Objective Existing explorations of Chinese classical gardens have predominantly relied on qualitative analysis. The emergence of quantitative research using space syntax has offered a solution to this issue. Although the applicability of space syntax has been validated with eye-level and knee-level application patterns being explored, most of such applications lack systematic and in-depth analysis, thereby limiting their practical effectiveness. To address these issues, this research aims to integrate classical theory with quantitative methods. By extracting spatial indicators from classical theories, this research constructs a framework using quantitative methods such as space syntax and machine learning. Starting from the human perceptual level, this research aims to systematically measure the spatial indicators of classical gardens that were previously deemed “immeasurable”, while also supporting design practice.

Methods Theoretical framework: This research utilizes classic theoretical works to extract and summarize five spatial indicators that characterize the uniqueness and perceptibility of garden space: permeability, curvature, visibility, accessibility, and differentiation. To incorporate quantitative analysis, a multi-indicator overlay technique is employed to combine spatial indicators, spatial perception experience, and the meaning of visibility graph analysis (VGA) indicators. This approach presents a mapping framework that links indicators to spatial perception and VGA indices. Technical methods: To measure the indicators, VGA is combined with DepthmapX for research on the eye-level and knee-level models of garden space, which involves the calculation of such VGA parameters as connectivity, visual step depth, and integration. ArcGIS is then used to normalize different VGA index values and perform multi-model and multi-index superposition analysis concerning the mapping framework for spatial indicators, achieving preliminary measurement of spatial indicators. The density-based spatial clustering of applications with noise (DBSCAN) algorithm is employed for cluster analysis on the data obtained after spatial superposition analysis in ArcGIS, accurately identifying typical spaces under different dimensions and saliency levels. Liu Garden and the Humble Administrator’s Garden are chosen as measurement examples. To verify the scientificity of the aforesaid measurement methods, a small-scale spatial perception experiment is conducted, employing image questionnaires and perception heat maps to verify the consistency between the analysis results and actual human perception.

Results Permeability characterizes the spatial hierarchy of the gardens, and the high permeability areas in both gardens exhibit a scattered distribution. Curvature indicates the degree of spatial angle change, with the high curvature areas primarily located along the periphery of both gardens. Spaces with high visibility often take the form of sightseeing corridors, with Liu Garden forming a continuous high visibility channel from southwest to northeast, and visibility in the Humble Administrator’s Garden gradually increasing from south to north. The spatial differentiation in accessibility of Liu Garden diverges linearly to both sides, while that of the Humble Administrator’s Garden diverges from a central point. Differentiation reflects the misalignment of visual and moving lines in space. In Liu Garden, the spaces with high differentiation are mainly found in small-scale courtyards that rely on corridors and windows to create spatial interest. The differentiation cluster in the Humble Administrator’s Garden exhibits a scattered distribution, primarily located in the southern part. Additionally, this research analyzes the spatial characteristics of each level with Liu Garden as an example. Finally, through spatial perception experiments, the research reveals a high consistency between the results of quantified measurement and the subjective perceptions of the participants, providing preliminary evidence for the scientificity and rationality of the spatial indicators extracted and the analytical framework constructed for such spatial indicators.

Conclusion This research proposes a systematic spatial indicator framework. Compared to previous analyses, the new system more fully depicts the spatial characteristics of classical gardens. Additionally, this research combines various quantitative techniques to establish a deep and easily applicable measurement framework. With this method, a large-scale and refined measurement of existing representative Chinese classical gardens can be quickly achieved, deepening our understanding of the spatial art of classical gardens from a quantitative perspective and promoting the scientific and refined development of the research on spaces of Chinese classical gardens. Moreover, this research effectively empowers design practices by enabling a rapid quantitative evaluation of spatial layouts, organizational structures, and perceptual experience in existing design proposals. Finally, this research comprehensively applies various quantitative methods such as space syntax and machine learning, thereby expanding the technical and methodological resources for quantitative research on garden spaces.