Phase-based video magnification relies on being able to manipulate the local phase in image sub-bands. Riesz pyramid breaks the input image into non-oriented sub-bands using an efficient, invertible replacement for the Laplacian pyramid and then takes an approximate Riesz transform of each band. The Riesz transform is the natural rotation-invariant, 2D transform that allows for phase analysis without having to break the image sub-bands into multiple orientations. Motion processing with the Riesz transform occurs by phase-shifting an input signal along its dominant orientation to produce motion magnification. Temporal filtering and phase denoising is conducted to sharpen the signal and improve the results.
Additionally, processing is done entirely in the spatial domain. This gives an efficient and easy way to avoid the spatial wrap-around artifacts present in the frequency domain implementation of complex steerable pyramids. Building and collapsing the Riesz pyramid is efficiently implemented because of shared computation between bands, symmetry of the filters and because the Riesz transform is approximated by two three tap finite difference filters. Phase-based video magnification using the Riesz representation allows the production of high-quality motion-magnified videos in real time.