Section: New Results
Keywords : fire plume, multispectral image, natural risk, microcanonical multifractal formalism.
Plume detection in NOAA AVHRR datasets: use of the Microcanonical Multifractal Formalism
Participants : Hussein Yahia, Jacopo Grazzini [ FORTHIACM ] , Isabelle Herlin, Antonio Turiel [ ICM ] , Nektarios Chrysoulakis [ FORTHIACM ] .
This work takes place within the framework of the Egide PAI Plumesat. The greek partners have developped a pixelbased method allowing the characterisation of plume pixels in NOAAAVHRR data. The present work attempts at solving some remaining problems by use of the turbulent spatial information properties contained in the various channels of the NOAAAVHRR sensor.
The Microcanonical Multifractal Formalism (MMF) is a theoretical and algorithmic framework allowing the derivation of geometric structures in turbulent acquisition datasets; these geometric structures describe the multifractal hierarchy of transition fronts in the context of Fully Developped Turbulence (FDT). We make use of a fundamental property of MMF about reconstructible systems: the derivation of a synthesized multispectral reduced signal . We use the assumption that the MSM (Most Singular Manifold) computed in the thermal infrared band is directly related to the streamlines of the underlying fluid, so we take this set as the correct reference on the geophysical fluid flow dynamics. Consequently, we want to use the information of the MSM in combination with other spectral bands to provide a spatiallybased discrimination method for the determination of plumes. We will use the signal gradient of a function of channels c_{2} (near infrared) and c_{3} (middle infrared) to enhance the discrimination between plumes and others bodies taking into account temperature and reflectance information. Let (c_{2}, c_{3}) be a function of the pixel's greylevel values acquired in spectral bands c_{2} and c_{3} . We define a synthesized signal p by propagating 's gradient vectors from the MSM computed in channel c_{5} (thermal channel); that is, we use the MMF reconstruction formula in which the gradient information is replaced by 's gradient values :
with:

f = (f_{x}, f_{y}) is the twodimensionnal frequency vector.

The hat symbol refers to the Fourier transform.

is the signal's gradient restricted to the MSM.

The dot symbol · in formula (1 ) refers to vector dot product.
This formula means that the gradient of is diffused from the set of strongest transitions on the thermal infrared channel. Results are presentend in figure 3 in the case of the Genoa acquisition dataset.