**5. Conclusions**

This morphological similarity analysis represents a helpful analysis framework for many fields, such as typo-morphological, historical evolution, pre-design contextualization, and building energy performance. Finding cases in similar situations to the target could support designers in obtaining new information and knowledge resulting in better decision making and furthering scientific studies. Quantitative descriptions of urban morphology provide a baseline for in-depth urban fabric interpretation. This study aimed to develop a data-driven approach to quantitatively describe urban morphology and to develop a multi-dimensional case retrieval method for urban design decision-making in the early stage for association studies on morphology with specific social or economic aspects.

In this study, 3817 residential cases with geometrical and social service information from Nanjing, China, were filtered to construct the dataset. The data source was exported as figure–ground images for training the deep CNN GoogLeNet with the inception-v3 module, encoding the images into 2048-dimensional feature vectors based on grayscale values. The similarity analysis of the cases was verified by calculating the Euclidean distance between HDFV. A comparison study was conducted in the case retrieval process to integrate the morphological and infrastructural similarity.

This study demonstrated the feasibility and power of the deep learning network in urban morphological similarity analysis and multi-dimensional decision making. The deep learning algorithms provided a method to automatically extract/learn the intrinsic features from a large amount of data. The morphological features were represented by HDFV, which contained comprehensive information for the morphological characteristics.

The multi-dimensional case retrieval method can support comprehensive decisionmaking and morphology-related scientific studies by providing customers with many references in similar situations with the target based on the comprehensive and precise similarity analysis. This method is integrated with easy access to related infrastructure and social and economic information. Other information that is related to the specific task (e.g., culture, traffic, energy performance, and economic consequences) could be easily implemented under the same framework to support decision-making and further scientific studies regarding associations of morphology and other urban aspects.

Future work will focus on technological improvements and more application scenarios. Adding more dimensions to the data source, such as additional color values to indicate building heights, would be an effective improvement of the model performance. Approaches to using geometric spatial data as direct inputs to the neural network rather than figure–ground images will be explored for better computational efficiency and more precise case retrieval. More typo-morphology-related attributes could be added to the data sources according to specific scenes.

For example, energy performance, user testimonials, traffic conditions, industrial distributions, the natural environment, and so on could be introduced for more comprehensive similarity analysis to better support design decision making. In addition, the HDFV could serve as the interface for connecting retrieved cases and regeneration. For example, new design proposals could be generated derived from retrieved cases by implementing energy evaluation and optimization or rule-based generative design.

**Author Contributions:** Conceptualization, C.C.; Methodology, C.C., Z.G. and B.Z.; Software, C.C. and Z.G.; Validation, C.C. and Z.G.; Formal Analysis, C.C.; Resources, X.W.; Data Curation, X.W.; Writing—Original Draft Preparation, C.C.; Writing—Review and Editing, C.C., Z.G., P.T. and B.L.; Visualization, B.Z.; Supervision, B.L. and P.T.; Funding Acquisition, B.L., C.C. and Z.G. All authors have read and agreed to the published version of the manuscript.

**Funding:** This study was funded by the National Natural Science Foundation of China (NSFC) project (No. 51978139). This study was funded by China Scholarship Council (CSC) grant 201706090254 and 202006090151.

**Conflicts of Interest:** The authors declare no conflict of interest.
