Deformable shapes are crucial for various image analysis tasks, e.g., image registration for real-time image-guided navigation systems of tumor removal surgery, image classification for neuro-degenerative diseases, and template-based image segmentation. Although recent advances in deep learning-based image analysis have achieved groundbreaking performance by providing a universal mechanism to extract image features in the context of texture, intensity, or simple geometry features, they fall short in capturing much more complex and detailed geometric information behind the image data. This greatly hinders the power of image analysis models when analyzing and quantifying geometric shapes are important. The modeling of deformable shapes presents significant challenges due to their high-dimensional and non-linear nature of data. Existing deep learning algorithms suffer from high computational cost of network training and inference, as well as severely decreased model performance caused by broken assumptions of image quality (i.e., missing data, corrupted signals, or occurrence of new objects). To address these challenges, I first developed deep neural networks to learn low-dimensional shape representations based on fine-grained deformations derived from image registration algorithms with much lower computational complexity in training. I then investigated a new paradigm of deep learning models that are capable of analyzing such learned shape representations to improve the current performance of image analysis tasks, including but not limited to population-based image studies. In order to enhance the robustness of shape-based deep networks, I developed geometric metamorphic learning algorithms to properly consider image conditions where missing data, or appearance changes occur. The algorithmic foundation of my research work could potentially impact a variety of real-world clinical applications, including but not limited to automated diagnosis for neurodegenerative diseases (i.e., Alzheimer’s) and real-time image-guided navigation systems for neurosurgery (i.e., brain tumor resection).