## 2 Background (Research and Theoretical Framework)
### Analytical (Quantitative) Framework of the Urban Morphology  
The range of quantitative approaches to urban morphology facilitates complex and meaningful comparative studies in morphological contexts. This section presents relevant methods for quantitatively investigating urban form. [PERSON] advances the understanding of cities towards the quantitative side [33] (p. 15), shifting from a top-down to a bottom-up approach [34] to capture the degree of diversity while explaining relationships within the hierarchy [35]. According to his way of thinking, urban form--differentiated from one to another or over time--is defined by the geometry of size and shape, scale, and dimension. Morpho is a methodology for quantitatively assessing urban form at different scales, using various criteria such as street and block accessibility, building age, dimensions of street blocks and plot series, building alignment, the ratio of building height to street width, and building usage. This methodology focuses on both synchronic (current) and diachronic (historical) analysis, allowing for the monitoring of the evolution of urban form over time [36]. Urban morphology addresses different aspects, different scales, and different elements of urban form, providing a consistent descriptive language for understanding the spatial structures and processes of urban development and transformation [31]. Morphometrics involves the quantitative investigation and description of urban morphology by quantifying and classifying urban elements based on characteristics such as size and shape, using multivariate statistical analysis [37]. Quantitative urban morphological analysis [37; 38] is used to systematically characterize urban form elements based on their attributes, measurements, and metrics at different scales of the built environment. [PERSON] et al. [10] proposed urban morphometric methods following the analogy with biological morphometrics for the systematic investigation of the evolution of urban form. These methods quantify the size, shape composition, density, usage, and arrangement of urban form elements using multivariate statistics for rigorous description and classification. In a subsequent study, [PERSON] et al. [39] applied this urban morphometrics approach to characterize city forms and their changes over time. By measuring and comparing key morphological features, this method identifies similar and recognizable patterns, which are defined by statistical recurrence. [PERSON] and [PERSON] [9] employed a morphometric method to define a set of attributes related to urban morphology at various scales, including objects, compositions, neighborhoods, and municipalities. This approach allows for the identification of typologies at these scales and classifies the built environment into distinct typological classes. Space syntax, a quantitative assessment of the urban morphology developed by [PERSON] and [PERSON] in (1984) [40], employs a syntactic analysis of street networks and configurational assessment to explore various forms and configurations. This method focuses on the geometric and topological attributes and measurements of the built environment. The configurational approach in urban morphology involves understanding the relationship between voids and solid spaces [31], where their spatial configuration is the result of a generative process. The notion of configuration itself represents the relationships between different levels of urban forms, which can adapt and evolve over time due to changes or variations, leading to the creation of different types [31]. To effectively distinguish the similarities and differences in configuration, it is necessary to establish a clear definition of various street patterns, enabling comparison and the recognition of distinctive types [41]. This helps generate meaningful types and establish an effective typology by offering choices among them.