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Identifying symmetry in scalar fields.

Talha Bin Masood


Study of symmetric or repeating patterns in scalar fields is important in scientific data analysis because it gives insights into the properties of the underlying phenomenon. Identifying symmetry in scalar fields has largely remained unexplored till now. A few approaches for finding global symmetry in scalar fields and finding symmetry in scalar field topology have been proposed recently. Existing methods for identifying symmetry in scalar field topology completely ignores the geometry, and hence may report non-intuitive symmetric regions. In this report we provide a more precise definition for symmetry in scalar fields that incorporates the geometry and propose an approach for identifying partial and approximate symmetry in 2D and 3D scalar fields. The proposed approach overcomes the shortcomings of identifying symmetry based solely on topology.