Optical flow and depth from motion for omnidirectional images using a TV-L1 variational framework on graphs

This paper deals with the problem of efficiently computing the optical flow of image sequences acquired by omnidirectional (nearly full field of view) cameras. We formulate the problem in the natural spherical geometry associated with these devices and extend a recent TV-L1 variational formulation for computing the optical flow. The discretization of differential operators occurring in this formulation turns out to be an extremely sensitive point, in particular for the TV part of our algorithm. We show that these difficulties can be very efficiently overcome using a graph-based formulation of TV denoising, which we solve by introducing a graph version of Chambolle´s algorithm. A slight modification of the original framework allows us to solve the depth from motion problem using the same techniques. In both cases, our graph-based algorithms provide computationally efficient solutions and significantly outperform naive implementations based on direct discretization of the operators, or on neglecting the influence of geometry.