Superquadric Glyphs for Symmetric Second-Order Tensors

—Symmetric second-order tensor fields play a central role in scientific and biomedical studies as well as in image analysis and feature-extraction methods. The utility of displaying tensor field samples has driven the development of visualization techniques that encode the tensor shape and orientation into the geometry of a tensor glyph. With some exceptions, these methods work only for positive-definite tensors (i.e. having positive eigenvalues, such as diffusion tensors). We expand the scope of tensor glyphs to all symmetric second-order tensors in two and three dimensions, gracefully and unambiguously depicting any combination of positive and negative eigenvalues. We generalize a previous method of superquadric glyphs for positive-definite tensors by drawing upon a larger portion of the superquadric shape space, supplemented with a coloring that indicates the tensor’s quadratic form. We show that encoding arbitrary eigenvalue sign combinations requires design choices that d...

• Type: Journal
• Year: 2010
• Where: TVCG
• Authors: Thomas Schultz, Gordon L. Kindlmann
• Keywords: Second-order Tensors, Symmetric Second-order Tensors, Tensors, TVCG 2010