Contribution of the methodologies development for the analysis of remote sensing data

Emna Karray, Mohamed Anis Loghmari, Hela Elmannai and Mohamed Saber Naceur Laboratoire de Teledetection et Systeme d informations a Reference spatiale

Ecole National D Ingenieurs de Tunis BP-37 Belvedere Tunis, Tunisia

ekarray@yahoo.fr, MohamedAnis.loghmari@isi.rnu.tn, hela.elmannai@gmail.com and Saber.Naceur@insat.rnu.tn

Abstract—In this paper, we consider the problem of Blind source separation (BSS) method by taking advantage of the sparse modeling of the hyperspectral images. These images are produced by sensors which provide hundreds of narrow and adjacent spectral bands. The idea behind transform domains is to apply some transformations to illustrate the dataset with a minimum of components and a maximum of essential information. To take advantages from the new representation of hyperspectral data, a novel classification approach based on using Binary Partition Trees (BPT). The BPT is obtained by iteratively merging regions and provided a combined and hierarchical representation of the image in a tree structure of regions.

Keywords-component; source separation; sparse; hyperspectral; hierarchical representation; binary partition trees

I. INTRODUCTION A fundamental problem in remote sensing discipline is to

extract the useful information and to find a suitable representation of multivariate-observed data [1]. Given that this information is subject of several perturbations, it is in generally, not directly accessible. The main aims of this work are; firstly, to identifying the transfer function of linking signals of interest (sources) to the observations and secondly to envisage the restoration of valuable information [2]. Accordingly, we proceed by representing complex data such as hyperspectral images in a manner allowing efficient extraction of the essential structures of these data. This new representation is obtained by developing an approach based on the blind source separation (BSS) in frequency domain. The signal is called sparse in the transformed domain when most of its energy is concentrated on very few coefficients. It must evidently contain the same information in order to highlight the specific characteristics of the original signal and examine it from another way. To benefit from the new representation of hyperspectral data, we will precede to the classification approaches source by source in order to obtain good correspondence class/source. Therefore, to achieve the best performance for image classification, several runs using different parameters should be chosen according to the characteristics of dataset. In particular, the integration of spatial information crucial for the analysis of images and spectral information constitutes the richness of dataset.

II. DOMAINS OF DATA REPRESENTATION

A. Problematic We consider a set of images I

{ },),( lkVi ),1(),1(),,1( LlandKkIi ∈∈∈ are the coordinate of a pixel of the image i. Blind Source Separation (BSS) consists in the processing of these images in the following form

∑ =∈= I

i ijij JjlkVBlkS1

),1(),,(),( (1)

The matrix B is called separation or unmixing matrix. To determine this matrix and therefore the sources, we assume that the images are linear mixture of sources and by the inverse relationship we can write

∑ =+= J

j ijiji lkNlkSAlkV1

),(),(),( (2)

Where A is a mixing matrix and Ni an additive noise matrix. In most cases, we admit that this noise is Gaussian, stationary and white. Such is the case for most separation algorithms, the noise is ignored and we can consider that the matrices A and B are inverses of each other. It is obvious that (1) corresponds to an ill-posed problem. In the case of an ignorance of both: original sources and separating matrix B, Jutten et al. then Comon introduced the constraint of a research from independent sources. In order to clarify this notion, many criteria have been introduced and have resulted in precious algorithms such as FastICA, JADE and SOBI [3]-[4].

B. Source separation in image-domain The source separation method can be applied to

hyperspectral imaging to separate the components and make them statistically independent. This method is the most appropriate for our study, since the observation images show a strong correlation between them. The principle of source separation technique consists in the extraction of unknown source signals from their instantaneous linear mixtures by using a minimum of prior information: The mixture should be “blindly” processed. So, we describe this technique from m random processes or observations, noted {x[k]} kϵN (x[k] =[x1[k]…xm[k]]T) that result from a linear mixture of n random

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processes or sources, noted {s[k]} (s[k] =[s1[k]…sn[k]]T). The general configuration of sources separation is shown in Fig.1.

Figure 1. General configuration of source separation

Signals received by sensors can be modeled by the source signals in the following general form

][][][ kbkAskx += (3) Where x[k] is a m×T noisy instantaneous observed signals, s[k] is a n×T source signals, (b[k] = [b1[k]…bm[k]]T) is a m×T additive noise corrupting the observation images and A is a m×n mixing application. BSS technique consists of finding an application B known as a separator, such that:

][][ kBxky = (4) The BSS on the hypothesis of an instantaneous linear

mixing has and continues to stimulate a great interest in several applications. Therefore we emphasize, in this work, on the method of source separation using second and fourth order statistics for hyperspectral images to obtain more accurate representation of the ground surfaces.

C. Source separation in frequency-domain To provide a valid decomposition of the hyperspectral

images, we adopted a blind and automated procedure that relies on an optimal decomposition of the image spectra [5]. The frequency approach used in this work is implemented by mixing DCT and second/fourth order statistics. Since DCT is a linear orthogonal transformation, it can be applied either on spatial or on spectral data. The used criterion should provide independent information tuned to distinct spectra. The extracted independent components may lead to a meaningful data representation which permits to extract information at a finer level of precision. The positive effect of such transformation is the removal of redundancy between neighbouring pixels in the first stage and the discrimination between low and high frequency of bands in the second stage. The particularity of our approach is to implement the DCT in order to extract independent spatial-frequency sources. The DCT exploits interpixel redundancies to turn into excellent decorrelation for most natural images. The frequency source separation method can be modelled by the following form

Tdct

Tdct

Tdct NASX += . (5)

Hence, the source separation problem is transformed to the DCT domain. The superscript T indicates that the related matrix is of T columns. Furthermore, DCT exhibits excellent energy compaction for highly correlated images such as hyperspectral images and because the noise produces DCT

coefficients that are close to zero at a smaller frequency, we can model our frequency based approach by a free noisy form

'' T

dctTdct ASX = (6)

where TdctX is a m×T’ matrix and 'T

dctS is a n×T’ matrix with T’ << T. T’ is chosen to give the most important coefficients. So, T' is the result of sorting coefficients and they are taken the largest in terms of energy at low frequencies of transformed images.

Figure 2. Transformed domain 2D-DCT of hyperspectral images

The separation complexity can be reduced by manipulating T’ DCT coefficients instead of T pixel values. Then, to ensure the identification of the sources and to improve the statistical efficiency, we estimate the dominant independent orientation from only the most significant DCT coefficients. In fact, we adopt in our work an algorithm of independent component analysis in the frequency domain.

D. Evaluation of sparsity decomposition Sparsity has emerged as being a very effective way to

distinguish the sources. In fact, representing the hyperspectral images in well suited database functions provide allows for distinction of various types of objects. So, we explore in this work the use of sparse decomposition techniques of hyperspectral data: Discrete Cosine Transform (DCT) and we will show and compare the effect of sparse basis on dataset. In this work, we use the Compact Airborne Spectrographic Imager (CASI)

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Figure 3. Power spectral density of the image-domain source

components based on (the left) the use of second order statistics and on (the right) the use of higher order statistics.

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Figure 4. Power spectral density of DCT-domain source components

based on (c) the use of second order statistics and on (d) the use of higher order statistics

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Image domain source (2nd order statistics)

Image domain source (higher order statistics)Dct domain source (2nd order statistics)

Dct domain source (higher order statistics)

Figure 5. (On the left) Power spectral density of the observation components and (on the right) the mean power spectra of the original bands, image domain sources and DCT-domain sources based on the

use of second and higher order statistcs

This sensor can acquire up to 228 spectral bands between the wavelengths 400 to 1000 nanometers. Thereafter, we illustrate the performance of our approach on hyperspectral data, which are known to be sparse in the DCT-domain. At the beginning, we consider the hyperspectral observations. Before processing, we show the power spectral density of these images “Fig. 5-(a)”. This figure illustrates the huge correlation between the power spectral densities of the hyperspectral images. In Fig. 4-(c, d), the source power spectral densities look more separated using second and fourth order statistics in the spatial domain. It is interesting to note that the most important spectral components of the new sources “Fig. 4- (c)” are accumulated in the same frequency range 0-15 Hz of original images “Fig. 5- (a)”; as opposed to the power spectra of the spatial domain sources “Fig. 5- (e)”, which are ranging in a larger frequency domain. The result of Fig. 5- (f) is in excellent agreement with the previous results. In the other step, a classical classification method result was done using fifteen input classes identified from a ground truth chosen by experts who are familiar with the terrain. (a) (b) (c) (d)

Figure 6. Classification result for (a) initial bands; ER=14.54%, (b) image-domain sources; ER=12.14%, (c) DCT-domain sources based

on the use of second order statistics; ER=11.97% and (d) DCT-domain sources based on the use of higher order statistics;

ER=11.93%,

III. METHODOLOGY DEVELOPMENT OF CLASSIFICATION

A. Motivation The remote sensing images are used to extract meaningful

and useful information by detecting and characterizing all the component elements. The classification of scenes and the extraction structures (roads, buildings, objects, textures, etc…), are indispensable tools to interpret the remote sensing data. In fact, classification approach is one among the interpretative methods of images. It aims to assign each pixel in the image a label identifying what it represents in a scene. The result of a classification process usually depends on two important choices: the classification method of making a decision between all classes and the set of parameters describing each class which that they could be selected to best represents the characteristics of each class compared to other [6]. In this work, we implement a method of combined and hierarchical classification based on parameters such as mean and standard deviation to define the class attributes. As a result from previous approach based on sparse decomposition, we will process sources that are independent, uncorrelated and with the most significant components.

B. Combined and hierarchical classification of sparness sources The advent of hyperspectral remote sensing image

currently imposes to reconsider other methods of interpretation of scenes specifically the classification [8]. In this context, we propose a combined classification approach that combines information from all sources and based on hierarchical attributes of classes that will be introduced in the classification procedure. The original aspect of this method is the fact that we do not decompose the histogram of each source in the exact number of classes present in the ground truth. Each source is decomposed into G Gaussian that they chosen to obtain a good approximation with a low number of classes.

Figure 7. Proposed methodology for a combined and hierarchical

classification

The expectation maximization (EM) algorithm optimizes the parameters of the single distributions in an iterative process until a stopping-criterion is met. The result is a partitioning of the image and the number of regions must be specified a-priori. At each pixel and for each source is assigned a Gaussian gj(k, l) with the maximum posteriori probability.

• Combined procedure

From sources extracted images, we will start by specifying the number of regions for each source. The next step is the selection of pixels belonging to different classes. Seen that there is a complementarily of information between different results, a combination will be effected. The problem of this combination is the appearance of classes that are empty and classes that contain very few components. Consequently, a very large number of classes appear and we obtain GJ possible class. But not all are occupied. By adopting an algorithm for counting making source by source, we could determine the not empty classes. The number of classes of the ground truth P is probably much lower than GJ. This progressive procedure leads us to obtain a combined label classified image with a large number of classes G’ with P <G’< GJ.

• Hierarchical classification procedure

In this step, the homogenous image classes or regions are extracted from combined image. So this is a region-based process which the first stage is based on assigning for each class spatial features. Furthermore, the characteristics of these features enrich significantly the available information contained in the image. Indeed, data will be treated as attributes and not as the vector image data or labels. As indicators to characterize each region: the mean and standard deviation such as in the following matrix of attributes

jJ cGcG

cc

cc

mu

mu

mu

σ

σσ

22

11

(7)

In this context, to achieve hierarchical multi-scale description of image content, we implement an agglomerative approach where we begin with each individual class and merge the two closest classes. A region merging classification is based on the series of information such as: Average and Standard deviation features as shown in the matrix of attributes. The second step of agglomerative hierarchical classification algorithm is based on conversion of classes’ features to G’× G’ distance matrix.

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21221

11112

kkkk

kk

kk

ij

ddd

ddd

ddd

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…

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(8)

With k indicate the index of class number.

This representation is based on using Binary Partition Trees (BPT) [7]. The BPT is obtained by iteratively merging regions and provided a hierarchical representation of the image in a tree structure of regions. The proximity between object can be measured as distance matrix. The complete definition of the merge algorithm requires first determining the model region to represent a region and to characterize the union of two regions. In the second place, it is also necessary to determine the merging criterion C (Ri, Rj) to choose the distance between Ri and Rj to determine the merging order of regions and hence the structure of the tree. We use Euclidean distance; we can compute the distance between objects using the following formula

∑ −=k

jkikij xxd 2/12 ))(( (9)

A step which is very important in this study is based on specifying how we can determine what class to link at another class. In fact, we can proceed by linking two closets classes through one of the linkage methods. To do this, we use a simple linkage or a single linkage. It is also called nearest

neighbor and uses the smallest distance between objects in the two classes.

),,(min(),( jmui xxdistmud σσ = (10)

),,(),,,( σxjjxii mu …… ∈∈

• Discussion and evaluation

In order to evaluate the performance of the proposed approach of classification, we compare two classification results of CASI image. We can note that the heterogeneousness of such images perturbs the method of pixel based method of classification “Fig.8” (left). So, this method leads to the appearance of isolated pixels in the final classification. However, we mention that some various region areas are well detected “Fig.8” (right). This is thanks to classes attributes in hierarchical classification based on BPT. But we must notice that we find confusion between some classes which share many similarities of information.

Figure 8. Classification results for (left) pixel based method and (right) hierarchical classification method

The obtained results show the efficiency of; firstly, separation of hyperspectral data in frequency domain and secondly, introduction of various attributes on the process of hierarchical classification. We propose in future work to consider more complicate attributes such as NDVI, shapes…etc to improve these results.

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[4] C. Jutten , J. Herault, “ Blind separation of sources, part i: an adaptative algorithm based on neuromimatic architecture”; Signal Process; 24 (1):1–10. (1991).

[5] J.Fadili, « Une exploration des problèmes inverses par les représentations parcimonieuses et l’optimisation non lisse », HDR, 2010.

[6] F.Calderero and F.Marques, “Region merging techniques using information theory statistical measures”. IEEE Trans.Image Precessing, 2010

[7] P.Salembier and L.Garrido. “Binary partition tree as an efficient representation for image processing, segmentation and information retrieval. IEEE Trans.Image Precessing, 2000.

[8] Y.Tarabalka, J.A.Benediktsson, J.Chanussot andJ.tilton, “Multiple spectral-spatial classification approach for hyperspectral data”. IEEE Trans.on Geoscience and Remote Sensing, vol.48(11), 2010.