Symmetry in Scalar Fields

Automatic detection of symmetry is a challenging problem because both the segmentation of the domain into potential symmetric segments and the correspondence between segments that are symmetric need to be determined. Moreover, real life data sets never exhibit perfect symmetry.

Since the search space for locating symmetric segments is quite large, it is also important to design an algorithm that is computationally efficient. Domain experts are interested in studying important features that provide insights about the underlying scientific phenomena that is being analyzed.

We have developed four different methods to detect symmetry in scalar fields. We have also demonstrated applications to symmetry-aware transfer function design, symmetry-aware isosurface extraction, and symmetry-aware editing and rendering enhance traditional visualization methods. We believe that the methods we propose for symmetry detection will open new frontiers in analyzing structural similarity of scalar fields and more applications of symmetry detection will emerge.

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