@ARTICLE{CoGiRu15,
author = {Sergio Conti and Janusz Ginster and Martin Rumpf},
title = {A {BV} Functional and its Relaxation for Joint Motion Estimation
and Image Sequence Recovery},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
year = {2015},
volume = {49},
pages = {1463--1487},
number = {5},
abstract = {The estimation of motion in an image sequence is a fundamental task
in image processing. Frequently, the image sequence is corrupted
by noise and one simultaneously asks for the underlying motion field
and a restored sequence. In smoothly shaded regions of the restored
image sequence the brightness constancy assumption along motion paths
leads to a pointwise differential condition on the motion field.
At object boundaries which are edge discontinuities both for the
image intensity and for the motion field this condition is no longer
well defined. In this paper a total-variation type functional is
discussed for joint image restoration and motion estimation. This
functional turns out not to be lower semicontinuous, and in particular
fine-scale oscillations may appear around edges. By the general theory
of vector valued BV functionals its relaxation leads to the appearance
of a singular part of the energy density, which can be determined
by the solution of a local minimization problem at edges. Based on
bounds for the singular part of the energy and under appropriate
assumptions on the local intensity variation one can exclude the
existence of microstructures and obtain a model well-suited for simultaneous
image restoration and motion estimation. Indeed, the relaxed model
incorporates a generalized variational formulation of the brightness
constancy assumption. The analytical findings are related to ambiguity
problems in motion estimation such as the proper distinction between
foreground and background motion at object edges.},
doi = {10.1051/m2an/2015036}
}