Quaternion-based Signal Processing

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 nd differences between subtlety varying images. This technique relies on applying a quaternionic Fourier transform, a quaternionic Gabor lter and exploits the symmetries inherent in the quaternion. Two applications of hypercomplex image disparity estimation are time lapse analysis and boundary detection.