Harmonic Field Analysis

Harmonic analysis techniques are established and successful tools in a variety of application areas, with the Fourier decomposition as one well-known example. In this chapter, we describe recent work on possible approaches to use Harmonic Analysis on fields of arbitrary type to facilitate global feature extraction and visualization. We find that a global approach is hampered by significant computational costs, and thus describe a local framework for harmonic vector field analysis to address this concern. In addition to a description of our approach, we provide a high-level overview of mathematical concepts underlying it and address practical modeling and calculation issues. As a potential application, we demonstrate the definition of empirical features based on local harmonic analysis of vector fields that reduce field data to low dimensional feature sets and offers possibilities for visualization and analysis.