  We propose the first approach for the decomposition of a monocular color
video into direct and indirect illumination components in real time. We
retrieve, in separate layers, the contribution made to the scene appearance by
the scene reflectance, the light sources and the reflections from various
coherent scene regions to one another. Existing techniques that invert global
light transport require image capture under multiplexed controlled lighting, or
only enable the decomposition of a single image at slow off-line frame rates.
In contrast, our approach works for regular videos and produces temporally
coherent decomposition layers at real-time frame rates. At the core of our
approach are several sparsity priors that enable the estimation of the
per-pixel direct and indirect illumination layers based on a small set of
jointly estimated base reflectance colors. The resulting variational
decomposition problem uses a new formulation based on sparse and dense sets of
non-linear equations that we solve efficiently using a novel alternating
data-parallel optimization strategy. We evaluate our approach qualitatively and
quantitatively, and show improvements over the state of the art in this field,
in both quality and runtime. In addition, we demonstrate various real-time
appearance editing applications for videos with consistent illumination.
