Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Mean Shift: A Robust Approach Toward Feature Space Analysis
IEEE Transactions on Pattern Analysis and Machine Intelligence
Computing contour trees in all dimensions
Computational Geometry: Theory and Applications - Fourth CGC workshop on computional geometry
Restricted delaunay triangulations and normal cycle
Proceedings of the nineteenth annual symposium on Computational geometry
Anisotropic polygonal remeshing
ACM SIGGRAPH 2003 Papers
A Reflective Symmetry Descriptor for 3D Models
Algorithmica
Partial and approximate symmetry detection for 3D geometry
ACM SIGGRAPH 2006 Papers
Analysis of scalar fields over point cloud data
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Topological Spines: A Structure-preserving Visual Representation of Scalar Fields
IEEE Transactions on Visualization and Computer Graphics
Symmetry in Scalar Field Topology
IEEE Transactions on Visualization and Computer Graphics
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Identifying symmetry in scalar fields is a recent area of research in scientific visualization and computer graphics communities. Symmetry detection techniques based on abstract representations of the scalar field use only limited geometric information in their analysis. Hence they may not be suited for applications that study the geometric properties of the regions in the domain. On the other hand, methods that accumulate local evidence of symmetry through a voting procedure have been successfully used for detecting geometric symmetry in shapes. We extend such a technique to scalar fields and use it to detect geometrically symmetric regions in synthetic as well as real-world datasets. Identifying symmetry in the scalar field can significantly improve visualization and interactive exploration of the data. We demonstrate different applications of the symmetry detection method to scientific visualization: query-based exploration of scalar fields, linked selection in symmetric regions for interactive visualization, and classification of geometrically symmetric regions and its application to anomaly detection.