In the rapidly evolving field of medical image analysis, the promise of Artificial Intelligence (AI)and Machine Learning (ML) to revolutionize diagnostic accuracy, speed, and patient outcomes is palpable. However, two critical challenges distinctively characterize this domain, shaping the trajectory of research and application development. Firstly, unlike domains awash with data, medical image datasets are inherently limited and difficult to acquire. This scarcity is driven by stringent privacy regulations, the high cost of data collection and annotation, and the variability across patient populations and imaging modalities. Secondly, the stakes of medical decision-making elevate the importance of interpretability in AI systems to paramount levels. Clinicians and patients alike demand transparency and explainability, not just predictions, from AI tools, to trust and effectively integrate these technologies into healthcare workflows. The constraints of data scarcity and the imperative for interpretability underscore the necessityto transcend traditional ML approaches that predominantly rely on vast datasets and opaque, complex models. Instead, there is a pressing need to integrate domain-specific knowledge into ML algorithms for medical image analysis. Such knowledge spans the biomechanics of biological systems, the established shape priors of organs, and the intricate mechanisms and hallmark features of diseases as manifested in imaging studies. By weaving this rich tapestry of medical and biological understanding into the fabric of AI models, we can augment the learning from limited data with insights drawn from centuries of medical practice and research. This integrated approach champions a more nuanced pathway to harnessing the power of AI inmedical imaging. It acknowledges that while learning from data is foundational, the incorporation of human expertise and domain knowledge is also critical. This dual strategy aims to enhance the performance and interpretability of AI systems, ensuring they are not only powerful tools for clinicians but also trustworthy companions in the journey towards improved patient care. In essence, the fusion of knowledge and learning in medical image analysis stands as a beacon of hope, promising to navigate the complexities of healthcare challenges with a more informed and nuanced approach. In this thesis, we concentrate on addressing vision correspondence and classification problems—twoof the most critical challenges in the medical domain. Our investigation spans a range of pivotal applications, including motion tracking in dynamic imaging, longitudinal studies for monitoring disease progression, surgical interventions for multi-view guidance, and the enhancement of computer-aided diagnosis systems. Through the lens of AI and ML, we endeavor to bridge the gap between clinical needs and technological capabilities, heralding a new era of healthcare innovation where precision and reliability are paramount.