O Regniers
email: olivier.regniers@ims-bordeaux.fr

L Bombrun

D Guyon

J.-C Samalens

C Tinel

G Grenier

C Germain

WAVELET BASED TEXTURE MODELING FOR THE CLASSIFICATION OF VERY HIGH RESOLUTION MARITIME PINE FOREST IMAGES

Keywords: forest structure, texture analysis, classification, very high resolution, wavelet

This study evaluates the potential of wavelet-based texture modeling for the classification of stand age in a managed maritime pine forest using very high resolution satellite data. A cross-validation approach based on stand age reference data shows that multivariate modeling of the spatial dependence of wavelet coefficients outperforms the use of features derived from co-occurrence matrices. Simultaneously adding features representing the color dependence and leveling the dominant orientation in anisotropic forest stands enhances the classification performances. These results obtained from panchromatic and multispectral PLEIADES data confirm the ability of such wavelet-based multivariate models to efficiently capture the textural properties of very high resolution forest data and opens up perspectives for their use in the mapping of mono-specific forest structure variables.

INTRODUCTION

Submetric images produced by Very High Resolution (VHR) sensors enable to capture the geometric aspect of small objects which are only observable through their spectral properties at lower resolution. This is for example the case for vegetation rows in vineyards, orchards and young trees in managed stands. Rather than depending on pixel-based information, the classification or the segmentation of such land cover types could therefore be improved by considering inter-pixel dependencies to capture the spatial organization of the vegetation cover. Approaches using textural analysis have proven to be a valuable solution in this VHR classification context with various commonly used tools such as Grey Level Co-occurrence Matrices (GLCMs), variograms or wavelet representations. All these tools enable to statistically analyze the local spatial dependency between a pixel and its neighboring pixels and lead to a small-sized representation of the textural content since only a few descriptors are extracted from the data. These descriptors can then be further used as input in a classifier or a segmentation algorithm.

In applications relative to forest classification, the existence of a correlation between forest structure variables and the tree spatial distribution is often considered. The forest spatial structure at the stand level indeed varies in time as a result of reforestation, tree growth and periodic thinning. In various studies [START_REF] Lévesque | Spatial analysis of radiometric fractions from high-resolution multispectral imagery for modeling individual tree crown and forest canopy structure and health[END_REF][START_REF] Kayitakire | Retrieving forest structure variables based on image texture analysis and IKONOS-2 imagery[END_REF][START_REF] Béguet | Retrieving forest structure variables from very high resolution satellite images using an automatic method[END_REF], GLCM-based descriptors are exploited in this context to describe the tree canopy spatial organization and are further used for the estimation of forest structure variables at the stand scale. Typically, variables retrieved in these studies are: age, tree height, stand density, crown diameter, basal area, etc.

In this paper, we propose to evaluate how texture features extracted from wavelet-based multivariate models can help in the classification of stand age in a managed maritime pine forest. Lately, wavelet decompositions have indeed emerged as an effective tool to describe textures. In [START_REF] Do | Wavelet-based texture retrieval using generalized Gaussian density and Kullback-Leibler distance[END_REF], Do & Vetterli suggested the use of probabilistic models to describe the distribution of wavelet coefficients. Further studies proposed to work with multivariate models to express the joint distribution of wavelet coefficients located in a neighborhood and thereby better approximate the local dependencies. Such multivariate models are for instance: multivariate Gaussian distribution, Spherically Invariant Random Vectors (SIRVs) [START_REF] Yao | A representation theorem and its applications to spherically-invariant processes[END_REF], or copula based models [START_REF] Kwitt | A joint model of complex wavelet coefficients for texture retrieval[END_REF]. Classification performances obtained with these models are compared with results derived from GLCM-based texture descriptors on VHR PLEIADES images of maritime pine forest.

STUDY SITE AND DATA

The study site is located in the Landes de Gascogne forest in the South West of France. This ecosystem is mainly dominated by even-aged maritime pine stands (Pinus pinaster). The stand age ranges from 0 (clear cuts) to approximately 50 years. Structure variations may appear between stands of the same age due to the site fertility, silvicultural management practices or natural disturbances.

In order to classify the forest age classes through textural analysis, we used a PLEIADES image acquired on this area of interest on 8 August 2012.

Stand age reference data were collected in 2013 from local forest land managers in the municipality of Audenge (44°70'N, 0°95'W). These data consist in a shapefile containing contours of 179 forest stands with their corresponding age ranging from 0 to 50 years by age group of 5 years. Clear-cuts are also included in the data. Age groups were rearranged in three classes: class 1 includes young stands of 1 to 9 years, class 2 corresponds to stands of 10 to 19 years, and class 3 covers a range from 20 to over 50 years. A fourth class contains the clear-cuts (Fig. 1).

FEATURE EXTRACTION

The purpose of the feature extraction step is to represent the spatial dependence and the color (i.e. spectral) dependence in each stand of the reference data by a finite set of descriptors. In this paper, two approaches are compared for the spatial dependence modeling using panchromatic data: the Grey Level Co-Occurrence Matrix (GLCM) and wavelet-based multivariate modeling. Only the latter is applied for the color dependence using multispectral data.

Grey-Level Co-Occurrence Matrix

The use of the GLCM involves the setting of two spatial parameters, i.e. the distance and the orientation between the pairs of sites. Previous results obtained on a maritime pine forest texture database in a content-based retrieval framework showed that pairs of sites at a distance of 2 pixels (i.e. 1 m in panchromatic) in four directions (0°, 45°, 90°, and 135°) give the highest retrieval rate [START_REF] Regniers | Texture based image retrieval and classification of very high resolution maritime pine forest images[END_REF]. Furthermore, a set of textural features derived from the GLCMs is selected out of the 14 second order statistics proposed by Haralick [START_REF] Haralick | Textural features for image classification[END_REF]. To achieve this, a principal component analysis was employed to identify the most discriminant features. As a result, a subset of four descriptors (homogeneity, entropy, correlation, and the Haralick's mean) was selected. For each forest stand of the database, a feature vector containing these four descriptors obtained for each direction (16 descriptors in total) is computed from the PLEIADES panchromatic band.

Wavelet-Based Multivariate Models

Prior to the modeling and the feature extraction, an orthogonal wavelet transform (Daubechies filter db4) is applied on an extract of the PLEIADES panchromatic band and multispectral data corresponding to the area of interest. Two scales and three orientations of decomposition are applied leading to the production of six wavelet subbands.

Two types of dependencies are considered in the modeling process:  First, the spatial dependence analysis is carried on the subbands derived from the panchromatic data. The wavelet coefficients located in a 3x3 neighborhoods around the current spatial position are clustered in a random vector.  Secondly, the color dependence analysis is applied on the wavelet subbands derived from the PLEIADES multispectral data. Here, the observed random vector contains the wavelet coefficients of each spectral band of the data. The distribution of these observations can be further modeled using multivariate probability density functions (pdf) whose parameters are estimated according to the maximum likelihood principle.

Several multivariate models are compared in this study: the multivariate Gaussian with a Sample Covariance Matrix (SCM) estimator and generalizations of the Gaussian distribution such as the SIRV model with a deterministic multiplier (SIRVgauss), the SIRV model with a G 0 distribution (SIRVg0) [START_REF] Freitas | The polarimetric G distribution for SAR data analysis[END_REF] and the Gaussian copula [START_REF] Kwitt | A joint model of complex wavelet coefficients for texture retrieval[END_REF].

Note that the considered SIRV models (SIRVgauss and SIRVg0) were already applied in texture retrieval experiments on forest texture databases and showed interesting retrieval rates [START_REF] Regniers | Texture based image retrieval and classification of very high resolution maritime pine forest images[END_REF]. In the next section, we investigate the potential of such models in a cross-validation classification framework.

APPLICATION

For each stand of the reference data, feature sets describing the spatial dependence (SP) were extracted using the GLCM and the four wavelet-based multivariate models: SCM, SIRVgauss, SIRVg0 and copulas. In parallel, feature sets describing the color dependence (COL) were computed using the same four models. In a third modality, spatial dependence features and color dependence features are concatenated in a unique vector (SP+COL).

Anisotropy is an important texture property, especially when investigating row-planted vegetation. For both investigated approaches (GLCM and multivariate models), computed texture features are not rotation invariant as they are by definition specific to a particular orientation. To evaluate the impact of this lack of rotation invariance on classification accuracy, a second reference image database was produced by rotating each stand displaying an anisotropic texture so that its orientation is forced to 0°. New sets of features describing the spatial dependence of this new database were then extracted for the GLCM and multivariate models (SProt). These new sets of features were also combined with color dependence features in a fifth and last modality (SProt+COL).

To compare the classification accuracies of the proposed models and assess the pertinence of spatial and color dependence modeling, we chose a cross-validation approach. For each iteration of this procedure, the reference database is randomly split in training data (50%) and validation data (50%). A distance matrix is then built between feature sets of the training data and those of the validation data. For multivariate models, a Rao geodesic distance is chosen as it exists in a closed form for all the proposed multivariate models. In the case of similarity measurement between GLCM features, a Mahalanobis distance is applied. The classification is next performed using a k Nearest Neighbor classifier (kNN). The class of a stand is set to the most represented class in the kNN stands of the training data (k=5). The classification performances are next evaluated in terms of average overall accuracy over a hundred Monte Carlo runs.

RESULTS AND DISCUSSION

Cross-validation results are presented in Fig. 2 for the five tested modalities and for the five considered texture models.

The modeling of the spatial dependence (SP) is best achieved using SIRV-based models with slightly better classification performances for the SIRVgauss model. Overall, multivariate models are displaying higher performances than the GLCM with the exception of the SCM estimator. This confirms the interest of multiscale wavelet-based approach to describe the texture. The scales of the spatial distribution explored by the GLCM and the multivariate models are indeed different due to the parameterization we have chosen for both approaches. Where GLCM achieve its highest performances by only investigating short distances (1 m), wavelet-based approaches explore larger ranges of object size and are probably more appropriate to describe the variation of tree crown size depending on the stand age.

Besides, once the row orientation is forced to 0° in the SProt modality, the performances of the GLCM descriptors are significantly increased and exceed those of the multivariate models whereas results obtained with multivariate models are only moderately improved. Even though both GLCM-based and wavelet-based features are not rotation invariant due to the orientations considered during their computation, the latter probably better describes orientation-specific characteristics of the textures than the former. Also, the diversity of orientations present in the database could be enough to balance the lack of rotation invariance for both approaches. This could explain why rotation does not significantly improve the performances in the case of multivariate models. Nonetheless, once training and validation data display the same orientation, GLCM approach is more reliable.

Adding color dependence features to spatial dependence parameters (SP+COL) does not increase overall classification performances for any wavelet-based models. However, when combining color dependence with the removal of the orientation factor (SProt+COL), a synergetic effect is revealed for all multivariate models with the notable exception of SIRVg0. This modality displays the highest overall accuracy.

To better understand classification errors, it is also worth mentioning that a significant part of the reference data (approximately 15%) is composed of outliers in terms of texture content. These stands are not aberrant in terms of age but display a textural content that makes them look different from the average visual aspect of the class they belong to. Various local phenomena could be the source of these discrepancies. For instance, in stands of over 10 years (age classes 2 and 3), forest thinning operations induce changes in forest density and crown growth which consequently alter texture patterns. Residuals of storm damages also cause local changes in forest density. Middle-aged damaged forest stands (class 2) can thereby share common features with older forests with the appearance of large clearing patches. Forest management practices such as plantation density vary sometimes from one land owner to the other and differences in forest patterns occur between young tree stands. Finally, practices may also change within the same stand or the satellite data can be acquired during an ongoing clearing operation. Hence, different patterns may be observed within one stand.

All these phenomena illustrate the limits of the main a priori assumption of this study which is to consider that the relation between the age of a stand and the tree canopy spatial distribution is simple. Local management practices, site fertility and the past history of the studied stands are not to be neglected in the analysis. But, this also means that classification accuracies higher than 85% would be difficult to reach only through automatic textural analysis.

CONCLUSION

We investigated the interest of wavelet-based texture modeling for the classification of stand age in a managed mono-specific forest. Multivariate model based on the Gaussian SIRV configuration was confirmed as an interesting candidate approach for spatial dependence modeling in this context. Adding color dependence features and leveling the orientation in the database also proved to enhance the discrimination of age classes when used simultaneously. Nonetheless, the diversity of management practices, the site fertility or the past history of the studied stands will invariably introduce discrepancies between the observed texture of the stands and their actual age. Yet, the proposed models do most of the time fit the displayed texture and misclassifications are mainly due to these discrepancies. This suggests the potential interest of multivariate approaches for the estimation of other forest structure variables that are more directly related to the texture. For instance, the crown diameter, also a good indicator of the forest development stage, has a direct impact on the size of the object to be described and is related to the spatial distribution of these objects.

Fig. 1 .

 1 Fig. 1. Extracts of forest stands representing the forest age classes. A -Forest age class 1 (1-9 years), B -Forest age class 2 (10-19 years), C -Forest age class 3 (>19 years), D -Clear cuts.

Fig. 2 .

 2 Fig. 2. Mean overall accuracies obtained by cross-validation. SP = spatial dependency, COL = color dependency, SP+COL = combination of spatial and color dependencies, SProt = spatial dependency after rotation of oriented stands, SProt+COL = combination of spatial dependency after rotation of oriented stands and color dependency.

ACKNOWLEDGMENT

This work was supported by Aquitaine Regional Council and CNES (Centre National d'Etudes Spatiales) through the TOSCA project STELLA THR. The authors also wish to thank CNES and its Thematic Users Commissioning team for providing the PLEIADES data. The authors gratefully acknowledge Telespazio (EarthLab project) and Alliance Forêt-Bois for authorizing the use of their stand age reference data.


O Regniers
email: olivier.regniers@ims-bordeaux.fr

L Bombrun

V Lafon

A Dehouck

C Tinel

C Germain

WAVELET BASED TEXTURE MODELING FOR PANCHROMATIC VERY HIGH RESOLUTION IMAGE CLASSIFICATION: APPLICATION TO OYSTER RACKS DETECTION

Keywords: Texture analysis, classification, very high resolution, wavelet, oyster culture

This study evaluates the potential of wavelet-based texture multivariate modeling for the detection of cultivated oyster fields and their differentiation from abandoned fields in Very High Resolution panchromatic PLEIADES data. The proposed models are tested in a supervised classification context using a training database composed of extracted image patches representative of the land covers of interest. The obtained classification results exhibit high detection rate for cultivated fields. Classification errors appear however in the detection of abandoned fields. These results demonstrate the interest of such model for the characterization of intertidal ecosystems and opens up perspectives for their use in the management of oyster farming activities.

INTRODUCTION

Very High Resolution (VHR) imaging has been widely used in coastal monitoring for purposes such as coastline change detection or coastal resource management. Previous works using VHR airborne data showed the interest of such high resolution data for oyster reef monitoring [START_REF] Finkbeiner | Managing and monitoring intertidal oyster reefs with remote sensing in coastal South Carolina[END_REF][START_REF] Germain | Oyster bed mapping and evaluation of the Maritime Public Domain status[END_REF]. Recent VHR spaceborne sensors (e.g. PLEIADES, GeoEye, WorldView, Ikonos) enable to capture the geometric properties of small landscape objects. Inland, this is for instance the case for vegetation rows in vineyards, orchards and young trees in managed stands. On coastal areas, this is also true for oyster racks. The classification of such land cover types displaying regular patterns could therefore be improved by considering inter-pixel dependencies to represent the spatial organization of these patterns.

Approaches using textural analysis have proven to be a valuable solution in this VHR classification context. Various tools such as Grey Level Co-occurrence Matrices (GLCM), variograms or wavelet representations are commonly used to characterize textured land covers [START_REF] Franklin | Texture analysis of IKONOS panchromatic data for Douglas-fir forest age class separability in British Columbia[END_REF][START_REF] Trias-Sanz | Texture orientation and period estimator for discriminating between forests, orchards, vineyards, and tilled fields[END_REF][START_REF] Aksoy | Automatic mapping of linear woody vegetation features in agricultural landscapes using very high resolution imagery[END_REF]. These approaches enable to statistically analyze the local spatial dependency between a pixel and its neighboring pixels. Descriptors can be extracted from these statistics providing small-sized representation of the textural content. These descriptors can be further used as input in a classifier or a segmentation algorithm.

Many works in textured image recognition have shown that the wavelet representation is a well-adapted domain to characterize texture, yielding to a multi-scale and multiorientation analysis scheme in which each wavelet subband is modeled separately. Some authors investigated the modeling of the empirical histogram of wavelet subbands using univariate models such as the Generalized Gaussian Distribution (GGD) [START_REF] Do | Wavelet-based texture retrieval using generalized Gaussian density and Kullback-Leibler distance[END_REF]. Nonetheless, these approaches do not fully exploit the textural information as they do not explore local spatial dependencies. To overcome this problem, some works have pointed out the pertinence of considering multivariate modeling such as multivariate GGD [START_REF] Verdoolaege | Geodesics on the manifold of Multivariate Generalized Gaussian Distributions with an application to multicomponent texture discrimination[END_REF], Spherically Invariant Random Vector (SIRV) [START_REF] Bombrun | Multivariate texture retrieval using the geodesic distance between elliptically distributed random variables[END_REF][START_REF] Freitas | The Polarimetric G Distribution for SAR Data Analysis[END_REF] and copula-based models [START_REF] Lasmar | Gaussian copula multivariate modeling for image texture retrieval using wavelet transforms[END_REF] in order to take into account this spatial dependency of wavelet coefficients.

Here, we investigate how these multivariate models applied in the wavelet domain can help in the characterization of an inter-tidal ecosystem. In particular, we focus on the differentiation of cultivated and abandoned oyster fields in a supervised classification context. This paper is structured as follows. The next section presents the image data as well as the test site with a brief description of the oyster farming activities in the area and their related management problems. The third section describes the proposed methodology with details on the feature extraction step. Finally, the results, discussion and conclusions are detailed in the last two sections.

STUDY SITE AND DATA

The study site is located in the Arcachon Bay, a mesotidal lagoon of 180 km² located on the French Atlantic coast. In this ecosystem, shell farming and in particular oyster farming is an important economic activity. Recently, it underwent recurrent lethal crisis that implies the necessity to improve management operations of both farms and natural growing areas. Areas occupied by oyster cultures in the Arcachon Bay are indeed in a constant evolution, some parks being abandoned and others re-cultivated. An environmental management tool used for mapping oysterfarming activities of the Arcachon lagoon was previously designed [START_REF] Lafon | Cartographie de l'état du Domaine Public Maritime par télédétection très haute résolution : Application au Bassin d'Arcachon[END_REF]. It is based on a semi-automatized detection method of the nature and status (clean/dirty) of oyster farms. It exploits very high resolution remote sensing imagery and uses texture indicators derived from Grey Level Cooccurrence Matrices to extract oyster field contours. Although interesting in the first steps of the oyster fields mapping since it enables to detect oyster fields either cultivated or not, this strategy does not allow discriminating the first from the second ones. Therefore, an alternative methodology has been developed in order to map cultivated parcels.

To achieve this objective, we used the panchromatic band of a PLEIADES data acquired at low tide on 25 April 2013. It covers a large central part of the Arcachon Bay where oyster farming is predominant. The PLEIADES sensor provides a VHR panchromatic band with a 0.7 m resolution resampled to 0.5 m. Oyster racks typically have a width of 1 m. The level of precision provided in the PLEIADES panchromatic band is thereby sufficient to clearly distinguish them in the image (Fig. 1-A).

METHODOLOGY

The methodology used in this study is divided in two steps. The first step is dedicated to the training phase during which a textural feature set is extracted from each image patch of a training database using wavelet-based multivariate modeling. In the second step, the supervised classification process is carried out on an extract of the PLEIADES panchromatic band corresponding to an area of interest. Both steps are detailed below.

Feature Extraction

In order to perform the classification, a training database was created by extracting image patches (128x128 pixels) representative of three identified classes of interest: cultivated oyster racks, abandoned oyster fields and foreshores (Fig. 1). Prior to the feature extraction, an orthogonal wavelet transform (Daubechies filter db4) is applied on each of the image patches. Two scales and three orientations of decomposition are applied leading to the production of six wavelet subbands.

In each of these subbands, the wavelet coefficients located in a 3x3 neighborhood around the current spatial position are clustered in a random vector k. The dimension of each observed vector k equals 9 (3x3). The distribution of these observations can be further modeled using multivariate probability density functions (pdf) whose parameters are estimated according to the maximum likelihood principle.

In this paper, we consider a generalization of the multivariate Gaussian distribution, i.e. the Spherically Invariant Random Vector SIRV. In SIRV-based models, the observed vector k can be decomposed as where τ is a scalar random variable called the multiplier and z a real independent Gaussian vector with zero mean and covariance matrix [M]. The multiplier τ is used to modulate the Gaussian distribution of vector z to better fit the heavy-tail behavior of the wavelet coefficients. Various models were proposed in the literature to represent the multiplier τ. Here, we chose a configuration using an inverse gamma distributed multiplier τ leading to a SIRV k vector with a G 0 (student-t) distribution (SIRVg0 in the following) [START_REF] Freitas | The Polarimetric G Distribution for SAR Data Analysis[END_REF]. For each image patch, a feature vector containing the estimated covariance matrix and the parameters of the multiplier distribution is extracted for each wavelet subband.

Supervised Classification

In order to stay in an object-oriented context, the image to classify is first segmented using a Mean-Shift algorithm [START_REF] Comaniciu | Mean Shift: A robust approach toward feature space analysis[END_REF]. The result is deliberately over-segmented (Fig. 2) to preserve the contours of the small oyster fields (minimum region size = 100 pixels).

The classification is performed according to the maximum likelihood principle. The same wavelet decomposition as the one used during the training phase is applied on the extract of the PLEIADES panchromatic data to classify. For each region of the pre-segmentation, a likelihood criterion is computed between the observed local

RESULTS AND DISCUSSION

Classification result obtained on an extract of the PLEIADES panchromatic band with SIRVg0 waveletbased model is shown in Fig. 2. Overall, cultivated fields are visually well detected and well separated from abandoned fields confirming the interest of such multivariate models for the detection of oyster racks. This result along with classification results obtained on three other areas of interest in the Arcachon Bay were further validated with in situ observation data (Natura 2000 at Sea and Direction Départementale des Territoires et de la Mer de Gironde) as well as with the oyster parcel plan for a total of 1021 validation points. Each point indicates whether it corresponds to cultivated or abandoned fields.

Oyster racks are well detected with a producer's accuracy of 98%. Detection errors occur nevertheless in partially submerged areas where the contrast between oyster racks and their surroundings is reduced. Besides, in a significant number of cases (66 out of 405 points), abandoned parks are misclassified as cultivated parks. These classification errors are mainly due to the presence of recently abandoned racks or of dense unstructured abandoned parks, both sharing common characteristics with cultivated fields. The overall accuracy is nonetheless satisfactory (92%) and the classification result provides an efficient separation between the cultivated parks and the abandoned fields.

CONCLUSION

We investigated the interest of wavelet-based texture modeling using SIRV-based models for the detection of cultivated oyster racks in VHR PLEIADES panchromatic data. The obtained supervised classification results showed that these models enable to efficiently detect cultivated racks and differentiate them from abandoned fields. Nonetheless, some classification errors occur.

Improvements in the characterization of abandoned fields could probably be achieved with the use of other type of classifier such as SVM. Considering filtering operations such anisotropic diffusion filters prior to the presegmentation could also enhance the quality of the contours of the regions to be classified and further improve classification results.

ACKNOWLEDGMENT

This work was supported by Aquitaine Regional Council and CNES (Centre National d'Etudes Spatiales) through the TOSCA project STELLA THR. The authors also wish to thank CNES and its Thematic Users Commissioning team for providing the PLEIADES data. Right -Classification results obtained with SIRVg0 wavelet-based models.

Fig. 1 .

 1 Fig. 1. Texture classes. A -Cultivated oyster racks, B -Abandoned fields, C -Foreshore.

Fig. 2 .

 2 Fig. 2. Left -Pre-segmentation obtained by Mean-Shift (green lines indicate the limits of the regions).Right -Classification results obtained with SIRVg0 wavelet-based models.