study, 26 participants freely explored the virtual city of Westbrook (Figure 1b–c) in an immersive virtual reality (VR) setup (Figure 1a), and subsequently completed an immersive pointing-to-building task within the same environment (Schmidt et al., 2023b). Eye-tracking data was collected with a mean sampling rate of 90 Hz using the head-mounted Vive Pro Eye. All participants were seated on a swivel chair that allowed them to fully rotate their bodies while they controlled their walking speed with the controller (Figure 1a). In the first part of the study, participants explored the city for five 30-min recording sessions, thus for a total of 2.5 h. After the exploration phase, the participants performed the pointing-to-building task, in which they were teleported to different locations in the city and asked to point to the task buildings with their controller. In addition, prior to the experiment, participants completed the FRS questionnaire (in German: Fragebogen Räumliche Strategien FRS, translated: questionnaire of spatial strategies), which assesses spatial strategies via self-report questions on participants’ use of spatial navigation strategies in everyday situations and perceived orientation ability (Münzer and Hölscher, 2011).

2.1 Gaze graphs

To investigate visual behavior during 2.5 h of free spatial exploration in a large urban environment, the eye tracking analysis needed to address the variability of the participants’ behavior. Specifically, participants were able to move their heads and eyes freely without any restrictions, in addition to freely walking within the whole city (approximately 996m x 758m ∼ 75.5 ha) while only being limited to the road network and other walkable areas (other narrow stone or grass paths, parking areas, grass patches, etc.). As a result, participants explored different areas of the city and focused on various objects at any given time, as exemplified by the walking paths (Figure 2a) and gaze locations (Figure 2b) of six example participants during the first 5 minutes of the experiment. We addressed this behavioral variability by applying the graph-theoretical analysis approach from our earlier work (Walter et al., 2022). By transforming the eye-tracking data of the 2.5-h exploration into gaze graphs, we reduced the dimensionality of the eye-tracking data, thereby making the relevant features of the data accessible and excluding variation due to participants’ freedom of movement.

We transformed the eye-tracking data into gaze graphs using a standardized process. First, a cleaning and pre-preprocessing pipeline was applied (see 4.7 Data pre-processing and gaze classification). Then, each viewed building was represented as a graph node, with edges connecting nodes when a participant made a direct gaze transition between the respective buildings at any time of the experiment (Figure 2c). Importantly, the gaze graph only reflects gaze transitions, not the participant’s physical location, and is undirected and unweighted. Consequently, the gaze graph only contained information about whether a participant performed a direct gaze transition between two buildings, but not any information about the directionality or the frequency of this gaze transition (see 4.8 Gaze graph creation). In short, the 2.5 h of eye-tracking data recorded in the exploration phase were reduced to one gaze graph for each participant (Figure 2d). In the following, we examine gaze graph characteristics and identify common visual patterns in participants’ exploration of the city. This includes extending the graph-theoretical analysis pipeline from our earlier work (Walter et al., 2022), integrating new analytical approaches, and ultimately linking questionnaire responses, visual behavior, and gaze graph measures to individual task performance.

2.2 Gaze graph properties and spectral graph analysis

As a first step in the graph-theoretical analysis, we aimed to assess the overall connectivity of the gaze graphs. This step serves as a methodological check to determine whether the environment can be treated as a unified whole or as a separate set of loosely connected areas in subsequent analyses. As gaze graphs capture transitions in visual attention between locations in space, their connectivity provides an indirect measure of how participants structure the environment. Specifically, we assessed whether participants’ visual behavior reflects a unified spatial representation or suggests distinct areas within the environment.

The spectral graph analysis evaluates the connectivity of the gaze graphs based on the eigenvalue spectrum of the Laplacian matrix, specifically the second-smallest eigenvalue and corresponding vector: the Fiedler value and Fiedler vector. Across all gaze graphs, we found a mean Fiedler value of 0.353 (SD = 0.093), consistent with low global connectivity, i.e., sparsity, in the gaze graphs.

As a second step, we identified the Fiedler vector, the eigenvector corresponding to the second-smallest eigenvalue. This vector partitions the graph into two clusters based on its positive or negative values and provides insights into node connectivity within clusters. However, the Fiedler vector values of the gaze graphs were distributed mostly around 0, indicating no clear separation into distinct clusters. Visualization of the adjacency matrix, sorted by the Fiedler vector, did not reveal a modular block pattern, further supporting the lack of a clear cluster separation.

Finally, we partitioned the gaze graphs based on the sparsest cut approximated by the Fiedler vector and assessed the connectivity before and after partitioning. Prior to partitioning, the gaze graphs contained on average 1,295.1 edges (SD = 206.3) with a density of 0.046, representing 4.6% of all possible edges. Partitioning the gaze graph required cutting an average of 122.8 edges (SD = 29.5), which corresponds to 9.39% of the graph’s edges on average (SD = 1.2%). The resulting two clusters had a similar edge count (cluster 1: M = 584.7, SD = 155.7; cluster 2: M = 587.7, SD = 212.0). Partitioning the gaze graphs increased the intra-cluster density (M = 0.0873, SD = 0.0133) while the inter-cluster density decreased (M = 0.0092, SD = 0.0024), indicating a stronger internal connectivity within clusters and weaker connectivity between them. However, it also required removing a comparatively large proportion of edges, given the sparsity of the graphs. Consequently, while spectral partitioning was possible and increased intra-cluster density, it required removing a substantial proportion of the graph’s existing edges (9.39%), suggesting that although a partition is mathematically possible, it is not strongly supported by the intrinsic structure of the data.

Overall, while the spectral partitioning provides an optimal cut from a mathematical standpoint, it does not reveal a meaningful modular structure or clear cluster separation in the gaze graphs. The gaze graph structure is therefore consistent with the city of Westbrook being visually perceived as a cohesive unit, supporting its treatment as a single unified environment in subsequent analysis.

2.3 Gaze-graph-defined landmarks

To identify possible gaze-graph-defined landmarks, we assessed the distribution of node degree centrality for all participants and buildings (Figure 3a). When averaged across participants, our results showed a considerable variation in the node degree values of individual buildings (M = 10.62, SD = 4.96, Figure 3b,f). In addition, we assessed the hierarchical configuration of the gaze graphs (Rodrigue, 2024). The hierarchy index describes how strongly the network is organized around a few highly connected buildings versus many weakly connected ones (see Section 4.7). Applying this measure revealed that all gaze graphs exhibited a strongly hierarchical organization (hierarchy index: M = −3.1, SD = 0.47) (Figure 3e), resulting in a small number of nodes with very high node degree values for each participant, thereby highlighting the importance of these highly connected nodes within the gaze network. Further examination of the distribution of the buildings’ mean node degrees revealed a small subset of buildings that clearly stood out (Figure 3d), suggesting that important nodes were consistent across participants.

When considering node degree values at the participant level, variability was lower (M = 10.62, SD = 1.69) than across buildings. To directly assess consistency, we computed pairwise Pearson correlations between participants’ node-degree distributions. Correlations were high (M = 0.74, SD = 0.12; Figure 3c), indicating strong agreement in which specific buildings exhibited high or low connectivity across participants’ gaze graphs. Together, these findings suggest that viewing behavior, as captured by buildings’ node degrees, was highly comparable across individuals. Taken together, these findings indicate that a small and consistent subset of buildings emerges as highly connected hubs across participants’ gaze graphs, providing a basis for identifying gaze-graph-defined landmarks.

Next, we applied the node degree threshold to formally identify gaze-graph-defined landmarks, defined as two standard deviations above the mean node degree across all participants and buildings (Walter et al., 2022). Five buildings exceeded this threshold (mean + 2 SD = 20.53). Altogether, the combined evidence from network structure and inter-participant consistency supports the identification of five gaze-graph-defined landmarks.

2.4 Location and appearance of gaze-graph-defined landmarks

To further characterize the gaze-graph-defined landmarks, we examined their locations and appearances in the environment. We found that all five gaze-graph-defined landmarks had a very distinct visual appearance and were always located at a crossing, therefore making them visible from multiple angles (Figure 4). In addition, the five gaze-graph-defined landmarks were distributed across the central-western area of the city. Therefore, all identified gaze-graph-defined landmarks matched the appearance and location characteristics of the gaze-graph-defined landmark definition (Walter et al., 2022). Furthermore, when comparing the identified gaze-graph-defined landmarks with the four buildings that were explicitly designed to be tall, distinctive landmarks during the development of the city (Schmidt et al., 2023b), we found that only one of these designed landmarks also emerged as a gaze-graph-defined landmark.

To further examine the relationship between landmark category and building properties, we analyzed the correlation between mean node degree (averaged over participants), visibility, and building height. Building height was extracted from the virtual environment in two variables: absolute height representing the highest building point in the environment, irrespective of ground level, and relative building height corresponding to building height relative to the surrounding ground level. Building visibility was calculated by dividing the city into a 4 × 4 m grid and identifying the number of grid cells from which participants viewed each building. We included only grid cells visited by at least one participant, although most of the walkable area was explored by all participants (Figure 5a). Accordingly, a building was considered visible at a given location if it was viewed from that grid cell by at least one participant. Visual inspection of the scatter plot indicated a clear positive relationship between node degree and visibility, with gaze-graph-defined landmarks scattered in the extremes of both variables (Figure 5c). In contrast, no clear relationship between node degree and absolute height could be observed, although the designed landmarks and also gaze-graph-defined landmarks appear to be larger compared to other buildings (Figure 5d). This pattern was further supported by Spearman rank correlations (Figure 5e), which only showed a strong association between node degree and visibility (ρ = 0.93), whereas building height was only weakly correlated with node degree (absolute height: ρ = 0.27; relative: ρ = 0.23) and visibility (absolute height: ρ = 0.19; relative: ρ = 0.19). Descriptive comparisons across building categories (gaze-derived landmarks, designed landmarks, and other buildings) further supported this pattern. The five gaze-derived landmarks exhibited the highest mean visibility overall (M = 7.21%, SD = 0.57%), followed by the remaining three designed landmarks that were not identified as gaze-graph-defined landmarks (M = 4.94%, SD = 1.37%), and all other buildings (M = 2.74%, SD = 1.45%). In contrast, the three designed landmark buildings showed the largest mean height (absolute: M = 38.023 m, SD = 8.61 m; relative: M = 41.62 m, SD = 7.19 m), followed by gaze-graph-defined landmarks (absolute: M = 27.85 m, SD = 23.20 m; relative: M = 28.41 m, SD = 24.44 m), and all other buildings (absolute: M = 11.72 m, SD = 5.33 m; relative: M = 13.0 m, SD = 5.05 m). Additionally, the high-silo building, which is the only gaze-graph-defined landmark that is also a designed landmark, is the tallest building in the city (absolute = 66.7 m, relative = 70.1 m), but ranks fifth in both mean node degree and visibility. Together, these findings suggest that gaze-graph-defined landmarks are characterized more strongly by their overall visibility within the environment than by height alone.

Finally, to assess the potential of gaze-graph-defined landmarks to be utilized for triangulation, directional cues, or beacons, we calculated their visibility with respect to the walkable area and weighted by the time participants spent in different parts of the city. We found that in 29% of the traversed area, at least one gaze-graph-defined landmark was visible (Figure 5b). More specifically, in 7% of the traversed area, two or more gaze-graph-defined landmarks were visible at the same time. This could have allowed participants to triangulate their position using two or more gaze-graph-defined landmark cues. Correspondingly, in 22% of the traversed area, exactly one gaze-graph-defined landmark was visible, thus offering the basis for directional cues and beacon navigation (Figure 5b). In the remaining 72% of the city, no gaze-graph-defined landmark was visible (Figure 5b). Despite covering only about 29% of the traversed area, locations where at least one gaze-graph-defined landmark was visible accounted for 46.9% of exploration time. Of this time, 31.8% was spent where exactly one gaze-graph-defined landmark was visible, and 15.1% where two or more were visible. The remaining 53% was spent where no gaze-graph-defined landmarks were visible. Taken together, these findings indicate that gaze-graph-defined landmarks are characterized by their high visibility, which cannot be explained by height alone, but could account for their outstanding node degree values. The high visibility of gaze-graph-defined landmarks also supports their potential functional use for navigation, such as triangulation, directional guidance, or beaconing across substantial portions of the walkable area.

2.5 Interconnectedness of gaze-graph-defined landmarks

To identify whether the identified gaze-graph-defined landmarks are also preferentially connected to each other, we applied the rich club analysis pipeline (Walter et al., 2022). First, we computed the mean adjusted rich club coefficient, which compares the gaze graph’s connectivity to that of 1,000 random graphs with similar node degree distributions. The coefficient is calculated by averaging the ratios of the gaze graph’s rich club coefficient to those of the 10 most similar random graphs. A mean adjusted rich club coefficient greater than 1.0 indicates preferential connectivity.

As a second step, we systematically removed low-degree nodes from the calculation and observed that with an increasing minimum node degree, the mean adjusted rich club coefficient showed a consistent increase across all participants as well (Figure 6a). This indicates that nodes with higher node degree centrality were more densely interconnected than expected by chance. However, the increasing node-degree threshold also reduces the number of nodes included in the calculation. Therefore, the estimate’s uncertainty increases with the increasing node-degree threshold. To account for this, we set the threshold at one sigma above the mean node degree for reliable calculations (Walter et al., 2022). Consequently, nodes with a node degree of 15 and higher exceeded the calculation cut-off threshold and were also interconnected the most in the gaze graph, thus high node degree buildings formed a rich club within the gaze graph.

As a final step in the pipeline, we identified which buildings appeared most often in the rich club across participants. Specifically, we counted the number of times buildings were part of the final set of nodes considered for calculating the adjusted rich club coefficient before the cut-off threshold, i.e., buildings with a node degree of 15 and higher, across participants. Then, we identified the buildings exceeding the threshold of two standard deviations above the mean count. These 14 buildings appeared most often in the strongest rich club across participants and included all five gaze-graph-defined landmarks (Figure 6b). Therefore, high node degree buildings and gaze-graph-defined landmarks were preferentially connected and part of the strongest rich club within the gaze graphs.

2.6 Spatial navigation performance

To assess participants’ spatial knowledge, they performed an immersive pointing-to-building task after completing the free exploration of the city of Westbrook (Schmidt et al., 2023b). In the pointing-to-building task, participants were asked to point toward specific buildings from several locations within the city (Figure 7a). The task utilized eight task buildings and eight starting locations that were directly located in front of each task building (Figure 7b,c). The buildings were distributed evenly over the city (Figure 7b) and selected so that they were not visible from any other starting location. Participants were teleported to each of the starting locations in randomized order and rotated to a randomized degree during the teleportation. During the task, participants were free to rotate their head and body in any direction but were restricted from walking. At each starting location, they were shown a picture of the target building and asked to point towards its location using their controller. In the participant’s view, the pointing direction was visualized as a green ray originating from the controller (Figure 7a). The participants logged their pointing response with a button press. At each task location, the participants pointed to the remaining seven other buildings, resulting in 56 unique start and target building combinations. After completing the task, the participants repeated all trials in a newly randomized order. Overall, each participant performed 112 trials in the pointing-to-building task.

We assessed participants’ performance by calculating the absolute pointing error deviation from the correct direction. Here, a pointing error of 0° represents the best possible task performance, and a pointing error of 180° represents the worst possible task performance. In Figure 8a, all pointing errors for each participant and each unique start-target-building combination are displayed. The mean performance of participants varied considerably between the best-performing participant (pointing error: M = 15.2°) and the worst-performing participant (pointing error: M = 74.0°), resulting in a 58.8° difference in pointing error between the best- and worst-performing participants (Figure 8b). Thus, we found considerable variance in task performance between participants.

Next, we assessed systematic differences in participants’ performance during the repetition trials, specifically, the performance differences between the initial and repeated presentations of each trial. When visually inspecting the pointing error distributions of the initial and repeated trials, they appeared to be quite similar (Figure 8c). Additionally, the distribution of the differences in pointing direction, for example, the change in the pointing direction between the initial and repeated response for the same trial, appeared to be normally distributed (Figure 8d). However, when performing a repeated-measures ANOVA to examine the effect of trial repetition order (initial answer and repeated answer) and trial identity (unique-start-target-building combination), we found a significant main effect of repetition order, F(1, 25) = 6.97, p = 0.014. For trial identity and the interaction between repetition order and trial identity, the Mauchly’s test indicated that the assumption of sphericity was violated, therefore, degrees of freedom were corrected using Greenhouse-Geisser estimates (ε = 0.26, ε = 0.26). We found a highly significant main effect of trial identity, F(14.56, 364.1) = 7.11, p < 0.001. The interaction between repetition order and trial identity was not significant, F(14.3, 357.48) = 1.16, p = 0.304. On average, participants’ pointing errors decreased by 5.1° (SD = 9.9°) when repeating the trial a second time during the task repetition. To summarize, participants performed significantly better during the task repetition, showing an average 5.1° improvement in pointing accuracy.

2.7 Modeling individual differences in spatial task performance

In the following, we examined how participants’ task performance relates to their visual behavior during the free spatial exploration of the city and their self-assessed spatial navigation skills (FRS questionnaire (Münzer and Hölscher, 2011)). As a first step, we quantified the contribution of the task performance patterns identified in the previous section to the total trial-level variance. Specifically, we assessed the extent to which variability in pointing error is associated with performance differences in the repeated trials and with differences between participants. Subsequently, we modeled participants’ mean task performance using predictors grouped into three conceptually distinct models: a questionnaire-based model, a gaze metrics-based model, and a gaze graph-based model, with particular interest in identifying which conceptual model provides meaningful explanatory power.

To quantify the variance in pointing error that can be attributed to inconsistencies across repeated trials, we computed the intra-participant variance for each unique start-target-building combination. For each unique combination, the variance across the two repetitions was calculated as x 1 − x 2 2 2 and then averaged across all trials and participants to obtain a group-level estimate. Formally, the group-level intra-participant variance can be expressed as:

V i n t r a , g r o u p = 1 P · m ∑ p = 1 P ∑ k = 1 m x 1 , k p − x 2 , k p 2 2

• P = number of participants
• m = number of unique start-target-building combinations/unique trials.

We found that the intra-participant variance across all unique trials and participants (1,358.08) accounted for 65.64% of the total pointing error variance (2,069.13), indicating that differences between repeated presentations of the same trial contribute substantially to overall trial-level variability (Figure 9a).

To assess how stable individual differences contribute to overall trial-by-trial performance, we first modeled performance with participant identity as a predictor. A linear model with participant identity as a fixed effect is highly significant (F(25, 2,886) = 11.66, p < 2.2 × 10⁻¹⁶⁾), yet it explains only a modest amount of variance (R² = 0.092, adjusted R² = 0.084) (Figure 9a). A corresponding linear mixed-effects model with random intercepts for participants yielded a comparable conditional R ^*2* = 0.087 (variance component σ ^*2* _{*participant*} = 180.4, residual σ ^*2* _*residual* = 1,895.6, ICC = 0.087), confirming that this variance reflects true between-participant differences rather than trial-level noise. Notably, analysis of intra-participant variability across repeated presentations of unique trials revealed that trial-to-trial variability within individuals accounted for an even larger fraction of overall performance variance than the stable differences between participants (Figure 9a). This highlights that, while individual differences are present, within-subject variability is a dominant source of fluctuations in trial-level performance.

To assess how stable individual differences relate to participants’ self-assessed spatial navigation skill and visual exploration behavior, we modeled participants’ mean task performance using three conceptually distinct sets of predictors: a questionnaire-based model, a gaze metric-based model, and a gaze graph-based model.

For the questionnaire-based model, we modeled the mean pointing error of each participant using participants’ responses to the FRS questionnaire. The 19 questions of the FRS questionnaire are based on a 7-point Likert scale and correspond to three subscales: global-egocentric, survey, and cardinal directions (Münzer and Hölscher, 2011). We calculated participants’ mean response to each FRS subscale, resulting in the following summary statistics: global-egocentric (M = 4.4, SD = 0.95, range = 2.5 - 5.8), survey (M = 3.85, SD = 1.1, range = 1.7 - 6), and cardinal directions (M = 2.54, SD = 0.65, range = 1 - 6). These mean responses of the three FRS subscales served as the predictors of participants’ mean angular pointing error in a linear model. However, the model explained only a little of the between-participant variance (R ^*2* = 0.068, Adjusted R ^*2* = −0.059, p = 0.663) (Figure 9b), and none of the FRS subscales were significant (Table 1). Additionally, simple linear regression models of the individual FRS subscales were also non-significant and resulted in very low R² values as well (Table 1). Overall, the FRS questionnaire subscales did not explain the observed individual differences in task performance.

TABLE 1. Linear Model: individual differences and FRS questionnaire.

This table presents the results of the linear model using the FRS questionnaire scales as predictors of participants’ mean task performance, i.e., the mean pointing error for each participant (0°–180°). In addition to the full model, the results of the simple regression for each predictor of the full model are included.

Secondly, we investigated the link between individual differences and participants’ visual behavior during spatial exploration using general gaze metrics. For the gaze metrics-based model, we model participants’ mean performance with three predictors: the number of uniquely viewed buildings, the number of gazes on buildings compared to other objects, and the total gaze duration/dwell time on buildings compared to other objects in the environment. The resulting model also performed poorly (R ^*2* = 0.079, Adjusted R ^*2* = −0.047, p = 0.6) (Figure 9b), and none of the predictors were significant in the full model or individual linear regressions (Table 2). Consequently, general gaze metrics did not explain the observed individual differences in task performance.

TABLE 2. Linear Model: individual differences and general gaze metrics.

This table presents the results of the linear model using general gaze metrics as predictors of participants’ mean task performance, i.e., the mean pointing error for each participant (0°–180°). In addition to the full model, the results of the simple regression for each predictor of the full model are included.

Thirdly, we modeled participants’ mean pointing error as a function of their visual behavior during the exploration phase using five global gaze graph measures that characterize different aspects of the gaze graph architecture: number of nodes, number of edges, density, diameter, and graph hierarchy index (see 4.7 Graph-theoretical measures). The gaze graph-based model was statistically significant (F(5,20) = 2.822, p = 0.044) and explained 41% of the variance in individual performance differences (R ² = 0.413, Adjusted R ^*2* = 0.267) (Figure 9b). Out of the five predictors, only diameter was significant (Table 3). Additionally, we examined the variance reduction when removing each predictor from the full model and modeled the association between each gaze graph measure and mean performance individually using simple linear regressions. Gaze graph diameter showed the largest reduction, i.e., uniquely explained variance, and both graph diameter and density were significant in the individual regressions (Table 3). These results illustrate strong associations between gaze graph measures, particularly graph diameter, and individual differences in task performance. Specifically, better-performing participants (lower pointing errors) were related to gaze graphs with shorter diameters and higher density, whereas low-performing participants were associated with longer diameters and lower density. In addition, pairwise correlations from the Pearson correlation matrix indicated strong associations between several predictors, which were consistent with these relationships (Figure 9c). In particular, graph diameter was negatively correlated with the number of nodes, edges, density, and hierarchy index, while the other measures were positively correlated with one another (Figure 9c). Taken together, these patterns suggest that the selected graph measures capture related aspects of gaze graph organization rather than entirely independent properties. Accordingly, variance inflation factors (VIFs) revealed substantial multicollinearity among several predictors (VIF values: number of nodes: 84.491, number of edges: 2,475.244, density: 2,048.571, diameter: 1.352, hierarchy index: 1.365), indicating considerable shared variance across several measures. Therefore, the individual contribution of any single predictor should be interpreted with caution, as the shared variance between predictors limits the ability to attribute explained variance uniquely.

TABLE 3. Linear Model: individual differences and global gaze graph measures.

This table presents the results of the linear model using the global gaze graph measures as predictors of participants’ mean task performance, i.e., the mean pointing error for each participant (0°–180°). In addition to the full model, the results of the simple regression for each predictor of the full model, as well as the unique variance explained by these predictors, are included.

To address the high multicollinearity and evaluate the model’s out-of-sample generalizability, we performed a regularized Ridge regression with Leave-One-Out Cross-Validation (LOOCV) as a sensitivity analysis. The regularized model (λ _min = 5.60) explained 38.4% of the in-sample variance (R ² = 0.384). In addition, the cross-validated model retained out-of-sample explanatory value, explaining 20.3% of the out-of-sample variance (R c v 2 = 0.203, RMSE_cv = 12.30°). Although lower than the in-sample estimate, the cross-validated results indicate that the relationship between gaze-graph architecture and spatial performance persisted after regularization and retained meaningful explanatory power for unseen participants.

Overall, these findings indicate that gaze graph architecture captures meaningful variance in individual performance differences, while the high intercorrelations among graph measures suggest that they should be interpreted as complementary aspects of a shared underlying visual organization rather than as independent predictors. Specifically, higher task performance appeared to be associated with gaze graphs that display a higher density, number of nodes and edges, and overall shorter diameters, and lower performing participants appear to have sparser gaze graphs, with fewer nodes and edges and longer diameters. Figure 10 shows example gaze graphs from a higher- and lower-performing participant that, consistent with the results, show the higher-performing participant (Figure 10a) to exhibit a visibly denser graph structure with more nodes, edges, and a shorter diameter compared to the lower-performing participant (Figure 10b).

Taken together, these findings indicate that measures of gaze graph architecture capture a substantial portion of individual performance variance. Importantly, unlike the questionnaire-based and gaze metrics-based models, only the gaze graph-based model demonstrated meaningful explanatory power, suggesting that stable individual differences in spatial task performance were reflected in the structural patterns of visual behavior during spatial exploration (Figure 9b).

3 Discussion

In this study, participants answered a spatial strategy questionnaire, freely explored the virtual city of Westbrook for an extended time, and performed an immersive pointing-to-building task. We transformed the recorded eye tracking data into gaze graphs and applied a graph-theoretical analysis. The spectral analysis of gaze graphs revealed no meaningful modular structure or clear cluster separation, indicating that the city of Westbrook was perceived as a whole without easily separable blocks. Furthermore, the node degree analysis identified five gaze-graph-defined landmarks that were preferentially interconnected, highly visible, and shared key characteristics of classical landmarks related to appearance and location. When analyzing participants’ spatial task performance, we found systematic improvements across repeated trials alongside stable individual differences. Modeling participants’ mean task performance with questionnaire data, gaze-metrics, and gaze-graph measures revealed that only the gaze graph-based model demonstrated meaningful explanatory power, capturing stable individual differences through patterns in visual behavior during spatial exploration. The following sections examine these results in relation to how gaze graph structure characterizes visual exploration and its consistency across environments, the functional characterization of gaze-graph-defined landmarks, the behavioral dynamics captured by gaze graph architecture that may explain individual differences in navigation performance, and the implications of these findings for the role of vision in spatial navigation.

3.1 Gaze graphs as a representation of visual behavior during free spatial exploration

Eye tracking in virtual reality allows for natural movement and facilitates viewed object classification, but it also requires addressing participant variability in analysis. In this study, participants freely explored a 75.5-ha city, viewing all 244 buildings and a multitude of other objects from various angles and locations. To identify common patterns in visual attention, we used a dimensionality-reducing approach to isolate relevant behavioral patterns. Our graph-theoretical approach focuses on gaze transitions, since we assume that participants acquired spatial knowledge about the location and layout of two buildings within the city through direct gaze transitions between them. In general, investigating gaze transitions has been a focus of eye tracking research for decades, specifically scanpaths and other sequential analyses of visual attention (Noton and Stark, 1971; Anderson et al., 2015; Fahimi and Bruce, 2021). However, traditional scan-path approaches often assume controlled stimuli and do not account for the variability in timing, perspective, or visual angle of naturalistic immersive VR environments (Duchowski et al., 2010; Goldberg and Helfman, 2010; Raschke et al., 2014; Anderson et al., 2015; Fahimi and Bruce, 2021). Other gaze-transition analysis approaches, such as transition matrices and gaze transition entropy, focus on the predictability or randomness of gaze transitions (Krejtz et al., 2015; Shiferaw et al., 2019). In our earlier work, we addressed this gap by proposing an alternative graph-theoretical analysis approach that transforms eye-tracking data into gaze graphs, where buildings are represented as nodes and direct gaze transitions as edges (Walter et al., 2022). This method removes timing and perspective variability, allowing for a comparative analysis of visual attention patterns across participants, while also offering insights into the importance and configuration of buildings as reflected by participants’ perception of the city.

In addition, since this study combines new analyses with the approach from our previous work (Walter et al., 2022) and the two experimental designs were highly similar, we can examine whether characteristics of gaze graphs and visual behavior generalize across virtual environments. A detailed overview of the experimental design and results from both studies is provided in Tables 4–7. For clarity, we refer to the current study as “WB” (Westbrook) and our previous work as “SH” (Seahaven).

TABLE 4. Comparison of experimental design and pre-processing pipeline of the Westbrook (WB) and Seahaven (SH) projects.

This table presents the details of the experiment design and pre-processing pipeline of the current study (Project Westbrook, WB) and our earlier work (Project Seahaven, SH (Walter et al., 2022)).

TABLE 5. Comparison of the graph partitioning analysis results of the Westbrook (WB) and Seahaven (SH) projects.

This table presents the graph partitioning results of the current study (Project Westbrook, WB) and our earlier work (Project Seahaven, SH (Walter et al., 2022)).

TABLE 6. Comparison of the results of the gaze-graph-defined landmarks, walked area, and visibility analysis of the Westbrook (WB) and Seahaven (SH) projects.

This table presents the details of the gaze-graph-defined landmarks, walked area, and visibility analysis of the current study (Project Westbrook, WB) and our earlier work (Project Seahaven, SH (Walter et al., 2022)).

TABLE 7. Comparison of the rich club analysis results of the Westbrook (WB) and Seahaven (SH) projects.

This table presents the details of the rich club analysis results of the current study (Project Westbrook, WB) and our earlier work (Project Seahaven, SH (Walter et al., 2022)).

In general, there were many similarities between the experimental design of this (WB) study and our earlier SH study. In both studies, participants freely explored a large virtual city with more than 200 buildings for several 30-min sessions in an immersive VR setting with a head-mounted VR headset and eye tracker. However, the city of Westbrook in this study is larger (75 vs. 21.55 ha, WB and SH, respectively) and contains more buildings (244 vs. 213 buildings, WB and SH, respectively) (Table 4). Also, participants explored the city for 2.5 h vs. 1.5 h, WB and SH, respectively (Table 4). Despite these differences, the eye-tracking data of both studies was pre-processed with the same preprocessing pipeline, and the gaze graphs were created with the same logic. Importantly, when comparing the gaze graph architecture in both studies, we found similar patterns in gaze graph structure. Specifically, while the gaze graphs of this study (WB) contained more edges on average compared to the previous study (1,295 vs. 883, WB and SH, respectively), the mean percentage of instantiated edges (density) was very similar in both studies (4.56% vs. 4.1%, WB and SH, respectively) (Table 5). The spectral graph analysis and partitioning showed a difference in the average number of edges cut to separate the graph into two components using the sparsest cut approximated by the Fiedler vector (122.8 vs. 82.6, WB and SH, respectively), yet the respective mean percentage of removed edges from the existing graph during the partitioning was very similar (9.39% vs. 9.30%, WB and SH, respectively) (Table 5). Furthermore, we found similar mean Fiedler values (0.353 vs. 0.300, WB and SH, respectively) (Table 5), similar distributions of Fiedler vector values, and no modular block structure in the corresponding visualizations. Therefore, we concluded in both studies that the cities were perceived as a whole and could be treated as such for any further graph-theoretical analysis. Altogether, despite minor differences in exploration duration and city area, we find similar patterns in the gaze graph architecture in both studies, overall highlighting the consistency of gaze graph architecture.

3.2 Gaze-graph-defined landmarks

The concept of gaze-graph-defined landmarks (Walter et al., 2022) describes buildings with high node degree centrality, i.e., buildings that were viewed exceptionally often just before or after multiple distinct buildings, therefore, representing consistently important nodes in visual exploration across participants. In the present study, we identified five gaze-graph-defined landmarks that appeared to be visually distinctive, freestanding, and located near intersections, making them visible from multiple vantage points. These characteristics match the visual and spatial properties of gaze-graph-defined landmarks in Walter et al. (2022) as well as characteristics of both global and local landmarks (Lynch, 1960; Steck, 2000; Chan et al., 2012; Yesiltepe et al., 2021).

In contrast, out of the four buildings that were intended as landmarks when building the VR city (Schmidt et al., 2023b), only one, the high-silo building, was also identified as a gaze-graph-defined landmark. Although the designed landmarks were among the tallest buildings in the environment, their visibility and mean node degree were lower compared to the gaze-graph-defined landmarks. In general, across all buildings, node degree showed a strong association with visibility but only a weak association with height. Within this overall pattern, gaze-graph-defined landmarks emerge as outliers with particularly high node degree and visibility, whereas the designed landmarks are primarily characterized by their height, yet remain comparatively less visible. This suggests that height alone does not determine landmark potential, instead, spatial placement, especially central location and proximity to decision points, appears to play a crucial role. This interpretation is consistent with our observation that most gaze-graph-defined landmarks were located next to intersections in central areas of the city, whereas the designed landmarks were placed at the city’s edges. The high-silo building may compensate for its peripheral position through its exceptional height. Overall, these findings indicate that observed visibility, shaped by both location and gaze behavior, may be more critical for landmark utility than formal design intentions.

The observed properties of gaze-graph-defined landmarks also offer insights into their potential role for spatial navigation. Specifically, the central placement of gaze-graph-defined landmarks near decision points makes them well-suited as orientation cues (Mallot and Gillner, 2000; Chan et al., 2012; Richter and Winter 2014; Wang et al., 2014). Gaze-graph-defined landmarks were also among the most visible buildings in the environment, with at least one gaze-graph-defined landmark being visible in more than one-fourth of the explored area (exactly one in 21.86%, two or more in 6.62%), supporting their potential function as directional cues, beacons, reference points, and, where multiple landmarks were visible, triangulation (Mallot and Gillner, 2000; Waller and Lippa, 2007; Chan et al., 2012; Richter and Winter 2014; Wang et al., 2014; Ekstrom and Isham, 2017; Ekstrom et al., 2018; Yesiltepe et al., 2021; Parra-Barrero et al., 2023). Additionally, gaze-graph-defined landmarks were preferentially connected with each other, forming a rich club, which suggests they may act as a protomap that anchors participants’ emerging mental maps and supports the development of allocentric representations. Together, these findings suggest that gaze-graph-defined landmarks may support navigation at multiple spatial scales, from guiding local route decisions to anchoring the development of allocentric spatial representations.

Finally, comparison with earlier work (Walter et al., 2022) showed that, although the number and spatial coverage of landmarks varied between cities, their core characteristics, distinct appearance, central location, and strong interconnectivity, remained consistent across environments and methods (Table 6,7).

Overall, the present findings refine and extend the concept of gaze-graph-defined landmarks as a data-driven, behaviorally grounded definition of landmarks rooted in collective visual exploration. Unlike the designed landmarks, whose intended function was not consistently reflected in participants’ gaze behavior, gaze-graph-defined landmarks emerge directly from collective patterns of visual attention and show consistent characteristics across different virtual environments. By linking node degree centrality with visibility rather than height, this study highlights the importance of buildings’ spatial placement and perceptual accessibility over purely structural properties. Moreover, their central location, high visibility, and strong interconnectivity suggest that gaze-graph-defined landmarks not only support multiple classical landmark functions but may also act as anchors for emerging mental maps. These findings demonstrate that gaze-graph-defined landmarks capture a fundamental aspect of visual behavior, offering a refined understanding of why certain buildings become functionally relevant during navigation and how they differ from structurally prominent but visually less important elements.

3.3 Individual differences in spatial navigation performance

The immersive pointing-to-building task captures participants’ survey knowledge (Schmidt et al., 2023b) and mental map accuracy (He et al., 2023; Hegarty et al., 2023), thereby providing a behavioral measure of spatial knowledge acquisition. Our analysis revealed considerable individual differences in spatial task performance, which are a robust phenomenon widely documented in the literature (Ishikawa and Montello, 2006; Wolbers and Hegarty, 2010; Gramann, 2013; Weisberg and Newcombe, 2014; 2016; 2018; Weisberg et al., 2014; Ekstrom and Isham, 2017; Hegarty et al., 2018; 2023; Newcombe, 2018; Boone et al., 2019; Zanchi et al., 2022; He et al., 2023; Ishikawa, 2023; Maxim and Brown, 2023; Newcombe et al., 2023; Schinazi et al., 2023; Spiers et al., 2023). Beyond these between-participant differences, participants showed a small but reliable improvement during repeated trials, with pointing error decreasing by 5.1°. This improvement likely reflects general learning or task-related adaptations, rather than newly acquired spatial knowledge alone. Variance decomposition further indicated that nearly two-thirds of the total variance was driven by within-participant fluctuations across repeated trials, whereas stable between-participant differences accounted for a smaller proportion. To focus on modeling these stable individual differences, we aggregated the trial-based performance into participant means. This allowed us to examine how conceptual predictors explain systematic differences between individuals, rather than variability that occurs from trial to trial.

To explain individual differences in task performance, we compared three conceptually distinct models that relate participants’ mean task performance to questionnaire data, general gaze metrics, and gaze graph architecture. Both the questionnaire-based model (FRS subscales) and the gaze metrics-based model explained little variance in performance and were not statistically significant, indicating that neither self-reported spatial abilities nor general gaze metrics accounted for the observed variability. In contrast, the gaze graph-based model explained a substantial portion of the variance (R² = 0.41), suggesting a strong relationship between performance and the underlying patterns in visual exploration captured by gaze graphs.

Although the gaze-graph-based model demonstrated meaningful explanatory power, several graph measures also showed strong multicollinearity and high pairwise correlations, limiting the interpretation of individual predictors. This is partly expected, as graph measures often capture related aspects of gaze graph architecture. Consequently, the explanatory power of the model likely reflects shared structural properties captured by multiple measures rather than the isolated influence of a single metric. The regularized sensitivity analysis further supports this interpretation by showing that the association between gaze graph architecture and spatial performance persisted after accounting for the high shared variance among the graph-theoretical measures and under leave-one-out cross-validation. Rather than indicating that one graph measure is uniquely responsible for the observed relationship, these findings suggest that performance is associated with the overall structural organization of gaze behavior captured jointly by the graph-theoretical measures. In particular, higher graph density, together with a greater number of nodes and edges, was associated with lower graph diameter, indicating a more connected and therefore a more efficient overall structure. Since gaze graphs represent visual transitions between buildings during the exploration, a more efficient gaze graph architecture appears to reflect more informative visual sampling of the spatially relevant features of the environment. In gaze graphs, edges correspond to unique gaze transitions between distinct buildings, thus, denser and more efficient gaze graphs emerge when participants continue to make new gaze transitions between already viewed buildings throughout exploration. Overall, our results suggest that better spatial task performance was associated with more efficient gaze graph architecture, which could reflect a more informative visual sampling of the environment through the continued integration of previously encountered buildings with novel gaze transitions.

In contrast, the gaze metrics-based model accounted for little variance in performance and was not statistically significant, despite also relying on gaze data. The three included predictors primarily captured the quantity of attention directed toward buildings, the most spatially informative objects in the environment, by assessing the number of viewed buildings, the proportion of gazes directed toward buildings relative to other objects, and the proportion of dwell time allocated to buildings relative to other objects. Therefore, our results suggest that spatial learning cannot be explained solely by the overall quantity of visual attention directed towards relevant objects, but rather by the underlying patterns of visual attention reflected in gaze transition dynamics. This highlights the importance of considering higher-order patterns of visual behavior instead of isolated gaze statistics.

The questionnaire-based model likewise showed limited explanatory power, which points to the limitations of self-report measures in this context. Although the FRS questionnaire has been validated (Münzer and Hölscher, 2011) and shown to be associated with spatial performance in prior studies, e.g., (Münzer and Stahl, 2011; Münzer and Zadeh, 2016; Brunyé et al., 2018; Löwen et al., 2019), both our findings and other recent work also reported weak or non-significant correlations (Credé et al., 2019; König et al., 2019; 2021; Wunderlich and Gramann, 2021). This inconsistency likely reflects the substantial variability in tasks and experimental conditions across studies, a common challenge in research on individual differences in spatial navigation (Newcombe et al., 2023), and could help explain the limited explanatory power observed here. Furthermore, the FRS questionnaire may not fully generalize to the complex and naturalistic VR setting in this study. Therefore, while the FRS appears sensitive to changes in self-assessed abilities (Schmidt et al., 2023b), it did not account for between-participant performance differences, highlighting the importance of including continuous behavioral measures, especially visual behavior, into spatial navigation paradigms.

Furthermore, our results provide a new perspective on the factors underlying individual differences in spatial navigation. While prior research has emphasized environmental, cultural, linguistic, and cognitive abilities (Haun et al., 2011; Hund et al., 2012; Weisberg and Newcombe, 2016; Coutrot et al., 2018; 2022; Spiers et al., 2023) rooted in embodiment (Gramann, 2013) and modulated by stress, anxiety, motivation, and instructions (Boone et al., 2019; Maxim and Brown, 2023; Schinazi et al., 2023; Varshney et al., 2024), our findings suggest that these influences may manifest in how individuals visually explore spatial environments during learning. Specifically, better spatial task performance was associated with visual exploration patterns consistent with more informative sampling of spatially relevant features in the environment, as reflected in more efficient gaze graph architecture. Importantly, self-reported spatial abilities and general gaze metrics did not explain the observed performance differences, indicating that spatial learning is not solely determined by overall attention allocation, but by the patterns of gaze transitions between relevant environmental features. Altogether, our findings identify gaze graph structure as a promising behavioral measure associated with individual differences in spatial navigation performance and suggest visual exploration dynamics might shape the acquisition of spatial knowledge.

3.4 Vision in spatial navigation

Vision plays a central role in spatial navigation by providing continuous perceptual input of space independently of physical distance, thereby supporting landmark-based guidance at decision points, spatial updating, and flexible navigation across different reference frames (Foo et al., 2005; Chan et al., 2012; Ekstrom, 2015; Ekstrom and Isham, 2017). Our findings support and extend this framework. While the observed relationship between gaze transition dynamics and navigation performance is consistent with the view that vision supports spatial knowledge acquisition through continuous perceptual updating, our findings further suggest that spatial learning also depends on how the visual information is sampled. Specifically, we found that the underlying patterns of gaze dynamics with respect to relevant environmental features accounted for a large fraction of the variability in spatial task performance, whereas visual attention allocation did not. Importantly, more informative patterns of visual sampling, as reflected in more efficient gaze graph architecture, were associated with better spatial learning outcomes, suggesting that how information is actively acquired through gaze transitions is critical for the efficient formation of spatial knowledge. In that sense, the contribution of vision to spatial navigation appears not to simply depend on visual exposure to the environment, but on the underlying patterns of how visual information is actively sampled and integrated from the environment during spatial learning.

This interpretation is further supported by our findings with respect to gaze-graph-defined landmarks, designed landmarks, and the relationship between buildings’ node degree centrality, visibility, and height. Importantly, the visibility of buildings was strongly associated with the mean node degree but not building height. Similarly, gaze-graph-defined landmarks were characterized by both high visibility and high mean node degree centrality, whereas the designed landmarks were viewed across a much smaller spatial extent, despite being the tallest buildings in the city. This suggests that the importance of environmental features like landmarks for spatial knowledge acquisition is best explained by their perceptual accessibility within the context of active visual exploration, rather than by intrinsic properties alone. Altogether, our findings indicate that the role of vision for spatial learning and navigation extends beyond merely providing access to environmental information, but is instead characterized by the patterns through which visual information is actively sampled and integrated during exploration, which determine how efficiently spatial knowledge is acquired and ultimately shape which environmental features become functionally relevant for spatial navigation.

3.5 Limitations and future directions

While this study provides a novel framework for analyzing visual exploration, several limitations should be considered. First, the small sample (N = 26) increases the risk of overfitting. Although regularized ridge regression with leave-one-out cross-validation (LOOCV) supported the robustness of the association between graph architecture and performance, these findings remain exploratory and require larger, independent validation samples for generalizability.

Second, the definition of visibility in this study reflects observed behavior rather than objective visibility (theoretical line-of-sight). This choice reflects the study’s goal of developing a behaviorally grounded definition of landmarks, and our findings suggest that landmark status may be driven more by active perceptual accessibility than by intrinsic physical properties. Nevertheless, objective visibility would provide a valuable comparison in future VR studies.

Third, the street-art photography task may have biased visual sampling toward specific buildings. While this design simulated realistic, goal-directed exploration (e.g., tourism) and helped to sustain engagement throughout the 2.5-h exploration duration, future research should compare these findings with unstructured exploration to isolate task-driven gaze behavior.

Fourth, the gaze graph represented only buildings as nodes, excluding other environmental features. Although appropriate for a building-dominated virtual city and necessary for the graph-theoretical framework, this simplification omits non-building cues and may link buildings that were not viewed within a single saccade, which should be considered when interpreting the resulting gaze graph structure.

Finally, the use of seated locomotion and the exclusion of participants susceptible to motion sickness may reduce ecological validity and limit generalizability. Future research incorporating natural walking and a broader sample of VR tolerance would provide a more complete picture of visual exploration in real-world urban environments.

Furthermore, while the present graph-based approach captures meaningful patterns in the visual exploration behavior, future work could extend this framework by incorporating more fine-grained temporal and directional information. In particular, directed and weighted gaze graphs capturing the frequency and directionality of gaze transitions could provide deeper insights into the gaze dynamics underlying spatial learning and knowledge formation. Likewise, examining the temporal development of gaze graphs throughout exploration, rather than aggregating 2.5 h of visual behavior into a single graph, could help characterize how visual behavior exploration patterns and gaze-graph-defined landmarks evolve over time, particularly with respect to changes in gaze-graph structure and behavior related to gaze-graph-defined landmarks. Such future work would also benefit from a more fine-grained gaze classification method than the current threshold-based pre-processing, such as the velocity-based gaze detection algorithm proposed by Nolte et al. (2024). Additionally, while prior work has linked movement and exploration patterns to the space syntax of the environment (Brunec et al., 2023) and human agents (Sánchez Pacheco et al., 2025), the contribution of visual behavior remains unclear. Integrating the temporal development of graph-theoretical measures, visual attention, and movement behavior offers promising opportunities to better understand spatial learning, knowledge formation, and the functional role of landmarks over time.

3.6 Conclusion

Overall, this study highlights that vision contributes to spatial navigation not simply through access to environmental information, but through dynamic patterns of visual exploration that shape spatial learning. By applying a naturalistic immersive eye tracking paradigm combining free exploration with immersive spatial tasks, we were able to show that individual differences in navigation performance are best explained by gaze transition dynamics reflected in gaze graph architecture rather than general measures of visual attention or the FRS questionnaire. Importantly, better task performance was associated with a more efficient gaze graph architecture, which could reflect more informative visual sampling of the environment. Therefore, gaze graph architecture may represent a promising behavioral measure of individual differences in spatial performance. Additionally, gaze-graph-defined landmarks show consistent characteristics of both global and local landmarks, but their importance is better explained by visibility and location than by height. Extending the graph-theoretical approach to directed or weighted graphs and investigating the development of gaze graphs over time offer promising opportunities for future research. Altogether, our findings underscore the value of graph-theoretical approaches for capturing meaningful patterns of visual behavior and identify visual exploration dynamics as an important target for understanding individual differences in spatial navigation, with more efficient visual sampling linked to improved spatial learning and navigation performance.

4 Materials and methods

4.1 Study design and participants

The work presented here is part of a larger mixed-methods study examining behavioral and self-reported changes related to spatial knowledge acquisition. Other behavioral results of this study, including a comparison to a group of participants that were trained to use an augmented exploration, are reported in Schmidt et al. (2023b). The present study focuses on general behavioral patterns, specifically visual behavior, during spatial navigation and therefore only includes the control group. Participants were screened using age (18–39) and the absence of motion sickness, substance abuse, psychotropic drug use, cognitive-impacting medical abnormalities, and neurological history. Of 28 recruited participants, two withdrew due to acute motion sickness, resulting in a final sample of 26 individuals aged 18 to 35. Participants received either monetary compensation or university-internal participation credits, according to their preference.

4.2 Virtual reality setup and data collection

The experiment was conducted in an immersive virtual reality using the Vive Pro Eye headset (Resolution: 1,440 × 1,600 pixels per eye (2,880 × 1,600 pixels combined), Refresh rate: 90 Hz, Field of view: 110°) and Valve Index controller (Figure 1a). Participants were seated on a swivel chair that allowed them to fully rotate their bodies (Figure 1a). During the exploration phase of the experiment, participants were able to walk in the environment using their controller, with the forward direction of walking determined by the chest-mounted HTC tracker. Therefore, participants were free to rotate their head without any interference with their walking direction, providing more naturalistic conditions for the head movement behavior and further minimizing the risk of motion sickness. Participants’ height in the virtual city was set to 1.50 m to standardize the viewing perspective.

Eye tracking was performed using the Tobii eye tracker integrated in the Vive Pro Eye headset (accuracy: 0.5°–1.1°, trackable field of view: 110°), calibrated with the 5-point SRanipal system calibration, and validated using a custom-built validation procedure to ensure the calibration error did not exceed 1° visual angle. A full calibration and validation procedure was performed before every 30-min exploration session, with an additional 1-point validation every 10 min, followed by a full calibration and validation procedure if the error exceeded the 1° threshold. The eye tracking functionality was integrated in Unity with the HTC SRanipal interface. Eye tracking, head tracking, and body tracking data was synchronized and collected at runtime with a mean sampling rate of 90 Hz.

4.3 Experimental procedure

The experiment consists of five phases:

• Completion of the FRS questionnaire on spatial strategies and preferences
• Movement training in VR (training environment)
• Free exploration of the virtual city of Westbrook for 2.5 h (5 × 30-min exploration sessions across several days)
• Task training in VR (training environment)
• Spatial navigation tasks within Westbrook

At the start of the experiment, participants were asked to answer the FRS questionnaire on spatial strategies (Münzer and Hölscher, 2011). The FRS questionnaire is a self-report tool that aims to measure a respondent’s likelihood to apply certain spatial strategies and their spatial abilities. These are divided into the categories: global-egocentric spatial knowledge, survey knowledge, or cardinal directions. For example, the FRS questionnaire contains questions like “I always imagine the surroundings as a 'mental map'” or “My sense of orientation is very good.”

During movement training, participants learned to navigate in VR using body rotation and controllers, and practiced taking a picture of the environment using their controller. The training was completed once the participants demonstrated fluent walking behavior in VR and took at least one picture.

In the exploration phase, participants explored the virtual city of Westbrook by freely walking around using the road network and any walkable terrain. In order to provide additional motivation to explore the various city streets and paths, participants were instructed to photograph buildings with street art. At the start of each 30-min session, participants were placed at the same central location, whereas they continued at the location they last visited, after completing the one-point validation checks every 10 min. Additionally, participants were allowed to request a break at any point they desired during the experiment. In the case of an additional break or if the headset was moved, a full calibration and validation procedure for the eye tracker was performed. The 30-min exploration sessions were conducted on 5 separate occasions, always with at least 6 h and a maximum of 3 working days in between the appointments. Thereby, we could ensure that all participants received similar learning and consolidation intervals.

Following 2.5 h of free exploration, participants performed three types of spatial navigation tasks: a pointing-to-building task, a pointing-to-north task, and a ghost-house-building-placement task (Schmidt et al., 2023b). Before performing the tasks in the virtual city, participants received the task instructions and performed practice trials in a training environment. After successfully answering several training questions of each task type, a full calibration and validation procedure was performed, and participants were teleported to their first task location. The two pointing tasks were performed first, however, it should be noted that the order of the pointing-to-building and pointing-to-north tasks was randomized, consequently, some participants performed a pointing-to-north task before the pointing-to-building task (Schmidt et al., 2023b).

The current study focuses on the pointing-to-building task, which measures participants’ spatial knowledge, specifically their survey knowledge (Schmidt et al., 2023b) and mental map accuracy (He et al., 2023; Hegarty et al., 2023). During the task, participants were teleported to different locations in the city and asked to point towards task buildings (Figure 7a). The task consisted of eight task buildings that all featured street art but varied in size and appearance (Figure 7c). The eight task locations were directly located in front of the corresponding task building. The task buildings and locations were evenly distributed over the city area (Figure 7b), and at each task location, none of the other seven task buildings were visible. During the task, participants were teleported to the eight task locations in the city while being rotated to a random degree, placed directly in front of the “start” building for the respective set of trials, and asked to point to the remaining seven task buildings, which served as the pointing targets. Throughout the task, participants were free to rotate their head and body in any direction, but were restricted from walking and translational movements. The order of task locations and pointing “target” buildings at each location was randomized. The participant performed 56 unique “start-target-building” pointing trials, which, upon completion, were repeated a second time in a newly randomized order to assess participants’ consistency, resulting in a total of 112 pointing-to-building trials. At each task location, the “target” building of each trial was displayed in a small square in the top center of the HMD, which could be enlarged with a button press. To point towards the “target” building, participants pointed their controller into the desired direction (Figure 7a). The pointing direction was displayed in the virtual environment in the form of a green beam. By pressing the trigger button of the controller, participants were able to freeze the pointing beam. Once satisfied with the pointing direction, participants could either confirm their response by pressing the trigger button again to proceed to the next trial or unfreeze the beam and adjust their selection.

4.4 The virtual town of Westbrook

The virtual town of Westbrook covers 75.5 ha (996 m × 758 m) and contains 244 unique buildings, including 232 unique residential and commercial buildings, a castle, a farm, a school, a silo, several garages (5 were separate free-standing buildings while all others were regarded as part of the neighboring building), and two cranes (Figures 1b,c). The environment additionally features various parks, construction sites, a bus stop, a basketball court, and a variety of small objects to increase the naturalistic feeling of the environment (e.g., benches, trees, cars, bicycles, lamps, traffic lights, fences, greenery, dirt piles, and scaffolding) (Figure 1b). The realistic road network consisting of streets and paths in various sizes was inspired by the city of Baulmes in Switzerland (though heavily modified).

In order to limit the amount of movement possibilities while preserving free exploration of the virtual town, the walkable area of the city was restricted to the road network, small trails, and shortcuts over grass, while natural visual barriers were used to indicate movement limits (e.g., curbs, steps, hedges, walls, and fences). No virtual characters were included to avoid social influences, though static objects like cars and bicycles enhanced ecological realism. Other environmental cues for orientation, specifically clouds and the sun, were minimized by modifying the skybox with repeated identical cloud patterns and disabling shadows. The aim of the virtual town of Westbrook was to provide an environment with optimal conditions to obtain data about spatial knowledge acquisition in a controlled setting that still feels naturalistic to the research participant.

4.5 Data pre-processing and gaze classification

The eye tracking and head tracking information was synchronized at runtime to calculate a gaze vector, which was used to perform a raycast in viewing direction and identify all hit colliders, i.e., physical object boundaries in VR. The hit colliders were sorted by distance from the gaze origin, and the two closest colliders were saved together with all other eye tracking, unity-specific, and raycast variables with a mean 90 Hz sampling rate.

In the pre-processing pipeline, the first hit collider was replaced with the second hit collider if it was transparent (e.g., invisible barriers for experiment functionality), see-through (e.g., wire-mesh fence, scaffolding), or belonged to a natural object (e.g., trees, bushes) while the second corresponded to a building. Next, the eye tracking data was cleaned based on the SRanipal variable “combined validity bitmask” and samples without a combined validity bitmask value of 3 were marked as invalid (4.75% of data).

The subsequent pre-processing, i.e., interpolation and gaze identification, was adapted from our earlier work (Walter et al., 2022). Consecutive data samples on the same collider were grouped into clusters. Short gaps (≤266.6 ms) between clusters of the same collider were interpolated and merged. Finally, clusters with a duration of at least 266.6 ms were classified as gazes, forming the basis for further analysis. On average, 72% of the data was classified as gazes.

4.6 Gaze graph creation

Gaze graphs were created for each participant, based on the identified gazes in the pre-processing, following the creation process and definitions of our earlier work (Walter et al., 2022). In the gaze graph, nodes represent buildings that were viewed at least once by the participant. Edges between nodes represent direct gaze transitions between the corresponding buildings. Gazes on non-building objects (e.g., road, trees, cars, etc.) were ignored in this process, thus, transitions across such objects were treated as direct connections between buildings. Importantly, gaze graphs were undirected and unweighted, therefore, neither the direction nor the frequency of gaze transitions was represented in the gaze graph. Data interruptions (e.g., remaining missing data clusters, breaks due to validation procedures, or session changes) resulted in disconnected graph segments, with no edge formed across these gaps. A detailed description of the gaze graph creation process, with additional visualizations and mock-up graphs with detailed descriptions of more complex graph-theoretical measures, can be found in (Walter et al., 2022).

4.7 Graph-theoretical measures

4.7.1 Number of nodes

Number of nodes N: total number of nodes in a graph.

Intuition for gaze graphs: number of viewed buildings in the city, i.e., unique buildings seen by the respective participant.

4.7.2 Number of edges

Number of edges E : total number of edges in a graph.

Intuition for gaze graphs: number of unique gaze transitions between distinct buildings in the city.

4.7.3 Density

Graph density D : the ratio of existing edges relative to all possible edges.

D = 2 E N N − 1

Intuition: Indicates how densely connected a graph is relative to its maximum possible connectivity.

4.7.4 Shortest path

Shortest path length d i , j: minimum number of edges required to connect the two nodes i and j.

Intuition for gaze graphs: measures the shortest distance between the two nodes in the graph, thus, the minimum number of gaze transitions needed to travel from one of the nodes to the other in the gaze graph (Figure 10).

4.7.5 Diameter

Graph diameter D = m a x i , j d i , j: length of the longest (maximum) shortest path length between any pair of nodes in the graph.

Intuition: graph diameter is the maximum shortest-path distance between any pair of nodes (or the worst-case shortest-path distance) in the graph (Figure 10).

4.7.6 Node degree centrality

Node degree k i : number of edges connected to node i.

k i = ∑ j i A i j

Intuition for gaze graphs: number of how many unique gaze transitions exist between this building and any other building in the city, or in other words, how often was this building viewed directly before or after viewing other buildings? How important is this building in the gaze graph?

4.7.7 Hierarchy index

The hierarchy index h: exponent of the slope of a power-law fit to the degree distribution in a bi-log plot of node frequency versus node degree (Rodrigue, 2024), calculated using only degrees above the median value.

Intuition for gaze graphs: measures the slope of the relationship between the number of connections per building and how often these buildings exist in the graph, considering only buildings with above-average connectivity, with higher values indicating a very small number of high-node degree buildings.

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Footnotes

Edited by: Jonathan Touryan, United States Army Research Laboratory, United States

Reviewed by: Gi-bbeum Lee, Korea Advanced Institute of Science and Technology (KAIST), Republic of Korea

Misun Kim, University College London, United Kingdom