Technical Report MSC-2007-21

Title: Symmetries of non-rigid shapes
Authors: Dan Raviv
Supervisors: Ron Kimmel
Abstract: Symmetry and self-similarity is the cornerstone of Nature, exhibiting itself through the shapes of natural creations and ubiquitous laws of physics. Since many natural objects are symmetric, the absence of symmetry can often be an indication of some anomaly or abnormal behavior. Therefore, detection of asymmetries is important in numerous practical applications, including crystallography, medical imaging, and face recognition, to mention a few. Conversely, the assumption of underlying shape symmetry can facilitate solutions to many problems in shape reconstruction and analysis. Traditionally, symmetries are described as extrinsic geometric properties of the shape. While being adequate for rigid shapes, such a description is inappropriate for non-rigid ones. Extrinsic symmetry can be broken as a result of shape deformations, while its intrinsic symmetry is preserved. Here we explore the problem of evaluating intrinsic symmetries in non-rigid objects. We define and visualize this new concept of symmetry, which can be considered as a generalization of the well studied Euclidean symmetries. We present an efficient mathematical framework for the evaluation of the level of symmetry.

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