A Gauss-Markov Model for Hyperspectral Texture Analysis of Urban Areas Guillaume Rellier, Xavier Descombes, Josiane Zerubia Ariana - projet commun Cnrs/Inria/Unsa INRIA, 2004 route des Lucioles, BP 93 06902 Sophia Antipolis Cedex, France
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Abstract
Fr´ed´eric Falzon Alcatel Space Industries Bd du Midi, BP 99 Cannes la Bocca Cedex, France
[email protected]
2 Multivariate Markovian texture model
In this paper we tackle the problem of texture segmentation using a joint spectral and spatial analysis of pixel distribution. Hyperspectral images are considered and using a Markovian model we develop a vectorial approach for this image type. A classification algorithm using this model has been implemented for extracting and classifying urban areas. Results obtained from AVIRIS images are shown.
1 Introduction Texture analysis is frequently used for disambiguating the classification process of remote sensing images. In particular, urban areas are not well classified by using only pixel radiometry. So, in order to decrease the classification error a segmentation of urban areas is performed using texture arguments and the classification of the other areas is based on radiometry analyses. Usually texture classification of urban areas is carried out using a panchromatic high resolution image, whereas classification of natural elements uses multi/super/hyperspectral images that have a better spectral resolution. The output of this process is a thematic map obtained by merging the result of the two classifications. In this framework, it is likely that urban areas can be better modelled by working jointly in spatial (contrast) and spectral (color) domains. So, in this paper, we focus on the determination and test of a texture model able to jointly characterize urban areas from spatial and spectral variations of hyperspectral remote sensing images. In the next section, we describe a Markovian texture model able to perform such an analysis. In section 3, we show how to insert it into a hyperspectral image classification algorithm. We present some results in section 4 and conclude in section 5.
In the case of a joint spectral and spatial texture analysis, classical texture features (gray level cooccurence matrices [2], Gabor transform [5], ...) can not easily be used. Indeed, algorithmic complexity, due to the huge amount of hyperspectral data, is high. In our case, we prefer to build one single compact operator capable of analyzing textures both spatially and spectrally, which is also well suited to classification. The proposed model, within a multivariate data analysis framework, is based on a Markov Random Field (MRF). The usual 2-D MRF model can be adapted in two ways for multispectral images : consider it as a 2-D spatial field of vectorial (spectral) measures (see e.g. [3]) or as a 3-D spatial-spectral field of scalar variables (see e.g. [8]). What follows id a description of a model of the first type.
2.1 Multivariate Gauss-Markov model We consider an hyperspectral image as a realization of a field , where each site is defined . by two spatial coordinates on a lattice of size Each is a random vector of dimension , the number of bands. The conditional probability of a Multivariate GaussMarkov Random field (MGMRF) is given by :
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