Abstract This study investigates the development and clinical applications of Large Deformation Diffeomorphic Metric Mapping (LDDMM) in medical image registration. Through systematic comparison between conventional optimization-based methods and contemporary deep learning techniques, we evaluate their respective performance in registration accuracy, computational efficiency, and clinical utility. Our methodology encompasses a thorough examination of both mathematical foundations and neural network implementations in LDDMM. Results demonstrate that traditional approaches maintain superior precision for complex anatomical variations via rigorous variational optimization, whereas deep learning methods achieve substantial computational acceleration (reducing processing time from hours to seconds) through learned deformation patterns. Critical analysis reveals important trade-offs: while deep learning offers remarkable speed improvements, traditional methods preserve accuracy advantages in specialized clinical scenarios. We identify key challenges including computational complexity, implementation difficulties, and domain adaptation limitations, while proposing hybrid architecture and transfer learning as potential solutions. The study concludes that integrating the mathematical robustness of conventional LDDMM with the computational efficiency of deep learning presents the most viable path forward. Such synergistic approaches promise to advance medical image analysis pipelines and promote wider clinical implementation of sophisticated registration technologies.