Driven by the increasing demands of producing consistent and high-quality crystals for high value-added products such as pharmaceutical ingredients, the operation and design of a crystallization process have phased from an empirical trial-and-error approach to the modern frameworks powered by the online process analytical technologies (PATs) and model-based process optimization techniques. The one-dimensional crystal size distribution (CSD) measured by the well-established PATs is inadequate due to the missing particle morphology information. A major contribution of this thesis is to develop an image analysis-based PAT powered by the deep learning image processing techniques, whose accuracy and functionality outperformed the traditional PATs and other image analysis techniques. The PAT was deployed to monitor and study the slurry mixture of glass beads and catalyst particles as well as a taurine-water batch crystallization process. The results confirmed the superb accuracy of two-dimensional size and shape characterization in a challengingly high solids concentration. The classification capability enabled unparalleled functionalities including quantification of agglomeration level and characterization of different polymorphs based on their distinct appearances. A computerized crystallization platform was built with the developed PAT, which could automate the time-consuming experiments for determining the metastable zone width (MSZW) and induction time of a crystallization system. The application of the PAT revealed the potential to simplify and speed up the research and development stage of a crystallization process. The rich two-dimensional crystal size and shape information provided by our PAT enabled more descriptive multi-dimensional modeling for the better prediction of the crystallization process. The novel population array (PA) solver developed in this thesis could solve the multi-dimensional crystallization population balance equation (PBE) more computationally efficient than the existing discretization-based numerical methods without compromising the accuracy. The PA solver could accurately model the complex phenomena including agglomeration, breakage, and size-dependent growth. The efficient computation enables solving the complex multi-dimensional PBE for crystal morphology modeling. The combination of the innovative PAT and modeling technique is a significant contribution to the crystallization field that enables better understanding and more effective control of a crystallization process.