Riesz pyramids for fast phase-based video magnification

We present a new compact image pyramid representation, the Riesz pyramid, that can be used for real-time phase-based motion magnification. Our new representation is less overcomplete than even the smallest two orientation, octave-bandwidth complex steerable pyramid, and can be implemented using compact, efficient linear filters in the spatial domain. Motion-magnified videos produced with this new representation are of comparable quality to those produced with the complex steerable pyramid. When used with phase-based video magnification, the Riesz pyramid phase-shifts image features along only their dominant orientation rather than every orientation like the complex steerable pyramid.

1. Introduction

Numerous phenomena exhibit small motions that are invisible to the naked eye. These motions require computational amplification to be revealed [10], [12], [19], [21]–. Manipulating the local phase in coefficients of a complex steerable pyramid decomposition of an image sequence is an effective, robust method of amplifying small motions in video [19], but complex steerable pyramids are very overcomplete (21 times) and costly to construct, requiring either a large number of filter taps or a frequency domain construction where care must be taken to avoid spatial wrap-around artifacts [11], [15]. The overcompleteness and high cost of implementing the complex steerable pyramid make current phase-based video magnification slow to compute.