Periodicity-Based Computation of Optical Flow

Abstract

The standard Brightness Constancy Equation states spatiotemporal shift-invariance of the input data along a local velocity of optical flow. In its turn, the shift-invariance leads to a periodic function of a real argument. This allows application of a known test for periodicity to computation of optical flow at random locations. The approach is valid also for higher dimensions: for example, it applies to a sequence of 3D tomography images. The proposed method has a reasonably high accuracy for continuous flow and is noise-tolerant. Special attention is paid to weak-signal input. It is shown that a drastic reduction in the signal strength worsens the accuracy of estimates insignificantly. For a possible application to tomography, this would lead to an unprecedented diminution of harmful radiation exposure.