Metropolitan cities are facing many socio-economic problems (e.g., frequent traffic congestion, unexpected emergency events, and even human-made disasters) related to urban crowd flows, which can be described in terms of the gathering process of a flock of moving objects (e.g., vehicles, pedestrians) towards specific destinations during a given time period via different travel routes. Understanding the spatio-temporal characteristics of urban crowd flows is therefore of critical importance to traffic management and public safety, yet it is very challenging as it is affected by many complex factors, including spatial dependencies, temporal dependencies, and environmental conditions. In this research, we propose a novel matrix-computation-based method for modeling the morphological evolutionary patterns of urban crowd flows. The proposed methodology consists of four connected steps: (1) defining urban crowd levels, (2) deriving urban crowd regions, (3) quantifying their morphological changes, and (4) delineating the morphological evolution patterns. The proposed methodology integrates urban crowd visualization, identification, and correlation into a unified and efficient analytical framework. We validated the proposed methodology under both synthetic and real-world data scenarios using taxi mobility data in Wuhan, China as an example. Results confirm that the proposed methodology can enable city planners, municipal managers, and other stakeholders to identify and understand the gathering process of urban crowd flows in an informative and intuitive manner. Limitations and further directions with regard to data representativeness, data sparseness, pattern sensitivity, and spatial constraint are also discussed.