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Improving within-genus tree speciesdiscrimination using the discretewavelet transform applied to airbornehyperspectral dataAsim Banskota a b , Randolph H. Wynne a & Nilam Kayastha a ba Department of Forest Resources and EnvironmentalConservation , Virginia Polytechnic Institute and State University ,Blacksburg, VA, 24061, USAb Geospatial and Environmental Analysis Program, VirginiaPolytechnic Institute and State University , Blacksburg, VA, 24061,USAPublished online: 28 Jun 2011.

To cite this article: Asim Banskota , Randolph H. Wynne & Nilam Kayastha (2011) Improvingwithin-genus tree species discrimination using the discrete wavelet transform applied toairborne hyperspectral data, International Journal of Remote Sensing, 32:13, 3551-3563, DOI:10.1080/01431161003698302

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International Journal of Remote SensingVol. 32, No. 13, 10 July 2011, 3551–3563

Improving within-genus tree species discrimination using the discretewavelet transform applied to airborne hyperspectral data

ASIM BANSKOTA∗†‡, RANDOLPH H. WYNNE† and NILAM KAYASTHA†‡†Department of Forest Resources and Environmental Conservation, Virginia Polytechnic

Institute and State University, Blacksburg, VA 24061, USA‡Geospatial and Environmental Analysis Program, Virginia Polytechnic Institute and

State University, Blacksburg, VA 24061, USA

(Received 6 March 2009; in final form 8 December 2009)

Discrete wavelet analysis was assessed for its utility in aiding discrimination of threepine species (Pinus spp.) using airborne hyperspectral data (AVIRIS). Two differ-ent sets of Haar wavelet features were compared to each other and to calibratedradiance, as follows: (1) all combinations of detail and final level approximationcoefficients and (2) wavelet energy features rather than individual coefficients. Weapplied stepwise discriminant techniques to reduce data dimensionality, followedby discriminant techniques to determine separability. Leave-one-out cross valida-tion was used to measure the classification accuracy. The most accurate (74.2%)classification used all combinations of detail and approximation coefficients, fol-lowed by the original radiance (66.7%) and wavelet energy features (55.1%). Theseresults indicate that application of the discrete wavelet transform can improvespecies discrimination within the Pinus genus.

1. Introduction

Effectively managing forests and assessing forest conditions require accurate mappingof forest species. Applications of remote sensing to forest species mapping over recentyears have improved substantially, with advances in spatial, spectral, temporal andradiometric resolutions and more advanced data processing techniques. Several stud-ies (Martin et al. 1998, Clark et al. 2005, Leckie et al. 2005, van Aardt and Wynne2007) have shown the potential of hyperspectral remote sensing data for discriminat-ing among tree species. Increased spectral detail, while clearly enhancing separability,also requires effective data processing techniques to address the increased complex-ity and dimensionality. Problems arise (e.g. the Hughes phenomenon; Hughes 1968)if too many spectral bands are used with finite training samples. As the dimensional-ity increases, the number of training samples required for training a specific classifieralso increases. Hence, dimension reduction has become a significant part of hyper-spectral image interpretation. Selecting bands which contain unique information andminimize classification error is a common way of reducing dimension (Schmidt andSkidmore 2003, Clark et al. 2005). However, band selection often degrades the perfor-mance of classifiers by discarding variables with important information (Brunzell and

*Corresponding author. Email: asimb@vt.edu

International Journal of Remote SensingISSN 0143-1161 print/ISSN 1366-5901 online © 2011 Taylor & Francis

http://www.tandf.co.uk/journalsDOI: 10.1080/01431161003698302

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Eriksson 2000, Miao et al. 2007). Alternatively, feature extraction techniques reducedata dimensionality while maintaining most information (and thus discriminationcapability) within an image.

Several feature extraction methods are commonly used to reduce the dimensional-ity of hyperspectral images, including principal component analysis (PCA), singularvalue decomposition (Lisowski et al. 1996) and maximum noise fraction (Green etal. 1988, Lee et al. 1990, Phillips et al. 2009). PCA is based upon the global covari-ance matrix, and thus is not explicitly sensitive to the class structure of the data(Richards and Jia 2006). The class structure of the data is also not taken into accountwith the maximum noise fraction and singular value decomposition. Hence, thesetechniques contribute little to class separability. Canonical analysis and discriminantanalysis feature extraction, while often useful when applied to multispectral data, havesome disadvantages when applied to hyperspectral data. These disadvantages includedifficulty in calculating covariance matrices with high dimensional data, and unre-liability of extracted features when the classes have similar means or when a classhas a very different mean from other classes (Richards and Jia 2006, Hsu 2007).More recently, wavelet transforms have been introduced for analysis of hyperspec-tral data as an efficient means of feature extraction (Moon and Merenyi 1995, Bruceet al. 2002). A wavelet is a mathematical function used to divide a function intodifferent frequency components, affording analysis of each component with scale-dependent resolution. A wavelet transform is the representation of a function bywavelets. The strength of the wavelet transform for hyperspectral feature extractionlies in this ability to analyse signal at different resolution or scales (Bruce et al.2001). The advantages of multiscale representation of hyperspectral data are twofold.First, subtle variation in spectral features in the original hyperspectral data might bedetected at different scales (Hsu 2007). Second, the useful information is representedby fewer wavelet features, effectively compressing the data (Bruce et al. 2002, Penget al. 2009).

Research has been reported on the use of wavelet transforms with hyperspectraldata for a variety of purposes, including quantifying pigment concentration in vegeta-tion (Blackburn 2007, Blackburn and Ferwerda 2008), automatic detection of subpixelhyperspectral targets (Bruce et al. 2001), automatic dimension reduction of hyper-spectral data (Kaewpijit et al. 2003), forest canopy structure identification (Bradshawand Spies 1992), forest leaf area index and crown closure mapping (Pu and Gong2004) and tropical species identification (Zhang et al. 2006). Results of these studieshave shown that wavelet analysis can be an effective tool for reducing the dimen-sionality of hyperspectral data while maintaining information content for a variety ofapplications.

The goal of this study was to assess the utility of the Haar discrete wavelet transform(DWT) as a discriminant analysis precursor for classifying three pine species (Pinusspp.) using airborne hyperspectral data (AVIRIS). We also examined two differentsets of wavelet features and their effect on overall classification accuracy.

2. Wavelet analysis

A brief introduction to wavelet analysis is given in this section. More detaileddiscussion can be found elsewhere (e.g. Graps 1995).

An oscillating function with a limited time duration that is irregular, asymmetric,and has an average value of zero can be regarded as a wavelet function. A wavelet

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transform enables signal (data) analysis at different scales or resolutions by creat-ing a series of shifted and scaled versions of the mother wavelet function. The term‘mother’ implies that a set of basis functions {ψα,b(λ)} can be generated from onemain function, or the mother wavelet ψ(λ) by the following equation (Bruce et al.2001):

ψa,b(λ) = 1√aψ

(λ− b

a

), (1)

where a is the scaling factor of a particular basis function and b is the translationvariable along the function’s range.

Wavelet analysis is based on the idea of projecting a signal onto the basis functionsto resolve the signal at different scales or resolutions (Hsu 2007). Resolving data intodifferent scales is analogous to looking at data with windows of different width. The‘gross’ features of data might be visible at large scales and ‘fine’ features with smallscales (Blackburn 2007). The results of wavelet analysis of a signal are wavelet coeffi-cients, which are a function of the scale of the analysing wavelet and the position of thesignal (part of the signal being analysed). Calculating wavelet coefficients at every pos-sible scale and position is computationally intensive and generates enormous amountsof data. In DWT, wavelet coefficients are usually sampled at some discrete scale andpositions based on powers of two (dyadic scales and positions). An efficient way toimplement this scheme using filters was developed by Mallat (1989).

The basic idea behind this fast algorithm is to represent the wavelet basis as aset of high-pass and low-pass filters. The high-pass and low-pass filters are related(their power sum is equal to one) and called quadrature mirror filters. Thus, thefirst level of DWT decomposition of a signal splits it into a low-pass version and ahigh-pass version. The second level of decomposition is performed on the low-passsignal obtained from the first level of decomposition. The wavelet decompositioncan be iteratively performed until a maximum scale is reached. The maximum scaleis dependent on the signal length and the wavelet basis length. Figure 1 illus-trates an example of the dyadic DWT analysis of a hyperspectral signal. The figureshows how the DWT decomposes the original hyperspectral signal into its coarserapproximation and detail information. The approximations are the coarse-scale, low-frequency components of the signal. The details are the fine-scale, high-frequencycomponents. At each level j, we build the jth-level approximation Aj and a devi-ation signal called the jth-level detail Dj. Summing up the approximation at levelJ and detail components at all scales, j = 1, . . ., J, J being the final decom-position level, results in the original signal, which is illustrated in equation (2)(Blackburn 2007):

S = AJ +∑j≤J

Dj, (2)

where S is the original signal. This property indicates that the DWT does not lose anyinformation in the original signal during transformation. Computation of a DWT isvery fast and the transformed results are often easier to manipulate than the originalspectra. The DWT provides a multiscale representation of hyperspectral data withlocal spectral variation in the spectral bands resolved at different scales.

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Figure 1. Original hyperspectral radiance (in W m−2 sr−1) curve of a randomly chosen short-leaf pine and its approximation (a1, a2, . . ., a6) and details (d1, d2, . . ., d6) up to six levels ofdecomposition.

3. Wavelet feature selection

The final results of a DWT decomposition of a spectrum are sets of wavelet coeffi-cients, with each wavelet coefficient directly related to the amount of energy in thesignal at different positions and scales. The next step is to select the wavelet featuresthat contain the maximum amount of useful information for a particular classifica-tion problem. The best wavelet features could be a subset of wavelet coefficients, theirenergy, and any combination of the two (Zhang et al. 2006).

Bruce et al. (2001) decomposed the original hyperspectral signal at the maximumpossible level and concatenated all the detail coefficients. Receiver operating charac-teristics curves were then used to evaluate the class-discriminating capability of eachwavelet coefficient and thus to determine the optimum subset of wavelet coefficients.Rather than using all the coefficients to determine the optimum subset, the waveletcoefficients can also be screened on the basis of their energy. The wavelet transformhas good energy concentration and, therefore, most coefficients have very little energy(Peng et al. 2009). Wavelet coefficients with energy values lower than a predeterminedthreshold value can be discarded without causing significant errors for signal repre-sentations (Peng et al. 2009). Okamato et al. (2007) used the retained energy of thecoefficient (its square) as a selection criterion. They found that only 50 out of a totalof 213 coefficients contained 99.7% of the total energy. They selected the effectivevariables using a forward stepwise variable selection procedure. Blackburn (2007) andBruce et al. (2001) used wavelet features based on calculation of an ‘energy feature

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vector’ from the wavelet coefficients of each spectrum. The 1 × (J + 1) feature vectorF̄ = [

Fj]

was derived from:

Fj =√√√√ 1

K

K∑k=1

∣∣Wj,k∣∣2

, (3)

where K is the number of coefficients at the jth decomposition level, Wj,k is the kthcoefficient at level j and J is the maximum number of decomposition levels. The fea-ture vector has a length (J + 1) due to the J levels of detail coefficients and one level offinal approximation coefficients. The wavelet energy feature vector provides informa-tion about how energy of the hyperspectral spectrum is partitioned according to scale(Bruce et al. 2001, Zhang et al. 2006).

4. Methods

4.1 Study area and ground data

The study area is located in the Appomattox–Buckingham State Forest, Virginia, USA(78◦ 40′ 30′′ W, 37◦ 25′ 9′′ N). This Virginia piedmont region consists of various pines,upland hardwood and mixed stands. The three pine species of interest are loblollypine (Pinus taeda), Virginia pine (Pinus virginiana) and shortleaf pine (Pinus echinata).This study used the same dataset as van Aardt and Wynne (2007). The dataset wascollected during September 1999. In situ samples for each of the three pine specieswere geolocated using a CMT March II GPS unit (CMTINC.COM, Corvallis, OR,USA). Each sampling observation was centred at a stem of the species in question,while at the same time ensuring that the surrounding vegetation (10 m radius) wasalso of the same species type. All of the GPS data were differentially corrected usingCMT PC-GPS software (Version 2.5). The total number of samples was 203, with 89loblolly, 49 shortleaf and 65 Virginia pine samples.

4.2 AVIRIS data

The AVIRIS image data were acquired in second week of November 1999 during alow-altitude campaign, resulting in 224 bands, ranging from 400 to 2500 nm (approx-imately 10 nm spectral resolution) at 3.4 m spatial resolution. As reported in vanAardt and Wynne (2007), four flight lines were used in the study, with the first beinggeo-rectified using identifiable ground control points (GPS collected and differentiallycorrected), while the remaining three flight lines were registered to an existing ortho-photograph (0.5 m spatial resolution). Root mean square errors were 0.33, 0.23, 0.24and 0.24 pixels for flight lines 1, 2, 3 and 4, respectively. The four flight lines weremosaicked using ERDAS Imagine 8.5 software (ERDAS, Inc., Atlanta, GA, USA),and subset to the area of interest to facilitate analysis. Raw radiance data were used.

The point map of field sampling plots was overlaid in the AVIRIS image data toextract a full range spectrum of radiance values for each sampling unit. Some of thebands in the shortwave infrared (SWIR) part of the spectrum were noisy (some pixelshaving either very low or missing values in those bands). Those noisy bands (1353–1445, 1803–1961, 2480–2510 nm) were removed, leaving 187 bands for further analysis.

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4.3 Data analysis

When computing the DWT, two input parameters are required: the choice of motherwavelet and the level of decomposition. We chose the Haar mother wavelet as recentinvestigations have illustrated its effectiveness for feature extraction of hyperspectraldata (Bruce et al. 2001, Li 2004, Zhang et al. 2006). The value of the decomposi-tion level is determined by the type of wavelet and the original signal length. In thisstudy, the decomposition level was chosen such that it is maximized (7 for 187 bandsusing the Haar wavelet). The DWT was implemented in Matlab (version 7.4, TheMathworks, Inc., Natick, MA, USA) using a dyadic filter tree as described in section 2.The hyperspectral signal in the spectral domain extracted for each pixel location waspassed through a series of low-pass and high-pass filters.

After feature extraction using the wavelet transform, two sets of wavelet featureswere selected, namely (1) all combinations of detail and final level approximationcoefficients (BEST WAVELET COEFFICIENTS), and (2) wavelet energy featuresrather than individual coefficients (ENERGY FEATURES). While obtaining BESTWAVELET COEFFICIENTS, all the detail wavelet coefficients calculated at eachlevel and approximation coefficients at final level were first concatenated. A simplefeature selection procedure with stepwise discriminant analysis (PROC STEPDISCin SAS Version 7.00, SAS Institute, Inc., Cary, NC, USA) was then used to select theoptimum set of wavelet features for separating the three different pine species. Stepwisediscriminant analysis selects the variables that minimize within statistical group vari-ance while maximizing the between group variance for a given significance (α) level.In this study, the α-level was chosen to be 0.05.

For ENERGY FEATURES, the energy feature vector was calculated using equa-tion (3). The feature vector has length eight (seven levels of detail coefficients and onelevel of final approximation coefficients). Finally, we had two sets of wavelet inputfeatures (BEST WAVELET COEFFICIENTS and ENERGY FEATURES) to use inthe classification. To compare the utility of these two sets of wavelet features againstthe untransformed original radiance data in discriminating among the pine species, aconventional technique of band selection was utilized. Each spectral band in the orig-inal hyperspectral signal was evaluated to determine its efficacy for separating knownclasses. Again, stepwise discriminant analysis was used for this purpose. The best sub-set of original spectral bands selected by the stepwise procedure was named BESTSPECTRAL BANDS.

4.4 Classification

Classification of the pine species was carried out using three sets of input vari-ables (BEST WAVELET COEFFICIENTS, ENERGY FEATURES and BESTSPECTRAL BANDS) with linear discriminant analysis (LDA) (PROC DISCRIMin SAS 9.1.3). In LDA, new variables and values are created. The new variables,called canonical variates, are selected to minimize within-group variation and max-imize between-group variation (Davies and Fearn 2008). A two-dimensional plotrepresented by the first two canonical variates provides the best possible view ofhow well groups are separated (Rencher 2002). LDA is sensitive to unequal sam-ple size (Morrison 1969, Finch and Schneider 2006). As such, a random subsampleof 49 was used for loblolly and Virginia pine to ensure an equal number of sam-ple observations (49) for each class. Classification results were verified by running aleave-one-out cross-validation routine within the discriminant procedure (with the

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leave-one-out method, all but one observation is used to apply the classificationdecision rule and this rule is used to classify the omitted observation). Plots ofthe canonical variates resulting from the discriminant procedure (RAFisher2cda.min Matlab 7.4, Trujillo-Ortiz et al. 2004) were used to examine the resultsvisually.

5. Results and discussion

5.1 Feature selection

Stepwise discriminant analysis selected eight wavelet coefficients as the best featuresfor BEST WAVELET COEFFICIENTS. The best detail coefficients correspond todifferent levels of decomposition (two from scale 1, one from scale 2, two from scale3, two from scale 4 and one from scale 5). These coefficients from different levels arefunctions of scale and position (fine detail versus global behaviour at various locationsin the hyperspectral signal). Selection of coefficients from different levels (or scales) asthe best features suggests that both the detail information and the overall trends ofthe hyperspectral signals were important for discriminating the pine species of inter-est. A spectral signature curve (figure 2) was reconstructed (with an inverse DWT)using these eight coefficients to see where the selected features reside in the originalspectrum.

Figure 2 shows the reconstructed curve using the best wavelet features and origi-nal radiance curve for a randomly chosen Virginia pine spectrum. The reconstructionhas a distinct square wave appearance due to the use of the Haar wavelet reconstruc-tion (Bruce et al. 2001). The small spikes in the reconstructed curve arise from thelowest level (finest scale) decomposition; the larger width square wave, in contrast,arises from higher level (coarser scale) decomposition. Accurate matching of the posi-tion of wavelet coefficients and the corresponding wavebands in the original spectra isnot possible, but is less ambiguous with fine scale coefficients than with coarser scalecoefficients. In figure 2, note that the best wavelet coefficients are centred on the chloro-phyll well, red edge and the infrared region of the spectrum. One of the best detailcoefficients was located at ≈700 nm and other one was located at ≈1075 nm. Thecoarser scale coefficients were also located around the red edge and a water absorptionregion (≈1400 nm).

Using a similar stepwise procedure with the original radiance data, five wave-bands centred on 547, 596, 673, 711 and 930 nm were chosen as the best featuresfor BEST SPECRAL BANDS at the 0.05 significance level. Visible and near-infraredregions were important in the spectral separation of the three pine species. However, incontrast to the wavelet features, the water absorption regions were not as important.

5.2 Classification

Cross validation results for the classifications are tabulated in table 1. Classificationwith BEST WAVELET COEFFICIENTS provided the highest overall cross-validation accuracy (74.2%). Classification with the BEST SPECTRAL BANDS(66.7%) was more accurate than classification using the wavelet ENERGYFEATURES (55.1%).

The results of this study show that Haar discrete wavelet analysis is a useful featureextraction tool for classifying the three pine species using hyperspectral data. DWT

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Figure 2. Study area: Commonwealth of Virginia, USA, showing general location of Appo-mattox–Buckingham State Forest (a) and false colour composite of AVIRIS image (red, 845 nm;green, 673 nm; blue, 596 nm) (b).

Table 1. Cross validation results (% accuracy) from discriminant analyses for the three differentinput datasets.

Input features Loblolly (%) Shortleaf (%) Virginia (%) Overall (%)

BEST SPECTRAL BANDS 61.2 53.1 83.7 66.7BEST WAVELET COEFFICIENTS 87.8 51.0 83.7 74.2ENERGY FEATURES 51.0 44.9 69.4 55.1

not only helped to summarize the important information in hyperspectral data at dif-ferent scales, but also enhanced the subtle spectral variation around key absorptionfeatures. The importance of the red edge and visible part of the spectrum for speciesdiscrimination has been demonstrated in many studies (Kokaly et al. 2003, Schmidtand Skidmore 2003, van Aardt and Wynne 2007). Similarly, varying spectral responsearound water absorption features for different species has been found to be equallyuseful in species discrimination (Clark et al. 2005, Stimson et al. 2005, Pu 2009).

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Figure 3. Randomly selected Virginia pine hyperspectral signal and reconstruction of the sig-nal using only the best eight wavelet detail coefficients selected as best wavelet coefficients.Radiance (in W m−2 sr−1) is shown on the y-axis and wavelength (in nm) on the x-axis. Notethat the reconstructed radiance curve includes both negative and positive values because onlydetail coefficients were used to reconstruct the radiance.

BEST WAVELET COEFFICIENTS contained detail coefficients from the red edgeand visible regions at different scales, as well as coefficients concentrated around waterabsorption features that afforded better separation among classes (figure 3).

The accuracy of the classification varies with the choice of wavelet feature set asinput to the classification. The best coefficients stemmed from fine scale (scale = 1and 2) as well as coarser scale (scale = 3, 4 and 5) decompositions in WAVELETCOEFFICIENTS. Hence, this feature set provided information on both narrow andwide absorption features. Similar results were found by Koger et al. (2003) whiledetecting pitted morning glory in soybean. Bruce et al. (2002) also found both finescale and coarser scale coefficients important for detecting weeds in agricultural crops.With the ENERGY FEATURES, cross validation accuracy was greatly decreased.The relative inability of ENERGY FEATURES to enable separation of the pinespecies could be due in part to the loss of information from important portions of thevegetation spectra (such as the red edge, chlorophyll well and water absorption fea-tures). Contrary to our results, Zhang et al. (2006) found that the BEST WAVELETCOEFFICIENTS and ENERGY FEATURES performed equally well for enhancingspectral separability of tropical tree species at La Selva, Costa Rica (though only 17trees were sampled). We posit that the difference between our results and those ofZhang et al. (2006) arises from the much more limited variability among the analysedspectra in our study, since they were all from within a single (Pinus) genus versus fivespecies from five different genera in the study by Zhang et al. (2006). However, otherdifferences between the studies could have been a factor, including differences in thecharacteristics of the data from the airborne sensors (AVIRIS versus HYDICE) andsampling (single pixels versus multipixel averages).

Figure 4(a) and (b) show the canonical discriminant plots for the classification usingBEST WAVELET COEFFICIENTS and BEST SPECTRAL BANDS, respectively.

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Figure 4. Canonical plots for two different datasets: (a) BEST WAVELET COEFFICIENTS,and (b) BEST SPECTRAL BANDS.

The group separability, or lack thereof, among species can be visually examined inthese canonical plots. Separation among the three groups is possible, although there isstill some confusion among classes. Figure 4(a) and (b) show that the best separationof loblolly pine from the other two species is achieved along the first canonical vari-ate, and the best separation between shortleaf and Virginia pine is achieved alongthe second canonical variate. The loblolly pine species is nicely grouped in figure4(a), whereas there is more intermixture of loblolly pine with other two species infigure 4(b). This visual interpretation can be confirmed with the results in table 1.Cross validation accuracy of loblolly pine was greatly increased from 61.2% withBEST SPECTRAL BANDS to 87.8% with BEST WAVELET COEFFICIENTS.Figure 4(a) shows that loblolly pine is separable whereas shortleaf pine is mixed withVirginia pine. Confusion between shortleaf and Virginia pine could be due to the sim-ilarity of their foliage structure, as well as their both having shorter, visibly darkerneedles than loblolly pine (van Aardt and Wynne 2007). However, the confusionbetween two classes seems to impact primarily the error rate for shortleaf classifi-cation, as shortleaf has the lowest cross validation accuracy (see table 1). In thisstudy, we did not further examine the cause of the greater misclassification rate for

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shortleaf pine, as our main objective was to investigate the utility of DWT for featureextraction.

6. Conclusion

The goal of this study was to assess the utility of the Haar DWT as a discriminantanalysis precursor for classifying three pine species (Pinus spp.) using airborne hyper-spectral data (AVIRIS). Two sets of wavelet features were examined for their effect onoverall classification accuracy. Our results suggest that the Haar DWT can be a veryuseful tool for pine species identification. Using all combinations of wavelet coeffi-cients with stepwise LDA for variable selection resulted in the highest accuracy. Theresults of the stepwise selection of wavelet coefficients showed that both fine and coarsescale detail coefficients related to key absorption features contained important infor-mation for classification of pine species. The lowest separability among pine specieswas observed when wavelet energy feature vectors were used as inputs to the classi-fication, reiterating the need for both fine and coarse scale detail coefficients whendiscriminating among pine species.

AcknowledgementsWe are grateful to Dr J.A.N. van Aardt, Rochester Institute of Technology, forsharing field data collected for another study. The comments from one of our anony-mous reviewers were thorough and extremely helpful. This work was funded by theGraduate School at Virginia Tech through a PhD 2010 fellowship (A. Banskota,Geospatial and Environmental Analysis Program, College of Natural Resources andEnvironment).

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