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 TermsBayesian 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 }i1...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 } kK of the latent field x can serve as linear projection coefficients. Another subset {xj }jJ 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 = jJ f (j) (u (i) j )+ kK 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 256 978-1-4673-1159-5/12/$31.00 ©2012 IEEE IGARSS 2012