Symmetry Shape Analysis

Symmetry is a fundamental and pervasive property found in both natural and man-made objects, playing a key role in aesthetics, structure, and function. In computational domains, symmetry serves as a powerful cue for data compression, structure inference, and shape understanding. This work presents a comprehensive overview of symmetry analysis in 3D shapes, with a particular focus on computational methods for symmetry detection and their applications in diverse fields such as CAD, computer vision, medicine, archaeology, and 3D modeling. We provide formal definitions of exact, approximate, and partial symmetries in the context of rigid transformations, and we survey five major categories of detection approaches: transformation-based, correspondence-based, voting-based, optimization-based, and learning-based methods. Special emphasis is placed on recent deep learning techniques, which have significantly advanced the state of the art yet face challenges in generalization and robustness. Finally, we identify key open problems and future directions, including the need for richer and more varied datasets, better generalization of learning-based models, effective formulations for symmetry detection in incomplete data, and the integration of symmetry priors in generative modeling. Our analysis highlights both the progress and the limitations of current methods and aims to guide future research toward more principled and capable symmetry-aware systems.