  Motion segmentation for natural images commonly relies on dense optic flow to
yield point trajectories which can be grouped into clusters through various
means including spectral clustering or minimum cost multicuts. However, in
biological imaging scenarios, such as fluorescence microscopy or calcium
imaging, where the signal to noise ratio is compromised and intensity
fluctuations occur, optical flow may be difficult to approximate. To this end,
we propose an alternative paradigm for motion segmentation based on optimal
transport which models the video frames as time-varying mass represented as
histograms. Thus, we cast motion segmentation as a temporal non-linear matrix
factorization problem with Wasserstein metric loss. The dictionary elements of
this factorization yield segmentation of motion into coherent objects while the
loading coefficients allow for time-varying intensity signal of the moving
objects to be captured. We demonstrate the use of the proposed paradigm on a
simulated multielectrode drift scenario, as well as calcium indicating
fluorescence microscopy videos of the nematode Caenorhabditis elegans (C.
elegans). The latter application has the added utility of extracting neural
activity of the animal in freely conducted behavior.
