Quaternion Atomic Phase Magnification for 2D and 3D Motion

The phase computation is used in many applications of signal and image processing such as edge, line, symmetry detection, image analysis and recently to show small motion or color changes. Eulerian video processing allows to show small color changes and motions invisibles to the naked eye. Eulerian motion magnification, was modify using the phase and the Riesz pyramid in order to reduce the noise amplification. In this work we introduced a novel phase magnification approach based on a infinitely differentiable unique compact supported window, an atomic function. Another contribution of our work was apply our quaternion phase and Eulerian magnification to 3D motion, which has not been reported so far, we propose to use simple projections of conformal algebra in order to do the magnification at any plane of the 3D space. We compare the phase (Riesz Pyramids), with the atomic Riesz pyramid, in our comparation our atomic pyramid Riesz preserves more information than the phase Riesz approximation, besides our approach is slower by 2.5 times. Finally, we compare method and the linear magnification (Laplace Pyramid) in terms of the Signal to Noise Ratio (SNR). We found that the phase magnifications has better response to noise than the linear method.