Quaternionic Representation of the Riesz Pyramid for Video Magnification

Abstract

Recently, we presented a new image pyramid, called the Riesz pyramid, that uses the Riesz transform to manipulate the phase in non-oriented sub-bands of an image sequence to produce real-time motion-magnified videos. In this report we give a quaternionic formulation of the Riesz pyramid, and show how several seemingly heuristic choices in how to use the Riesz transform for phase-based video magnification fall out of this formulation in a natural and principled way. We intend this report to accompany the original paper on the Riesz pyramid for video magnification.