  Viewing a data set such as the clouds of Jupiter, coherence is readily
apparent to human observers, especially the Great Red Spot, but also other
great storms and persistent structures. There are now many different
definitions and perspectives mathematically describing coherent structures, but
we will take an image processing perspective here. We describe an image
processing perspective inference of coherent sets from a fluidic system
directly from image data, without attempting to first model underlying flow
fields, related to a concept in image processing called motion tracking. In
contrast to standard spectral methods for image processing which are generally
related to a symmetric affinity matrix, leading to standard spectral graph
theory, we need a not symmetric affinity which arises naturally from the
underlying arrow of time. We develop an anisotropic, directed diffusion
operator corresponding to flow on a directed graph, from a directed affinity
matrix developed with coherence in mind, and corresponding spectral graph
theory from the graph Laplacian. Our methodology is not offered as more
accurate than other traditional methods of finding coherent sets, but rather
our approach works with alternative kinds of data sets, in the absence of
vector field. Our examples will include partitioning the weather and cloud
structures of Jupiter, and a local to Potsdam, N.Y. lake-effect snow event on
Earth, as well as the benchmark test double-gyre system.
