Aurélie Voisin

Vladimir A Krylov

Gabriele Moser

Sebastiano B Serpico

Josiane Zerubia

Multichannel hierarchical image classification using multivariate copulas

Keywords: supervised classification, multichannel data, multivariate copulas, hierarchical Markov random fields, mixture models, marginal posterior mode (MPM), wavelet transform, synthetic aperture radar (SAR), histological images

This paper focuses on the classification of multichannel images. The proposed supervised Bayesian classification method applied to histological (medical) optical images and to remote sensing (optical and synthetic aperture radar) imagery consists of two steps. The first step introduces the joint statistical modeling of the coregistered input images. For each class and each input channel, the class-conditional marginal probability density functions are estimated by finite mixtures of well-chosen parametric families. For optical imagery, the normal distribution is a well-known model. For radar imagery, we have selected generalized gamma, log-normal, Nakagami and Weibull distributions. Next, the multivariate d-dimensional Clayton copula, where d can be interpreted as the number of input channels, is applied to estimate multivariate joint class-conditional statistics. As a second step, we plug the estimated joint probability density functions into a hierarchical Markovian model based on a quadtree structure. Multiscale features are extracted by discrete wavelet transforms, or by using input multiresolution data. To obtain the classification map, we integrate an exact estimator of the marginal posterior mode.

INTRODUCTION

A wide variety of images are available nowadays, and the high diversity of camera/sensor properties explains the difficulty of developing general-purpose image processing algorithms. In this paper we develop a general classifier that can be used on both monoband and multiband imagery as well as at different resolutions, with the underlying assumption that the acquired data are coregistered [START_REF] Goshtasby | 2-D and 3-D image registration: for medical, remote sensing, and industrial applications[END_REF] . Initially developed to deal with Synthetic Aperture Radar 2 (SAR) image classification, the proposed model is sufficiently flexible to deal with other types of data, hence giving the method an additional degree of freedom by allowing the use of multisensor data.

A common way to classify multisensor data is to combine multiple classifiers, by various methods such as boosting [START_REF] Schapire | A brief introduction to boosting[END_REF] , bagging [START_REF] Breiman | Bagging predictors[END_REF] , majority voting 5 , decision fusion [START_REF] Benediktsson | Classification of multisource and hyperspectral data based on decision fusion[END_REF][START_REF] Waske | Classifying multilevel imagery from SAR and optical sensors by decision fusion[END_REF] , support vector machines (SVM) [START_REF] Waske | Fusion of support vector machines for classification of multisensor data[END_REF] or methods based on the Dempster-Shafer theory of evidence [START_REF] Al-Ani | A new technique for combining multiple classifiers using the Dempster-Shafer theory of evidence[END_REF] . In a Bayesian context [START_REF] Barnard | Studies in the history of probability and statistics: Ix. Thomas Bayes's essay towards solving a problem in the doctrine of chances[END_REF] , posterior probabilities are used for classification via statistical consensus theory [START_REF] Benediktsson | Consensus theoretic classification methods[END_REF] or neural networks [START_REF] Benediktsson | Hybrid consensus theoretic classification[END_REF] . In a same Bayesian context, it is also possible to model the likelihood term by a joint probability [START_REF] Solberg | A Markov random field model for classification of multisource satellite imagery[END_REF] , given the marginal probabilities related to each input data. The classification is then obtained by applying standard classification methods, such as, for instance, Markov random field (MRF)-based methods [START_REF] D'elia | A tree-structured Markov random field model for Bayesian image segmentation[END_REF] . The classification proposed in this paper is based on a Markovian context, and the likelihood term is estimated by combining the marginal probability density functions (PDFs) related to each input data by using multivariate copulas [START_REF] Nelsen | An introduction to copulas[END_REF] . Moreover, the use of a hierarchical Markovian model [START_REF] Graffigne | Hierarchical Markov random field models applied to image analysis: a review[END_REF][START_REF] Fieguth | Statistical image processing and multidimensional modeling[END_REF] allows to consider multiresolution acquisitions, without resorting to pixel-based fusion [START_REF] Wang | A comparative analysis of image fusion methods[END_REF] . Such classifiers can be used in different application fields such as medical or biological image processing, as well ♯ E-mail: aurelie.voisin@inria.fr as in remote sensing, where the classification may help to determine land-use or land-cover maps or damaged areas after a natural disaster.

The proposed supervised Bayesian classification method consists of two steps. The first one is the statistical modeling of the coregistered input images. Such statistical modeling is flexible enough to allow multisource data to be dealt with. For each class and each channel in the chosen stacked-vector input dataset, the class-conditional marginal probability density functions (PDFs) are estimated by finite mixtures of well-chosen parametric families [START_REF] Moser | Dictionary-based Stochastic Expectation Maximization for SAR amplitude probability density function estimation[END_REF] . For optical imagery, the normal distribution is an often accepted model, and the parameters of the employed normal PDF mixtures are estimated in the proposed method by the stochastic expectation maximization (SEM) [START_REF] Celeux | On stochastic versions of the EM algorithm[END_REF] algorithm. For SAR imagery, the generalized Gamma distribution 21 is an adequate choice, both thanks to its accurate results with this data typology and because it extends earlier developed classical parametric SAR models. Nevertheless, log-normal, Nakagami and Weibull distributions may be other feasible options [START_REF] Krylov | Enhanced dictionary-based SAR amplitude distribution estimation and its validation with very high-resolution data[END_REF] . The mixture parameters in the case of a SAR channel are determined by a modified SEM algorithm that integrates the method of log-cumulants (MoLC) [START_REF] Tison | A new statistical model for Markovian classification of urban areas in high-resolution SAR images[END_REF] instead of maximum likelihood estimates that are unfeasible for many SAR-specific parametric families. Next, the multivariate d-dimensional Clayton copula [START_REF] Nelsen | An introduction to copulas[END_REF] (d being the number of input channels) is applied to estimate multivariate joint class-conditional statistics, merging the marginal PDF estimates of the input channels. The copula parameters are estimated by using the relationship with the Kendall's tau correlation coefficient [START_REF] Nelsen | An introduction to copulas[END_REF] . As a second step, we plug the estimated joint PDFs into a contextual model that uses a multiscale approach via a hierarchical Markovian model [START_REF] Graffigne | Hierarchical Markov random field models applied to image analysis: a review[END_REF][START_REF] Fieguth | Statistical image processing and multidimensional modeling[END_REF] based on a quad-tree structure. Multiscale features are extracted by discrete wavelet transforms [START_REF] Mallat | A wavelet tour of signal processing[END_REF][START_REF] Daubechies | Orthonormal bases of compactly supported wavelets[END_REF] or by using input multiresolution data. The consideration of a quad-tree allows to integrate an exact estimator of the marginal posterior mode (MPM) [START_REF] Laferte | Discrete Markov modeling and inference on the quad-tree[END_REF] that aims to estimate the unknown class labels. The prior probability is iteratively updated at each level of the tree, leading to an algorithm more robust with respect to noise 27 (e.g., speckle in SAR acquisitions 2 ) when compared to a non-updated prior [START_REF] Laferte | Discrete Markov modeling and inference on the quad-tree[END_REF] .

For single-resolution data, it is also possible to use a spatial context via a hidden Markov random field (MRF) model 28 that employs a modified Metropolis dynamics (MMD) scheme [START_REF] Berthod | Bayesian image classification using Markov random fields[END_REF] or graph-cuts [START_REF] Boykov | Efficient approximate energy minimization via graph cuts[END_REF][START_REF] Kolmogorov | What energy functions can be minimized via graph cuts?[END_REF][START_REF] Boykov | An experimental comparison of min-cut/max-flow algorithms for energy minimization in vision[END_REF] for energy minimization. Comparisons between the two contextual methods (spatial and hierarchical) will be studied in Sec. 5.

The rest of the paper is organized as follows. In Sec. 2, we introduce the statistical multivariate copula-based model that combines marginal PDF models of the input images. In Sec. 3, we briefly recall the main concepts and properties of the hierarchical approaches. In Sec. 4, we develop the MPM model based on the quad-tree that we use to classify our data. In Sec. 5, we present classification results obtained on histological (medical) and on remote sensing imagery.

JOINT PDF MODEL

Considering the problem of supervised classification, we need to model the joint statistics of the input images. These inputs may be, for instance, color bands of optical images and/or single or multi-polarized radar images.

To proceed, we propose, first, to model independently the statistics of each input band for each class, and then to estimate a joint PDF for each class by using the statistical instrument of copulas.

Marginal PDF estimation

We want to model the distributions of each class ω m considered for the classification, m ∈ [1; M ], given a training set, for each input image. For each class, the PDF p m (z|ω m ) is modeled via finite mixtures [START_REF] Figueiredo | Unsupervised learning of finite mixture models[END_REF] of independent greylevel distributions:

p m (z|ω m ) = K i=1 P mi p mi (z|θ mi ), ( 1
)
where z is a greylevel, z ∈ [0; Z -1], and ω m is the m th class. P mi are the mixing proportions such that for a given m, K i=1 P mi = 1 with 0 ≤ P mi ≤ 1. θ mi is the set of parameters of the i th PDF mixture component of the m th class. The use of finite mixtures instead of single PDFs offers the possibility to consider heterogeneous PDFs, usually reflecting the contributions of the components present in each class (for instance, different kinds of crops for the vegetation class when considering high resolution remote sensing data). Moreover, the use of finite mixtures can be seen as a generalization of the determination of a single PDF, and allows to estimate both the best finite mixture model and/or the best single PDF model.

Optical case

When the input is an optical acquisition, we consider that the PDF p m (z|ω m ) related to each class can be modeled by a finite mixture of Gaussian distributions, hence

p mi (z|θ mi ) = 1 2πσ 2 mi exp - (z -µ mi ) 2 2σ 2 mi , with θ mi = {µ mi , σ 2 mi }, (2)
where the mean µ mi and the variance σ 2 mi are estimated within a stochastic expectation maximization 20 algorithm.

Radar case

The radar acquisitions are known to be affected by speckle 2 . For this reason, we use distributions more adapted to such images such as the generalized Gamma distribution [START_REF] Anastassopoulos | High resolution radar clutter statistics[END_REF] . Each class conditional PDF is then modeled by a mixture of generalized Gamma distributions, hence

p mi (z|θ mi ) = ν mi σ mi Γ(κ mi ) z σ mi κmiνmi-1 exp - z σ mi νmi , with θ mi = {ν mi , σ mi , κ mi }, (3)
where Γ(•) is the Gamma function [START_REF] Sneddon | The use of integral transforms[END_REF] .

When the generalized Gamma distribution is not applicable 36 , the PDF p mi (z|θ mi ) is automatically chosen among the following distributions: log-normal, Weibull, Nakagami. These distributions are commonly used to model radar imagery [START_REF] Krylov | Supervised high resolution dual polarization SAR image classification by finite mixtures and copulas[END_REF] . A modified SEM algorithm is then used to estimate the best-fitting mixture model for each considered class. It combines a density parameter estimation via the method of log-cumulants [START_REF] Tison | A new statistical model for Markovian classification of urban areas in high-resolution SAR images[END_REF] and a stochastic expectation maximization (SEM) algorithm [START_REF] Celeux | On stochastic versions of the EM algorithm[END_REF] . For more details concerning the mixture estimation, see Refs. 19, 22 and 37.

Combination of marginal distributions via multivariate copulas

We now very briefly introduce some relevant properties and definitions for copulas. For a comprehensive introduction see Ref. 15.

The multivariate copula is a d-dimensional joint distribution defined on [0, 1] d such that marginal distributions are uniform on [0, 1]. The importance of copulas in statistics is explained by Sklar's theorem [START_REF] Nelsen | An introduction to copulas[END_REF] , which states the existence of a copula C m that models the joint distribution function H m of arbitrary random variables {Z 1 , ..., Z d } with cumulative distribution functions (CDFs) {F 1m , ..., F dm }:

H m (z 1 , ..., z d ) = C m (F 1m (z 1 ), ..., F dm (z d )), (4)
for all z 1 , ..., z d in R.

Taking the derivative in Eq. ( 4) over the d continuous random variables {z 1 , ..., z d } with PDFs {f 1m , ..., f dm }, we obtain the joint PDF distribution:

h m (z 1 , ..., z d ) = d j=1 f jm (z j ) × ∂ d C m ∂z 1 ...∂z d (F 1m (z 1 ), ..., F dm (z d )) = d j=1 f jm (z j ) × c m (F 1m (z 1 ), ..., F dm (z d )). ( 5
)
We wish to estimate, for each class m, the joint PDF h m given the marginal distributions {f 1m , ..., f dm } that correspond to the marginal PDFs of the different input images, i.e. f jm = p m (z|ω m ) estimated for the j th input image and for the m th class. The CDF F jm is the integral on ] -∞; z j ] of its corresponding PDF f jm . Thus, the parameters of the cumulative distribution functions {F 1m , ..., F dm } are the same as the parameters of the marginal estimates in Eq. ( 1). According to Eq. ( 5), to determine h m , we have to determine the copula family C m .

(a) r • s - • • s • • s + • • • (b)
The bivariate copulas have been studied extensively in the literature, which is not necessarily the case for multivariate copulas. We only focus in this paper on the Clayton copula family, due to the fact that the densities of e.g., Frank or Marchal copulas, well-known in a bivariate case, are not straighforward for a d-dimensional case. The Clayton copula density can by written:

c m (u 1 , ..., u d ) = d j=1 u -(α+1) j • d-1 n=0 (1 + αn) • ( d j=1 u -α j -d + 1) ( -1-dα α ) where u j = F jm (z j ). (6)
To estimate the unknown copula parameter α, we use the relationship between copulas and Kendall's τ which is a ranking correlation coefficient [START_REF] Nelsen | An introduction to copulas[END_REF] . By definition, Kendall's τ is a concordance-discordance measure that can be empirically estimated by using the training sets. Once the estimate τ is computed, we get the parameter estimate α = 2τ 1-τ , according to Refs. 15, 38. Such procedure is stressed for each considered class.

THE HIERARCHICAL MODEL

Among the various techniques that can be applied on hierarchical graphs [START_REF] Graffigne | Hierarchical Markov random field models applied to image analysis: a review[END_REF] (renormalization group, [START_REF] Gidas | A renormalization group approach to image processing problems[END_REF] constrained configuration subspaces, 40 etc.), we employ an explicit hierarchical graph-based model [START_REF] Graffigne | Hierarchical Markov random field models applied to image analysis: a review[END_REF][START_REF] Laferte | Discrete Markov modeling and inference on the quad-tree[END_REF] to address our classification problem. The specific graphs on which we base our study have a tree structure. The set of sites s (s ∈ S) is, therefore, hierarchically partitioned as S = S 0 S 1 ... S R , where R corresponds to the coarsest resolution, the root, and 0 corresponds to the reference level (finest resolution). In this tree structure, there is a parent-child relationship: for each site s of any tree-level n a unique parent s -and several children s + can be defined. d(s) refers to the set including s and its descendants. For the specific case where s owns four children, the tree structure is called a quad-tree. Such a structure is depicted in Fig. 1.

Various good properties have led us to consider this type of hierarchical Markov random fields. First among them is the scale causality generated by the quad-tree structure, which allows a non-iterative algorithm to be used, thus implying a computational time decrease [START_REF] Fabre | New fast smoothers for multiscale systems[END_REF] . Second, the multigrid properties reduce the probability to find a local minimum, hence the applied algorithm is more likely to converge to a global solution. Moreover, such a model is able to take into account different kinds of statistics, and thus to use different kinds of images (different resolutions, different sensors, etc.) [START_REF] Laferte | Hierarchical statistical models for the fusion of multiresolution image data[END_REF] .

The aim of classification is to estimate a set of hidden labels X given a set of observations Y attached to the sites. X and Y are considered to be random processes. The restriction of X (resp. Y ) to the level n is

X n = {X s , s ∈ S n } (resp. Y n = {Y s , s ∈ S n })
where the realization x n takes its values in Ω. Some extra hypotheses are needed to ensure that X is a Markov random field on the graph: ∀s ∈ S, ∀x ∈ Ω,

(i) p(X = x) > 0, (ii) p(X s = x s |X t = x t , t ∈ S -{s}) = p(X s = x s |X t = x t , t ∈ V s ), V s describing the neighborhood of the site s.
One last hypothesis is the pointwise dependance of Y with respect to X, thus implying that each couple (X, Y ) is Markovian on the quad-tree:

p(y|x) = R n=0 p(y n |x n ) = R n=0 s∈S n p(y s |x s ).

HIERARCHICAL CLASSIFICATION APPROACH

A variety of algorithms were proposed to estimate the labels on hierarchical graphs [START_REF] Fieguth | Statistical image processing and multidimensional modeling[END_REF] . Typically, a global energy minimization is done via iterative relaxation algorithms [START_REF] Kato | A hierarchical Markov random field model and multitemperature annealing for parallel image classification[END_REF] . The consideration of a quad-tree allows to benefit from its good properties (e.g., causality) and to apply non iterative algorithms. To avoid the underflow generated by the use of the maximum a posteriori (MAP) criterion, we take into account an exact estimator of the marginal posterior mode (MPM) [START_REF] Laferte | Discrete Markov modeling and inference on the quad-tree[END_REF][START_REF] Marroquin | Probabilistic solution of ill-posed problems in computational vision[END_REF] . The cost function associated to this estimator offers the possibility to penalize the errors according to their number and the scale at which they occur: an error at the coarsest scale is more strongly penalized than an error at the finest scale, which is a desired property because a site located at the root corresponds to 4 R pixels at the finest scale.

To estimate the posterior probability, we need the following prior information: the likelihood, the prior probability and the transition probability at each site s of the quad-tree. In this section, we present how this information is estimated and then we focus on the maximization of the posterior probability. The employed likelihood model has already been developed in Sec. 2.

Transition probabilities

The fundamental hypothesis in the application of the described hierarchical MRF is that we consider the random process X Markovian with respect to scale, i.e. p(

x n |x k , k > n) = p(x n |x n+1 ) = s∈S n p(x s |x s -),
where n and k are scales. These transition probabilities between the scales, p(x s |x s -), determine the hierarchical MRF since they represent the causality of the statistical interactions between the different levels of the tree. We use the transition probability in the form introduced by Bouman et al. [START_REF] Bouman | A multiscale random field model for Bayesian image segmentation[END_REF] : for all sites s ∈ S and all scales n ∈ [0; R -1],

p(x s = ω m |x s -= ω k ) = θ n , if ω m = ω k 1-θn M-1 , otherwise , (7)
where m, k ∈ [1; M ]. This model favors an identical parent-child labeling. Typically, we choose a fixed θ n ≈ 0.8, which means that a site s at scale n has a probability of about 80% to belong to the same class as its ascendant s -. These transition probabilities are used to estimate the prior probabilities at different scales (see Sec. 4.2).

Prior probability

The prior distribution at level n in [0; R -1] is given by:

p(x n s ) = x n s - p(x n s |x n s -)p(x n s -). (8)
Thus, the prior information at the coarsest level R allows to determine the prior information at the other levels since the transition probabilities are known (see Sec. 4.1).

The first step is, thus, to determine the prior information at the coarsest level R. The priors at other scales are estimated by using Eq. (8). We choose to model by considering the equiprobability between classes. We then apply an MPM estimation on a R-scale tree, and use the classification results as an updated prior. Then, we consider a smaller tree of scale R -1 to which we apply the MPM algorithm to estimate a new prior. We proceed iteratively until scale 0 is reached. Such an update allows a better prior estimation, leading to a final classification map more accurate than without any prior update [START_REF] Laferte | Discrete Markov modeling and inference on the quad-tree[END_REF][START_REF] Voisin | Classification of very high resolution sar images of urban areas[END_REF] . This update is illustrated in Fig. 3.

To estimate the priors given a classification map, we use a Markovian model which takes into account the contextual information at each level, and therefore leads to a better prior estimation. By employing the Hammersley-Clifford theorem [START_REF] Besag | Spatial interaction and the statistical analysis of lattice systems[END_REF] , we can define a local characteristic for each site:

p(x s ) = 1 Z exp(-β s:{s,t}∈C δ xs=xt ) with δ xs=xt = 1, if x s = x t 0, otherwise , (9)
where Z is the normalization constant, s, t denote the sites in the same clique and x s , x t their labels. A clique is a non-empty subset c of neighboring sites of size equal to or higher than 1.

Instead of considering a widely used second-order neighborhood based on the 8 pixels surrounding a given pixel [START_REF] Geman | Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images[END_REF] , we suggest to use an adaptive neighborhood, which means that we consider different kinds of neighbor sets, as in Ref. 48 , and at each site we select the one that leads to the smallest energy [START_REF] Smits | Synthetic aperture radar image segmentation by a detail preserving Markov random field approach[END_REF][START_REF] Zhong | A new MRF framework with dual adaptive contexts for image segmentation[END_REF] . The adaptivity of the neighborhood aims to take into account the geometrical properties of the different areas in our original image, a spatial feature that plays a primary role especially in high-resolution imagery.

In Eq. ( 9), we notice the presence of an unknown positive parameter β to estimate. This parameter can be estimated by minimizing a pseudo-likelihood over a training set. We stress here that this method brings to adequate estimates only when using an exhaustive ground truth, or, at least, by taking into account a sufficient amount of class borders, which is rarely the case, in particular in remote sensing. For this reason, we determine this parameter by trial-and-error. The results of different experiments have led us to choose β = 4.8, which is quite a high value.

Posterior probabilities and their estimation using MPM

Since the quad-tree has, by definition, no cycles, the labels can be estimated exactly and non iteratively by MPM via a forward-backward algorithm, similar to the classical Baum algorithm for Markov chains [START_REF] Baum | A maximization technique occuring in the statistical analysis of probabilistic functions of Markov chains[END_REF]

.

A classical MPM algorithm [START_REF] Laferte | Discrete Markov modeling and inference on the quad-tree[END_REF] would need to estimate the posterior probability at level 0 given the observations at each level y = {y s , ∀s ∈ S, ∀n ∈ [0; R]}. This estimation is generally done in 2 passes, referred to as bottom-up ("forward") and top-down ("backward") passes. In our case, we truncate the top-down pass, by using the highest tree-level label estimates to update the prior, and to run a novel MPM algorithm on a smaller quad-tree (see Figs. 2 and3).

Bottom-up pass

This pass aims to estimate for each site s ∈ S the partial posterior marginals p(x s |y d(s) ) that are needed for the complete posterior probabilities p(x s |y) estimation (top-down pass). The probabilities p(x s |y d(s) ) at a given level n are used to estimate p(x s |y d(s) ) at level n + 1. In fact, Laferte et al. [START_REF] Laferte | Discrete Markov modeling and inference on the quad-tree[END_REF] showed that

p(x s |y d(s) ) =    p(x s |y s ) = 1 Z p(y s |x s )p(x s ), at level 0 1 Z p(y s |x s )p(x s ) t∈s + xt p(xt|y d(t) ) p(xt) p(x t |x s ) , otherwise . (11)
Thus, we proceed to a recursion, starting from the leaves and proceeding until the root is reached.

Top-down pass

As already mentioned, the modified MPM algorithm proposed in this paper combines the MPM-based algorithm of Laferte et al [START_REF] Laferte | Discrete Markov modeling and inference on the quad-tree[END_REF] this algorithm, we do not maximize directly p(x s |y), but minimize the negative of its logarithm instead, which is possible since the logarithm is an increasing function. MMD algorithm has good properties for both its relative low computation time and the good precision of its results [START_REF] Berthod | Bayesian image classification using Markov random fields[END_REF] .

Finally, in order to improve the properties of the classification maps reported by our MPM-based method, we have applied a morphological majority voting procedure [START_REF] Soille | Morphological Image Analysis -Principles and Applications[END_REF] . This smoothing part of the classification algorithm is optional and can be recommended when the final classification map demonstrates excessive salt-and-pepper type of noise due to the consideration of noisy input images (typically, SAR acquisitions).

EXPERIMENTAL RESULTS

The developed hierarchical classification approach is applied to three different data sets. Two of them are based on the classification of remote sensing images of cities, and the third one deals with the classification of an histological image. For each considered method and each data set, we give the final classification map and the corresponding classification accuracies, obtained on test sets that do not overlap with the training sets. Each training and test set is endowed with a manually annotated ground truth map and each represents between 7% and 10% of the whole image. In general, these manually-built ground truths are selected in homogeneous areas, meaning that the borders are not taken into account in order to guarantee the precision of the sets.

In the case of monoresolution acquisitions, we apply a 2-D discrete wavelet transform [START_REF] Mallat | A wavelet tour of signal processing[END_REF] to create a multiresolution input image that can be introduced in the hierarchical model. We then decompose our original image (mono-or multi-band) along different scales, corresponding to the tree levels. Empirically, we have concluded that good results are obtained with the hierarchical decomposition on R = 2 levels, R being the depth of decomposition. For each scale, we consider solely the approximation coefficients. The scale factor is always a power of 2, thus leading to the required quad-tree configuration. The approximation coefficients at scale 0 correspond to the original image. By filtering and decimating this image through the application of a low-pass filter to the rows and columns, we obtain the approximation coefficients for scale 1. Similarly, the approximation coefficients at scale j are decomposed by filtering and decimation so as to obtain the coefficients at scale j + 1, for j < R. A wide choice of wavelet functions exists, such as Daubechies, (bi-)orthogonal, and after comparison of the diverse classification performances, we finally chose Daubechies-10 wavelets [START_REF] Daubechies | Orthonormal bases of compactly supported wavelets[END_REF] to decompose SAR images and Haar wavelets [START_REF] Mallat | A wavelet tour of signal processing[END_REF] to decompose optical images.

The β parameter of the Markov random field in the MPM-based algorithm (see Sec. 4.2) was empirically set to β = 4.8. As already mentioned in the introduction, when considering monoresolution acquisitions, we can simply combine the mixture-based likelihood modeling to a spatial MRF (already used in Ref. 52), instead of using a hierarchical model. In that case, the β parameter (see Sec. 4.2) is set to β = 1.3, and the optimization is done preferentially via a graph-cut scheme [START_REF] Boykov | Efficient approximate energy minimization via graph cuts[END_REF][START_REF] Kolmogorov | What energy functions can be minimized via graph cuts?[END_REF][START_REF] Boykov | An experimental comparison of min-cut/max-flow algorithms for energy minimization in vision[END_REF] , faster than the MMD. We compared the two Markovian models on the remotely sensed and the histological images.

The use of graph-cuts for energy minimization has not been studied for the proposed MPM-based algorithm (Sec. 4.3). We did not apply the same graph-cuts implementation as in the MRF-based method because in this case, the Potts-based prior estimation is integrated in the graph-cut scheme. In the hierarchical model proposed in this paper, the prior is estimated preliminary. This main difference between the two algorithms also explains why the β parameter is set to different values.

Histological image

The considered image is a red, green, blue (RGB) histological image of the skin provided by Galderma of 550 × 1020 pixels. The R, G, and B bands are considered as the input features and the class conditional PDFs are modeled by using normal mixtures (see Sec. 2.1.1). This image is classified into 4 classes that were interpreted by a dermatological expert as the cytoplasm (in yellow in the classification maps), the nuclei (in blue) and the background (in red). The green class gathers the dermis matrix, the collagen and the stratum corneum keratin. Each of these classes is modeled by using our multivariate copula-based model (Sec. 2). Given the fact that this image is monoresolution, we applied, for comparison, the proposed hierarchical model and a single-scale MRF model. The multiresolution decompositions are obtained by Haar wavelet transform on R = 2 levels. For this specific case, by looking at both visual (Fig. 4) and numerical (Tab. 1) results, we can notice that the two Markovian-based methods lead to similar results. For this reason, we tend to favor the fastest method, that is the MRF-based method. In fact, we computed computation time for the various experiments that were conducted on Intel Xeon 2.40GHz, Linux system. The MRF-based algorithm runs in approximately 3 minutes, whereas our hierarchical method takes approximately 8 minutes to estimate the final classification map.

Amiens, France

The considered images are two single-pol COSMO-SkyMed SAR images of the city of Amiens (France) ( c ASI, 2011):

• a StripMap acquisition (2.5 m pixel spacing), HH polarized, geocoded, single-look image. 510 × 1200 pixels, shown in Fig. 5(a).

• a PingPong acquisition (5 m pixel spacing), HH polarized, geocoded, 255 × 600 pixels, shown in Fig. 5(b).

In this case, we deal with four classes: urban (in red), water (in blue), vegetation (in green) and trees (in yellow).

The hierarchical tree considered here has a scale R = 1.

To improve the urban area detection, we propose to extract a Greylevel co-occurrence matrix (GLCM)-based textural information from the original SAR images at each decomposition level, as already suggested in Ref. 52. The PDFs of both the SAR image and its textural feature are independently modeled by using generalized Gamma mixtures (see Sec. 2.1.2), and then combined via multivariate copulas.

The final classification map is given in Fig. 5(c). The final numerical results (Tab. 2) are more accurate when introducing a textural information that efficiently improves the urban area detection. The loss of accuracy in the vegetation class for all the methods (Tab. 2) is due to misclassifications of this area with trees at the bottom of the image. By visually analyzing the SAR image, we cannot really see a difference between these areas. Multiple polarization acquisition would be helpful in that case.

Port-au-Prince, Haiti

The considered input consists of two images of the quay of Port-au-Prince (Haiti):

• a single-polarized COSMO-SkyMed SAR image ( c ASI, 2010), HH polarization, StripMap acquisition mode (2.5 m pixel spacing), geocoded, single-look, 920 × 820 pixels, shown in Fig. 6(a).

• a coregistered panchromatic GeoEye acquisition ( c GeoEye, 2010), 920 × 820 pixels, shown in Fig. 6(b).

Five classes were chosen in that case: the water class (in blue in the classification maps), the urban areas (in red), the vegetation (in green), the sand (in yellow) and the containers (in pink). As in the case of the histological image, we compare visual (Fig. 7) and numerical (Tab. 3) results obtained when using the hierarchical and the monoresolution MRF-based methods. For the hierarchical method, the multiresolution decompositions are obtained by Haar wavelet (for panchromatic) and Daubechies (for SAR) transforms on R = 2 levels. Numerical results indicate that the MRF-based method leads to a higher numerical accuracy. But we stress here that the map obtained by using the MRF-based method is severely oversmoothed, and this affects only marginally the numerical accuracies due to the localization of the test samples inside homogeneous areas (see Fig. 6(c)). However, when looking at the classification maps (Fig. 7), we can notice that the classification is more detailed when using a hierarchical decomposition, that makes us favor this method for the optical/SAR classification. Moreover, we also compared numerically (Tab. 3) and visually (Fig. 7) the results obtained with the proposed hierarchical method when considering respectively only SAR, only panchromatic and both images. We can obviously see the improvements related to the combination of the two images. In fact, the optical image has a relevant effect in the sand discrimination, and the SAR acquisition is very helpful to detect the containers. Thus, the consideration of both of them allows to obtain good classification results for the container and the sand areas, and to improve the urban detection.

CONCLUSION

The method proposed in this paper allows to deal with multisensor, multiband, and/or multiresolution acquisitions. It combines a joint statistical modeling of considered input images (optical or radar imagery), with a hierarchical Markov random field, leading to a statistical supervised classification approach. We have proposed a copula-based multivariate statistical model that enables to fuse multisensor acquisitions, and we have developed a novel MPM-based hierarchical Markov random field model that iteratively updates the prior probabilities and, thus, leads to the improved robustness of the classifier. The hierarchical MRF considered here has two advantages: it is quite robust to speckle noise, and we can apply a non-iterative optimization algorithm (MPM estimation).

We analyzed the results obtained with the proposed method. Moreover, when dealing with monoresolution images, we compared the developed multiresolution hierarchical model to a spatial monoresolution MRF-based classification algorithm. The results were assessed both qualitatively (classification maps) and quantitatively (classification accuracies). The proposed method leads to good classification results for both optical and speckleaffected radar images. The MRF-based method is also efficient (faster and numerically better) and leads to good results. However, we could notice the smoothing effects of this method that may degrade the real accuracy of the final classification map by hiding some details.

The consideration of a quad-tree tends to limit the multiresolution approach by requiring a dyadic decomposition. A possible improvement would be then to find a new hierarchical Markovian-based algorithm that may take into account all resolution sizes, so as to make this method even more general.

Figure 1 .

 1 Figure 1. (a): Hierarchical model structure: quad-tree; (b): Quad-tree notations.

  . The aim is to maximize the posterior marginal at each site s: xs = argmax xs p(x s |y).

Figure 2 .

 2 Figure 2. Generic hierarchical graph-based model of the quad-tree.

Figure 3 .

 3 Figure 3. Proposed MPM estimation on the quad-tree represented in Fig. 2. In this representation, R = 2.

Figure 4 .

 4 Figure 4. Original RGB histological image and classification results obtained with the two contextual methods.Table1. Accuracy for each of the 4 classes and overall results for the test areas of the histological image.

Figure 5 .

 5 Figure 5. Original coregistered SAR images of Amiens in France acquired at different resolutions and the resulting classification map, obtained by using as input a combination of the SAR images and their GLCM textural features.Table2. Accuracy for each of the 4 classes and overall results for the test areas of Amiens.

Figure 6 .

 6 Figure 6. Original SAR image of Port-au-Prince in Haiti, coregistered panchromatic optical image and the selected ground truth used to test the results.Table3. Accuracy for each of the 5 classes and overall results for the test areas of Port-au-Prince.

  Figure 7. (a,b) Port-au-Prince classification maps obtained applying different Markovian contexts on optical/SAR data. (c) Classification map obtained with the hierarchical method applied to the SAR image.

Table 1 .

 1 Accuracy for each of the 4 classes and overall results for the test areas of the histological image.

			Histological image
		nuclei	dermis background cytoplasm overall
	Hierarchical MRF-based classif. 97.08% 99.87% 97.71%	97.13%	97.95%
	MRF-based classif.	99.92% 99.97% 97.72%	96.65%	98.56%

Table 2 .

 2 Accuracy for each of the 4 classes and overall results for the test areas of Amiens.

			Amiens
	water	urban	vegetation tree	overall

Table 3 .

 3 Accuracy for each of the 5 classes and overall results for the test areas of Port-au-Prince.

				Port-au-Prince
		water	urban	vegetation sand	containers overall
	Hierarchical MRF-based classif.	99.60% 94.15% 98.48%	100%	79.28%	94.30%
	MRF-based classif.	99.38% 100%	98.07%	100%	99.91%	99.47%
	SAR only (Hierarchical MRF)	99.08% 87.80% 95.41%	52.38% 84.26%	83.79%
	Panchro. only (Hierarchical MRF) 96.87% 89.48% 97.97%	100%	38.19%	84.50%

ACKNOWLEDGMENTS

The authors would like to thank:

• The Direction Générale de l'Armement (DGA, France) and Institut National de Recherche en Informatique et Automatique (INRIA, France) for the partial financial support.


Nader Ale Ebrahim
email: aleebrahim@siswa.um.edu.my

Shamsuddin Ahmed

Salwa Hanim

Abdul Rashid

Zahari Taha

Technology Use in the Virtual R&D Teams

Keywords: Collaboration teams, questionnaires performance, cross-functional teams, product development, structural equation modeling, measurement model, literature review, e virtual, 1

Problem statement: Although, literature proves the importance of the technology role in the effectiveness of virtual research and development (R&D) teams for new product development. However, the factors that make technology construct in a virtual R&D team are still ambiguous. The manager of virtual R&D teams for new product development does not know which type of technology should be used.

Approach: To address the gap and answer the question, the study presents a set of factors that make a technology construct. The proposed construct modified by finding of the field survey (N = 240). We empirically examine the relationship between construct and its factors by employing the Structural Equation Modeling (SEM). A measurement model built base on the 19 preliminary factors that extracted from literature review. The result shows 10 factors out of 19 factors maintaining to make technology construct.

Result: These 10 technology factors can be grouped into two constructs namely Web base communication and Web base data sharing. The findings can help new product development managers of enterprises to concentrate in the main factors for leading an effective virtual R&D team. In addition, it provides a guideline for software developers as well.

Conclusion:

The second and third generation technologies are now more suitable for developing new products through virtual R&D teams.

INTRODUCTION

A virtual team is defined as "a small temporary group of geographically, organizationally and/or time dispersed knowledge workers who coordinate their work, mainly with electronic information and communication technologies to carry out one or more organization tasks" (Ale Ebrahim et al., 2009b). Virtual R&D team is a form of a virtual team, which includes the features of virtual teams and concentrates on R&D activities (Ale [START_REF] Ebrahim | The Effectiveness of Virtual R&D Teams in SMEs: Experiences of Malaysian SMEs[END_REF].

The members of a virtual R&D team use different types of communication technology to complete the research beyond space, time and organizational boundaries (Ale [START_REF] Ebrahim | Virtual R&D teams and SMEs growth: A comparative study between Iranian and Malaysian SMEs[END_REF]. "We are becoming more virtual all the time!" is heard in many global corporations today [START_REF] Chudoba | How virtual are we? Measuring virtuality and understanding its impact in a global organization[END_REF]. On the other hand, new product development (NPD) is widely recognized as a key to corporate prosperity [START_REF] Lam | Self-assessment of conflict management in clientsupplier collaborative new product development[END_REF]. The specialized skills and talents needed for developing new products often remain locally in pockets of excellence around the company. Therefore, enterprises, have no choice but to disperse their new product development units to gain access into such dispersed knowledge and skills [START_REF] Kratzer | Keeping Virtual R&D Teams Creative[END_REF]. As a result, enterprises are finding that internal development of all technologies needed for new products and processes are difficult or impossible. They must increasingly receive technology from external sources [START_REF] Stock | External technology integration in product and process development[END_REF].

Virtualization in NPD has recently begun to make a serious headway due to the rapid growth of a large variety of technologies. This means that virtuality in NPD is now technically possible [START_REF] Leenders | Virtuality, communication, and new product team creativity: a social network perspective[END_REF]. Due to increasing and changing product features, by-and-large product development has become more complex, with increasing complexity in the supply chain. Therefore, more close collaboration between customers, developers, and suppliers has become vital. The foretold collaborations often involve individuals from different geographical locations that could now be brought together by using the various types of information technology (IT). IT offers a large number of benefits [START_REF] Anderson | Virtual team meetings: An analysis of communication and context[END_REF]. Although the use of the Internet for many purposes has received notable attention in the literature, little has been said about collaborative tool and effective virtual teams for NPD (Ale Ebrahim et al., 2009a). In addition, the literature did not reveal adequate focus on the factors which can construct a technological niche for a virtual R&D team for NPD. This aims to such a technological construct.

This paper is structured as follows. Firstly, based on prior research, we extracted the 19 factors of technology construct in the virtual R&D teams. Next, Structural Equation Modeling (SEM) was used as an analytical tool for testing the estimations and testing the technology construct measurement models. Then, we adjusted the preliminary technology construct model by fitting the model according to the SEM fitness indices and made a final measurement model. The paper infers with a discussion and future guidelines.

LITERATURE REVIEW

Virtual teams use digital communications, video and audio links, electronic whiteboards, e-mails, instant messaging, websites, chat rooms, etc. as substitutes for physical collocation of the team members [START_REF] Baskerville | Activating and Perpetuating Virtual Teams: Now That We're Mobile, Where Do We Go[END_REF]Nandhakumar, 2007, Pauleen and[START_REF] Pauleen | Facilitating virtual team relationships via Internet and conventional communication channels[END_REF]. Simple transmission of information from location A to another location B is not enough. However, a virtual environment presents significant challenges to effective communication [START_REF] Walvoord | Empowering followers in virtual teams: Guiding principles from theory and practice[END_REF]. Being equipped with even the most advanced technologies is not necessarily sufficient to make a virtual team effective, since the internal group dynamics and external support mechanisms must also be present for a team to succeed in the virtual world [START_REF] Lurey | An empirical study of best practices in virtual teams[END_REF]. Virtual teams are technology-mediated groups of people from different disciplines that work on common tasks [START_REF] Dekker | Cultural differences in the perception of critical interaction behaviors in global virtual teams[END_REF] and therefore, the way the information technology is implemented seems to make the virtual teams outcome more or less likely [START_REF] Anderson | Virtual team meetings: An analysis of communication and context[END_REF]. The virtual R&D team's instructor should choose the appropriate technology based on the purpose of the team (Ale Ebrahim et al., 2009d).

The factors which make technology construct in a virtual R&D team are still not clearly set in the literature. We extracted 19 important factors related to the technology construct, based on a comprehensive review on technology view in the virtual R&D team working. Table 1summarizes the factors and their supported references. E-mails and conference calls are generally known as first generation technologies whereas online discussion boards, Power Point presentations, video tools and online meeting tools are second-generation technologies. Third generation technology refers typically to web-enabled shared workspaces with the Intranet or Internet (Lee- [START_REF] Sankey | Global virtual teams for value creation and project success: A case study[END_REF].

Table 1 Summary of the factors related to technology construct in virtual teams

Factor name

Factor descriptions References

Tech1

Use internet and electronic mail [START_REF] Redoli | A model for the assessment and development of Internet-based information and communication services in small and medium enterprises[END_REF][START_REF] Pauleen | Facilitating virtual team relationships via Internet and conventional communication channels[END_REF][START_REF] Sankey | Global virtual teams for value creation and project success: A case study[END_REF][START_REF] Thissen | Communication tools for distributed software development teams[END_REF][START_REF] Townsend | Virtual Teams: Technology and the Workplace of the Future[END_REF])

Tech2

Online meeting on need basis [START_REF] Chen | Team Spirit: Design, implementation, and evaluation of a Web-based group decision support system[END_REF][START_REF] Sankey | Global virtual teams for value creation and project success: A case study[END_REF][START_REF] Pena-Mora | CAIRO: a concurrent engineering meeting environment for virtual design teams[END_REF][START_REF] Thissen | Communication tools for distributed software development teams[END_REF]

Tech3

Web conferencing [START_REF] Coleman | Collaboration 2.0: Technology and Best Practices for Successful Collaboration in a Web 2.0 World[END_REF][START_REF] Thissen | Communication tools for distributed software development teams[END_REF][START_REF] Zemliansky | Handbook of Research on Virtual Workplaces and the New Nature of Business Practices[END_REF], Ale Ebrahim et al., 2009d)

Tech4

Seminar on the Web (Zemliansky and Amant, 2008)

Tech5

Shared work spaces (Lee-Kelley and Sankey, 2008)

Tech6

Video conferencing [START_REF] Chen | Team Spirit: Design, implementation, and evaluation of a Web-based group decision support system[END_REF][START_REF] Zemliansky | Handbook of Research on Virtual Workplaces and the New Nature of Business Practices[END_REF][START_REF] Townsend | Virtual Teams: Technology and the Workplace of the Future[END_REF]

Tech7

Audio conferencing [START_REF] Chen | Team Spirit: Design, implementation, and evaluation of a Web-based group decision support system[END_REF][START_REF] Sankey | Global virtual teams for value creation and project success: A case study[END_REF][START_REF] Zemliansky | Handbook of Research on Virtual Workplaces and the New Nature of Business Practices[END_REF]

Tech8

Online presentations (Lee- [START_REF] Sankey | Global virtual teams for value creation and project success: A case study[END_REF]Sankey, 2008, Townsend et al., 1998)

Tech9

Share documents (off-line) [START_REF] Coleman | Collaboration 2.0: Technology and Best Practices for Successful Collaboration in a Web 2.0 World[END_REF], Ale Ebrahim et al., 2009d[START_REF] Townsend | Virtual Teams: Technology and the Workplace of the Future[END_REF])

Tech10

Share what is on your computer desktop with people in other locations (Remote access and control) [START_REF] Thissen | Communication tools for distributed software development teams[END_REF], Ale Ebrahim et al., 2009c[START_REF] Townsend | Virtual Teams: Technology and the Workplace of the Future[END_REF]

Tech11

Do not install engineering software (get service through web browser) [START_REF] Coleman | Collaboration 2.0: Technology and Best Practices for Successful Collaboration in a Web 2.0 World[END_REF][START_REF] Kotelnikov | Small and Medium Enterprises and ICT[END_REF][START_REF] Shumarova | Authority-based and Bottom-up Diffusion of Collaboration Information Technologies: Constraints and Enablements[END_REF])

Tech12

Access service from any computer (in Network) [START_REF] Thissen | Communication tools for distributed software development teams[END_REF][START_REF] Shumarova | Authority-based and Bottom-up Diffusion of Collaboration Information Technologies: Constraints and Enablements[END_REF])

Tech13

Standard phone service and hybrid services [START_REF] Thissen | Communication tools for distributed software development teams[END_REF], Ale Ebrahim et al., 2009d[START_REF] Townsend | Virtual Teams: Technology and the Workplace of the Future[END_REF])

Tech14

Access shared files anytime, from any computer (Lee- [START_REF] Sankey | Global virtual teams for value creation and project success: A case study[END_REF]Sankey, 2008, Townsend et al., 1998)

Tech15

Web database [START_REF] Coleman | Collaboration 2.0: Technology and Best Practices for Successful Collaboration in a Web 2.0 World[END_REF][START_REF] Zemliansky | Handbook of Research on Virtual Workplaces and the New Nature of Business Practices[END_REF], Ale Ebrahim et al., 2009d[START_REF] Townsend | Virtual Teams: Technology and the Workplace of the Future[END_REF]

Tech16

Provide instant collaboration [START_REF] Coleman | Collaboration 2.0: Technology and Best Practices for Successful Collaboration in a Web 2.0 World[END_REF]Levine, 2008, Thissen et al., 2007)

Tech17

Software as a service (canceling the need to install and run the application on the own computer) [START_REF] Coleman | Collaboration 2.0: Technology and Best Practices for Successful Collaboration in a Web 2.0 World[END_REF][START_REF] Thissen | Communication tools for distributed software development teams[END_REF][START_REF] Townsend | Virtual Teams: Technology and the Workplace of the Future[END_REF])

Tech18

Virtual research center for product development [START_REF] Zemliansky | Handbook of Research on Virtual Workplaces and the New Nature of Business Practices[END_REF]Amant, 2008, Townsend et al., 1998)

Tech19

Integratable/compatible with the other tools and systems [START_REF] Coleman | Collaboration 2.0: Technology and Best Practices for Successful Collaboration in a Web 2.0 World[END_REF][START_REF] Kotelnikov | Small and Medium Enterprises and ICT[END_REF][START_REF] Townsend | Virtual Teams: Technology and the Workplace of the Future[END_REF]

RESEARCH METHODOLOGY AND DATA COLLECTION

To build a measurement model of information technology construct in virtual R&D teams for new product development, we conducted a Web-based survey mainly in Malaysian and Iranian manufacturing enterprises, in a random sample of small and medium enterprises. Webbased survey method was selected because it is a costeffective and quick method to obtain feedbacks from the beliefs of the respondents. The rapid expansion of Internet users has given Web-based surveys the potential to become a powerful tool in survey research [START_REF] Sills | Innovations in Survey Research: An Application of Web-Based Surveys[END_REF]Song, 2002, Ebrahim et al., 2010). A Likert scale from one to five was used. This set-up provided the respondents with a series of attitude dimensions. For each factor, the respondents were asked whether the factor is unimportant or extremely important using a Likert scale rating. The questionnaires were e-mailed to the managing director, R&D manager, new product development manager, project and design manager and appropriate personnel who were most familiar with the R&D activities within the firm.

Invitation e-mails were sent to each respondent, reaching 972 valid email accounts, with reminders following every two weeks up to three months. 240 enterprises completed the questionnaire, for an overall response rate of 24.7% (Table 2).

ANALYSIS AND RESULTS

Gerbing and [START_REF] Anderson | Structural equation modeling in practice: A review and recommended two-step approach[END_REF] suggested using confirmatory factor analysis (CFA) for scale development because it affords stricter interpretation of unidimensionality than what is provided by traditional approaches such as coefficient alpha, item-total correlations, and exploratory factor analysis. The evidence that the measures were uni-dimensional, whereby a set of indicators (factors) shares only a single underlying construct, was assessed using CFA [START_REF] Anderson | Structural equation modeling in practice: A review and recommended two-step approach[END_REF]. According to [START_REF] Anderson | Structural equation modeling in practice: A review and recommended two-step approach[END_REF], after data collection, the measures' purification procedures should be used to assess their reliability, uni-dimensionality, discriminant validity, and convergent validity. For reliability analysis, Cronbach's alpha was employed to each factor. From Table 3, all items with Cronbach's α greater than the threshold value of 0.6 were included in the analysis and the rest were omitted from analysis. Hence, the factors Tech1, Tech10, Tech11 and Tech13 were excluded from further analysis. In general, the reliability of the contents in the questionnaire exhibits good reliability across the samples.

Structural Equation Modeling (SEM) using AMOS 18 was employed for validating the measurement model. The statistical analysis were estimated simultaneously for both measurement and structural models [START_REF] Dibrell | Fueling Innovation through Information Technology in SMEs[END_REF]. In order to ensure that the factors made the right construct, the measurement model was examined for its fit. Given this, the model was assessed for convergent and discriminant validity.

Convergent validity was established using a calculation of the factor loading, average variance extracted (AVE) and composite reliability (CR). The factors which have standardized loadings exceeding 0.50, were retained [START_REF] Dibrell | Fueling Innovation through Information Technology in SMEs[END_REF]. The initial measurement model consisted of 19 factors (Tech1 to Tech19). After revising the measurement model by deleting Tech1, Tech10, Tech11 and Tech13, the AVE and CR were calculated. AVE larger than 0.5 is the threshold [START_REF] Mcnamara | It's the Thought that Counts: The Mediating Effects of Information Processing in Virtual Team Decision Making[END_REF]. CR was calculated by squaring the sum of loadings, followed by division with the sum of squared loadings, plus the sum of the measurement error [START_REF] Lin | A model to develop effective virtual teams[END_REF]. CR should be greater than 0.6 [START_REF] Huang | Knowledge sharing and group cohesiveness on performance: An empirical study of technology R&D teams in Taiwan[END_REF]. The measurement model had acceptable convergent validity since the calculated CR and AVE were 0.930 and 0.613, respectively. For discriminant validity, we used AMOS software using the Maximum Likelihood method (ML). The fitting indices were checked with their respective acceptance values (Table 4). We ran the AMOS for the model Ver1 (information technology construct with 15 factors), and found a non-significant chi-square value per degree of freedom (CMIN/DF = 7.232). Most of the remaining fit indices were not within the acceptable range. Thus, referring to the AMOS modification indices (MI), some of the factors which had the lowest factor loading or the same effect of remaining factor, were deleted. With this modification, the measurement model Ver2 had a significant chi-square per degrees of freedom (CMIN/DF = 4.767); other fit indices, RMSEA, RMR, and GFI were also in the acceptable range. Therefore, the best fitting model was the measurement model Ver2 (Figure 1) and it was used for further analysis.

DISCUSSION ON VERIFIED MODEL

The final measurement was carried out based on measurement model ver2 by classifying the factors into two groups according to their relevant factor loading with a threshold value of 0.83. Referring to the Table 1, the proper name for each group can be Web-based communications and data sharing, respectively. From Figure 2, each factor loading with a value above 0.62 is significant. Overall, the final measurement model produced good fit indices (CMIN/DF = 2.889, RMR = 0.04, GFI = 0.929, RFI = 0.929, NFI = 0.949, TLI = 0.952, CFI = 0.966 IFI = 0.964, RMSEA = 0.089).

While fitting the information technology construct of the measurement model, the factors Tech14 (access shared files anytime, from any computer), Tech15 (web database), Tech16 (provide instant collaboration), Tech17 (software as a service (eliminating the need to install and run the application on the own computer) and Tech19 (can be integrated/compatible with the other tools and systems) were dropped. Modification indices (MI) based on regression weights showed that Tech17, Tech 18 and Tech19 were highly correlated, and therefore one representative (Tech18) from this group appeared to be adequate. Tech14 to Tech16 were strongly correlated with Tech12, and hence, the remaining factors represent the deleted ones.

The results of the final measurement model of information technology construct in virtual R&D team for new product development, showed the share of two main contrasts, which were strongly correlated to each other: 1.

Web-based communications consists of online meetings on a required basis, web conferencing, seminars on the web, video conferencing, audio conferencing and online presentations.

2.

Web-based data sharing consists of shared work spaces, shared documents (off-line), access service from any computer (in network) and virtual research centre for product development.

According to Lee-Kelley and Sankey ( 2008), these two constructs belong to the second and third generation technology. Well-equipped virtual R&D team members with the appropriate technology make the teams more effective. Therefore, managers of NPD should provide the facilities and infrastructures for the virtual R&D teams to achieve higher levels of team effectiveness.

CONCLUSIONS

This research explores the 19 factors related to communication strategy using information technology in virtual team environment. However, the factors which mainly contribute to the information technology construct in virtual R&D teams' communication for new product development were unknown in the preceding literature. The findings of this study will contribute some knowledge in the literature and build a foundation for further understanding of the technology elements in virtual R&D teams for new product development. The measurement model shows ten factors that made the information technology constructs. These ten factors can be sorted by their factor loading, which reflects the factor's weight. Therefore, the software developer or the managers of NPD are able to provide a better platform for virtual teams by concentrating on the main factors. The second and third generation technologies (refer to definition of Lee-Kelley and Sankey ( 2008)) are now more suitable for developing new products through virtual R&D teams.

Future research is needed to examine the effects of each factor to perform the virtual R&D teams whereas the other constructs of virtual teams such as process and people are taken into account. A new SEM is needed to demonstrative the relationships between factors-construct and construct-construct, which are not yet investigated.

Figure 1

 1 Figure 1 Measurement model Ver2

Figure 2

 2 Figure 2 Final measurement model

Table 2

 2

	Summary of online survey data collection
	Numbers of e-mails sent to enterprises	3625
	Total responses (Clicked the online web page)	972
	Total responses / received questionnaire (%)	26.8
	Total completed	240
	Total completed / received questionnaire (%)	24.7

Table 3

 3 Summary of the final measures and reliabilities

Factor name Corrected Item-Total Correlation Cronbach's Alpha if Item Deleted

			Tech11	0.571	0.943
			Tech12	0.686	0.940
			Tech13	0.519	0.943
			Tech14	0.624	0.941
			Tech15	0.696	0.940
			Tech16	0.642	0.941
			Tech17	0.678	0.940
			Tech18	0.649	0.941
			Tech19	0.615	0.942
	Tech1	0.525	0.943
	Tech2	0.755	0.939
	Tech3	0.777	0.939
	Tech4	0.717	0.940
	Tech5	0.759	0.939
	Tech6	0.722	0.940
	Tech7	0.731	0.939
	Tech8	0.780	0.939
	Tech9	0.610	0.942
	Tech10	0.576	0.942

Table 4

 4 Fitting indices (adopted from[START_REF] Byrne | Structural equation modeling with AMOS: Basic concepts, applications, and programming[END_REF]

	Fit Indices	Desired Range
	χ2 /degrees of freedom	≤ 2.00
	(CMIN/DF)
	IFI (Incremental Fit Index)	≥ 0.90
	CFI (Comparative Fit Index)	Coefficient values range from zero to 1.00, with values close to .95 showing superior fit
	RMSEA (Root Mean Square	values less than .05 show good fit, and values as high as .08 represent reasonable fit,
	Error of Approximation)	from .08 to .10 show mediocre fit, and those greater than .10 show poor fit.
	Root mean square residual	≤ 0.08
	(RMR)
	Goodness-of-Fit Index (GFI)	≥ 0.90
	Normed Fit Index (NFI)	Coefficient values range from zero to 1.00, with values close to .95 showing superior fit
	Relative Fit Index (RFI)	Coefficient values range from zero to 1.00, with values close to .95 showing superior fit
	Tucker-Lewis Index (TLI)	Values ranging from zero to 1.00, with values close to .95 (for large samples) being
		indicative of good fit.