Visualization of Two-Dimensional Symmetric Tensor Fields Using the Heat Kernel Signature

Abstract

We propose a method for visualizing two-dimensional symmetric tensor fields using the Heat Kernel Signature (HKS). The HKS is derived from the heat kernel and was originally introduced as an isometry invariant shape signature. The time parameter of the heat kernel allows a multiscale analysis in a natural way. By considering a positive definite tensor field as a Riemannian metric the definition of the HKS can be applied directly. To investigate how this measure can be used to visualize more general tensor fields we apply mappings to obtain positive definite tensor fields. The resulting scalar quantity is used for the visualization of tensor fields. For short times it is closely related to Gaussian curvature, i. e. it is quite different to usual tensor invariants like the trace or the determinant.