*2.2. Similarity Analysis of Urban Morphology*

A further step based on the extracted features is to use regression models to cluster the samples and analyze their similarities. Researchers have used multiple methods, such as classification, clustering, or ranking the solution-instances to manage the database [27]. In recent decades, researchers emphasized typo-morphology-related, context-sensitive, and systematic urban form studies, such as socio-ecological spatial morphology [28]. Mathematical methods can also be used for similarity analysis. In the study of case-based design with 3D mesh architectural models [29], a TRAMMA (Topology Recognition and Aggregation of Mesh Models of Architecture) method was proposed for the clustering, retrieving, and reconstructing architectural elements for a new architectural model.

For the urban renewal process, the Roma urban renewal [30] study built a similarity searching system based on the block shapes to search for cases similar to the new block shape and adapt the urban fabric to the new site to preserve the historical context. The

Roman study investigated the case retrieval method for finding a case with similar block shapes to the block to be designed. They adjusted the pre-defined indicators related to the cases' geometric characteristics for input, until they obtained satisfactory retrieved results. The referred retrieval indicators in the Roman study included the block area, building density, the block-to-bounding-box ratio, the length-to-width ratio, and the function type. Then, they generated the flyover above the railway station for their design proposal [31]. The case similarity was detected based on the evaluation of these indicators. Then, one case that met the input conditions was retrieved from the dataset.

Since the regeneration study based on the retrieved cases required efforts from other aspects related to specific design tasks, it is important to make the interface for connecting the case retrieval and regeneration periods. For example, Hua regenerated new 3D mesh models by combing the parts of the cases based on the extracted floor elements and the corresponding walls. The extracted elements are the interface connecting the retrieved cases and the regenerated models [29].

In the Roman study, the retrieved case was arbitrarily applied to a new block automatically by simple geometrical operations (e.g., scaling and rotation), and architects can adjust the applied results manually based on a visual model software [31]. Therefore, the regeneration period could be realized by multiple techniques as long as the case retrieval process is highly automated. Therefore, in this study, we focused on the morphological quantification method's efficiency, the ability to bring more cases, and the flexibility for implementing new datasets for case retrieval.
