Quaternion-based Signal Processing

Ben Witten and Jeff Shragge

ben@sep.stanford.edu

ABSTRACT

Hypercomlex numbers, which have primarily been used for pattern recognition, offer many useful applications to geophysics. Image disparity estimation is a hypercomplex, phase-based technique, using quaternions, that can find differences between subtlety varying images. This technique relies on applying a quaternionic Fourier transform, a quaternionic Gabor filter and exploits the symmetries inherent in the quaternion. Two applications of hypercomplex image disparity estimation are time lapse analysis and boundary detection.