Eulerian video magnification is inspired by a model in fluid mechanics called Eulerian specification of the flow field. Let's consider a moving, fluid body, such as a river. The Eulerian specification describes the river's velocity at a given position and time. The velocity would be fast in the mountains in springtime and slow at the river's mouth in winter. Also, the velocity would be slower at a silt-saturated point at the river's bottom, compared to a point where the river's surface hits a rock and sprays. An alternative to the Eulerian specification is the Lagrangian specification, which describes the position of a given particle at a given time. A given bit of silt might make its way down from the mountains to the river's mouth over a period of many years and then spend eons drifting around a tidal basin.
For a more formal description of the Eulerian specification, the Lagrangian specification, and their relationship, refer to this Wikipedia article http://en.wikipedia.org/wiki/Lagrangian_and_Eulerian_specification_of_the_flow_field.
The Lagrangian specification is analogous to many computer vision tasks, in which we model the motion of a particular object or feature over time. However, the Eulerian specification is analogous to our current task, in which we model any motion occurring in a particular position and a particular window of time. Having modeled a motion from an Eulerian perspective, we can visually exaggerate the motion by overlaying the model's results for a blend of positions and times.
Let's set a baseline for our expectations of Eulerian video magnification by studying other people's projects:
Now, let's discuss the functions that are building blocks of these projects and ours.