A BAYESIAN APPROACH TO SPACEBORN HYPERSPECTRAL OPTICAL FLOW
ESTIMATION ON DUST AEROSOLS
Fabian E. Bachl, Christoph S. Garbe
University of Heidelberg
Interdisciplinary Center for Scientific Computing
Heidelberg, Germany
Paul Fieguth
University of Waterloo
Dept. of Systems Design Engineering
Waterloo, Ontario, Canada
ABSTRACT
The significant role dust aerosols play in the earth’s climate sys-
tem and microbial nutrition cycles have lead to increased efforts of
employing remote sensing to monitor their genesis, transport and
deposition. This contribution extends earlier approaches of using
Bayesian hierarchical models to extract dust activity from multi-
spectral MSG-SEVIRI measurements by focusing on the signal-to-
noise ratio with respect to post hoc motion analysis via optical flow.
While interpreting also the latter in a completely Bayesian fashion,
we show that our novel dust indication scheme reduces background
noise and thereby renders the optical flow more decisive in terms of
detecting even faint dust plumes. As a side effect of the indicators
stability in case of dust absence, we point out the potential usage
of its temporal variance to characterize dust at an early stage of the
genesis and thus close to the corresponding source region.
Index Terms— Bayesian methods, Multispectral imaging,
Aerosols, Image motion analysis, Image segmentation
1. INTRODUCTION
Dust aerosol has a significant impact on the atmospheric radiation
budget by influencing microphysical cloud processes, scattering and
absorbing shortwave radiation and absorbing and re-emitting long-
wave radiation [1]. Its effect on the global climate system is addi-
tionally underlined by its global depositions that provides mineral
nutrients to oceanic and terrestrial ecosystems which ultimately in-
fluence the CO2-cycle [2].
Satellite remote sensing is a powerful instrument for assessing
atmospheric dust distribution. In particular the Meteosat Second
Generation (MSG) Spinning Enhanced Visible and InfraRed Imager
(SEVIRI) is well suited for this task. Using differences of its 8.7
μm, 10.8 μm and 12.0 μm infrared Brightness temperature (BT)
measurements, the instrument is capable of capturing sub-daily pro-
cesses like short-termed cycles of dust emission at intervals of 15-
minutes and a resolution of 3x3 km at nadir [3].
As shown by Bachl et al. [4], a Bayesian Hierarchical Model
(BHM) can be employed to generate a linear predictor (LP) from
SEVIRI data that serves as an indicator for the presence of dust and
facilitates determining the trajectory of dust plumes via optical flow.
Using the resulting flow field to warp back the thresholded LP can
then serve to point out spatial regions that are likely to be the source
of the plume (left columns of Figure 1). However, since the LP is
a background dependent linear mixture of infrared channels, it also
carries over the noise incorporated by the signal. This results in two
interwoven problems. On the one hand, as shown in Figure 1(b) and
(d), faint dust is easily underestimated by the LP but lowering the
detection threshold is likely to induce false positives which then in-
terfere with the source detection. On the other hand, as shown in
Figure 1(f), especially in cases of faint dust the movement as repre-
sented by the optical flow is a strong indicator for its presence.
In this contribution we extend previous approaches in the sense
that the LP is not a linear projection but a probabilistic mapping of
the signal. We show that this increases the temporal signal-to-noise
ratio of the LP forward differences, a quantity that enters the opti-
cal flow but also appears to be a promising indicator for dust source
detection. Additionally, our method also yields a higher expressive-
ness of the corresponding optical flow compared to flow based on
multiple channels or a projection according to Linear Discriminant
Analysis.
2. METHODS
We begin this section with an introduction into the class of models
we are employing as well as the type of inference we are performing.
Thereafter, different dust indication schemes are elucidated and a
Bayesian interpretation of optical flow is given.
2.1. Generalized Linear Models
Recent developments in computational statistics, known as Inte-
grated Nested Laplace Approximations (INLA), have paved the way
for efficient inference in a subclass of BHMs, the Generalized Linear
Model (GLM) [5]. In this class, each variable in the set of obser-
vations {yi }i∈1...N is assumed to come from an exponential family
distribution parameterized by the inverse image μi of a structured
additive predictor ηi under a link function g(·), i.e. g(μi )= ηi .
Each ηi is linearly generated by a subset of a possibly very high
dimensional latent Gaussian Markov Random Field (GMRF) x and
in most cases μi defines the mean of the distribution generating yi .
Using local covariate vectors z
(i)
and u
(i)
the process generating yi
can be work in two ways. A subset {x
k
}
k∈K
of the latent field x
can serve as linear projection coefficients. Another subset {xj }j∈J
can represent function evaluations f
(j)
:= xj at the covariate values
u
(i)
j
. Summing up over both sets then results in the following linear
predictor:
ηi =
j∈J
f
(j)
(u
(i)
j
)+
k∈K
x
k
z
(i)
k
(1)
The corresponding likelihood functions of yi as well as the prior
distribution of the latent field x themselves depend on a set Θ of
parameters that again obey predefined prior distribution. The overall
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