Student Member, IEEE Yuliya Tarabalka
email: yuliya.tarabalka@hyperinet.eu

Senior Member, IEEE Jocelyn Chanussot
email: jocelyn.chanussot@gipsa-lab.grenoble-inp.fr

Fellow, IEEE Jón Atli Benediktsson

Segmentation and Classification of Hyperspectral Images Using Minimum Spanning Forest Grown From Automatically Selected Markers

Keywords: Classification, hyperspectral images, marker selection, minimum spanning forest (MSF), segmentation

A new method for segmentation and classification of hyperspectral images is proposed. The method is based on the construction of a minimum spanning forest (MSF) from region markers. Markers are defined automatically from classification results. For this purpose, pixelwise classification is performed, and the most reliable classified pixels are chosen as markers. Each classification-derived marker is associated with a class label. Each tree in the MSF grown from a marker forms a region in the segmentation map. By assigning a class of each marker to all the pixels within the region grown from this marker, a spectral-spatial classification map is obtained. Furthermore, the classification map is refined using the results of a pixelwise classification and a majority voting within the spatially connected regions. Experimental results are presented for three hyperspectral airborne images. The use of different dissimilarity measures for the construction of the MSF is investigated. The proposed scheme improves classification accuracies, when compared to previously proposed classification techniques, and provides accurate segmentation and classification maps.

I. INTRODUCTION

I MAGE CLASSIFICATION, which can be defined as iden- tification of objects in a scene captured by a vision system, is one of the important tasks of a robotic system. On the one side, the procedure of accurate object identification is known to be more difficult for computers than for people [START_REF] Jain | Machine Vision[END_REF]. On the other side, recently developed image acquisition systems (for instance, radar, lidar, and hyperspectral imaging technologies) capture more data from the image scene than a human vision system. Therefore, efficient processing systems must be developed in order to use these data for accurate image classification.

Hyperspectral imagery records a detailed spectrum of light arriving at each pixel [START_REF] Chang | Hyperspectral Data Exploitation: Theory and Applications[END_REF]. Hyperspectral sensors measure the energy of the received light in tens or hundreds of narrow spectral bands (data channels) in each spatial position of the image (Fig. 1 shows the structure of a hyperspectral image). This rich information per pixel increases the capability to distinguish materials and objects and thus opens new perspectives for image classification. However, a large number of spectral channels, usually coupled with limited availability of reference data, 1present challenges to image analysis. While pixelwise classification techniques process each pixel independently without considering the information about spatial structures [START_REF] Landgrebe | Signal Theory Methods in Multispectral Remote Sensing[END_REF]- [START_REF] Camps-Valls | Kernel-based methods for hyperspectral image classification[END_REF], further improvement of classification results can be achieved by considering spatial dependences between pixels, i.e., by performing spectral-spatial classification [START_REF] Fauvel | Spectral and spatial methods for the classification of urban remote sensing data[END_REF]- [START_REF] Makrogiannis | A region dissimilarity relation that combines feature-space and spatial information for color image segmentation[END_REF].

Segmentation is an exhaustive partitioning of the input image into homogeneous regions [START_REF] Gonzalez | Digital Image Processing[END_REF]. Segmentation techniques are a powerful tool to define spatial dependences. In previous works, we have performed unsupervised segmentation of hyperspectral images in order to define spatial structures [START_REF] Tarabalka | Classification of hyperspectral data using support vector machines and adaptive neighborhoods[END_REF], [START_REF] Tarabalka | Segmentation and classification of hyperspectral data using watershed[END_REF], [START_REF] Tarabalka | Spectral-spatial classification of hyperspectral imagery based on partitional clustering techniques[END_REF]. Watershed, partitional clustering, and hierarchical segmentation techniques have been used for this purpose. Segmentation and pixelwise classification were performed independently, and then, the results were combined using a majority voting rule. Thus, every region from a segmentation map was considered as an adaptive homogeneous neighborhood for all the pixels within this region. The described technique led to a signification improvement of classification accuracies and provided more homogeneous (less noisy) classification maps when compared to classification techniques using local neighborhoods in order to include spatial information into a classifier.

However, unsupervised image segmentation is a challenging task. Segmentation aims at dividing an image into homogeneous regions, but the measure of homogeneity is image dependent [START_REF] Gonzalez | Digital Image Processing[END_REF]. Depending on this measure, the process can result in undersegmentation (several regions are detected as one) or oversegmentation (one region is detected as several ones) of the image. In previous works [START_REF] Tarabalka | Segmentation and classification of hyperspectral data using watershed[END_REF], [START_REF] Tarabalka | Spectral-spatial classification of hyperspectral imagery based on partitional clustering techniques[END_REF], we preferred oversegmentation to undersegmentation in order not to miss objects in the classification map. In this work, we aim to reduce oversegmentation and thus further improve segmentation and classification results. This can be achieved by using markers or region seeds [START_REF] Gonzalez | Digital Image Processing[END_REF], [START_REF] Soille | Morphological Image Analysis[END_REF]. In previous studies, a marker (an internal marker) was defined as a connected component belonging to the image and associated with an object of interest [START_REF] Gonzalez | Digital Image Processing[END_REF], [START_REF] Soille | Morphological Image Analysis[END_REF]- [START_REF] Noyel | Morphological segmentation of hyperspectral images[END_REF]. In our study, we define a marker as a set of image pixels (not necessarily connected; it can be composed of several spatially disjoint subsets of adjacent pixels) which is associated with one object in the image scene.

The problem of automatic marker selection has previously been discussed in the literature, mostly for gray-scale and color images. Markers are often defined by searching flat zones (i.e., connected components of pixels of constant gray-level value), zones of homogeneous texture, or image extrema [START_REF] Soille | Morphological Image Analysis[END_REF]. Gómez et al. [START_REF] Gómez | Image segmentation using automatic seeded region growing and instance-based learning[END_REF] applied histogram analysis to obtain a set of representative pixel values, and the markers were generated with all the image pixels with representative gray values. Jalba et al. [START_REF] Jalba | Automatic segmentation of diatom images for classification[END_REF] used connected operators filtering on the gradient image in order to select markers for a gray-scale diatom image. Noyel et al. [START_REF] Noyel | Morphological segmentation of hyperspectral images[END_REF], [START_REF] Noyel | Filtrage, Réduction de Dimension, Classification et Segmentation Morphologique Hyperspectrale[END_REF] performed classification of the hyperspectral image (using different techniques, such as Clara [START_REF] Kaufman | Finding Groups in Data. An Introduction to Cluster Analysis[END_REF] and linear discriminant analysis) and then filtered the classification maps class by class, using morphological operators, in order to select large spatial regions as markers. Furthermore, the authors proposed to use random balls (connected sets of pixels of randomly selected sizes) extracted from these large regions as markers. In the discussed studies [START_REF] Jalba | Automatic segmentation of diatom images for classification[END_REF], [START_REF] Noyel | Morphological segmentation of hyperspectral images[END_REF], [START_REF] Noyel | Filtrage, Réduction de Dimension, Classification et Segmentation Morphologique Hyperspectrale[END_REF], the objective was to segment specific structures (blood cells, diatoms, glue occlusions, and cancerous growth).

In our study, the objective is to mark (select a marker for) each significant spatial object in the image. Here, by significant, we mean an object of at least one-pixel size that belongs to one of the classes of interest. As remote sensing images contain small and complex structures, automatic selection of markers is an especially challenging task.

In this paper, a new scheme for marker-based segmentation and classification of hyperspectral images is proposed.

In particular, we propose to perform a probabilistic pixelwise classification first in order to choose the most reliable classified pixels as markers of spatial regions [START_REF] Tarabalka | Classification based marker selection for watershed transform of hyperspectral images[END_REF]. Furthermore, image pixels are grouped into a minimum spanning forest (MSF) [START_REF] Stawiaski | Mathematical morphology and graphs: Application to interactive medical image segmentation[END_REF], where each tree is rooted on a classification-derived marker. The decision to connect the pixel, which is not yet in the forest, to one of the trees in the forest is based on its similarity to one of the adjacent pixels already belonging to the forest. By assigning a class of the marker to all the pixels within the region grown from the considered marker, a spectralspatial classification map is obtained. Furthermore, the classification map is refined using the results of a pixelwise classification and a majority voting within the spatially connected regions [START_REF] Tarabalka | Spectral-spatial classification of hyperspectral imagery based on partitional clustering techniques[END_REF].

The construction of an MSF belongs to graph-based approaches for image segmentation [START_REF] Stawiaski | Mathematical morphology and graphs: Application to interactive medical image segmentation[END_REF]- [START_REF] Tao | Color image segmentation based on mean shift and normalized cuts[END_REF]. They introduce the Gestalt principles of perceptual grouping to the field of computer vision. The image is associated with a graph, the vertices of which correspond to the image entities (pixels or regions) and the edges correspond to relations between these entities. A weight associated with each edge indicates the (dis)similarity between two entities (pixels or regions). Morris et al. [START_REF] Morris | Graph theory for image analysis: An approach based on the shortest spanning tree[END_REF] have proposed to perform a graph-based image segmentation into R regions by constructing a shortest spanning tree on the image graph and then removing the R -1 edges with the highest weight. Furthermore, several graph-cut-based algorithms have been developed for image segmentation [START_REF] Shi | Normalized cuts and image segmentation[END_REF], [START_REF] Tao | Color image segmentation based on mean shift and normalized cuts[END_REF]. However, these methods perform unsupervised segmentation by splitting at each iteration one region into two subregions. This approach is fundamentally different from the work described in this paper. Several recent publications describe the use of an MSF rooted on markers for image segmentation [START_REF] Stawiaski | Mathematical morphology and graphs: Application to interactive medical image segmentation[END_REF], [START_REF] Allène | Some links between min-cuts, optimal spanning forests and watersheds[END_REF], [START_REF] Couprie | Power watersheds: A new image segmentation framework extending graph cuts, random walker and optimal spanning forest[END_REF]. However, the authors of these works do not investigate the problem of automatic marker selection. Their segmentation is based on markers provided by the user.

The proposed procedure of defining markers for each spatial object from probabilistic classification results and of building a spectral-spatial classification map for hyperspectral images by constructing an MSF rooted on classificationderived markers is a major contribution of this paper. Please note that, while, in previous studies, markers were used as seeds for image segmentation, in this paper, we introduce a new concept of the automatic marker-based spectral-spatial classification.

1) Markers are derived from probabilistic pixelwise classification results. 2) Each marker can be composed of several spatially disjoint subsets of adjacent pixels, and each marker has a class label. 3) By performing a region growing from the classificationderived markers, a spectral-spatial classification map is obtained.

Although the classification scheme proposed in this paper has been designed for hyperspectral data, the method is general and can successfully be applied for other types of data as well. Experimental results are demonstrated on hyperspectral airborne images recorded by the Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) over Northwestern Indiana's Indiana Pine site and over the region surrounding the volcano Hekla in Iceland, and the image acquired by the Reflective Optics System Imaging Spectrometer (ROSIS) over the University of Pavia in Italy.

The outline of this paper is as follows. In the next section, a classification scheme based on an MSF rooted on markers is presented. Experimental results are discussed in Section III. Finally, conclusions are drawn in Section IV.

II. SEGMENTATION AND CLASSIFICATION SCHEME

The flowchart of the proposed segmentation and classification method is shown in Fig. 2. On the input, a B-band hyperspectral image is given, which can be considered as a set of n pixel vectors X = {x j ∈ R B , j = 1, 2, . . . , n}. Classification consists in assigning each pixel to one of the K classes of interest. In the following, each step of the proposed procedure is described.

A. Pixelwise Classification

The first step consists in performing a probabilistic pixelwise classification of the hyperspectral image. We propose to use a support vector machine (SVM) classifier [START_REF] Vapnik | Statistical Learning Theory[END_REF] for this purpose. Other classifiers could be used. However, SVMs are extremely well suited to classify hyperspectral data [START_REF] Camps-Valls | Kernel-based methods for hyperspectral image classification[END_REF], [START_REF] Fauvel | Evaluation of kernels for multiclass classification of hyperspectral remote sensing data[END_REF], [START_REF] Licciardi | Decision fusion for the classification of hyperspectral data: Outcome of the 2008 GRS-S data fusion contest[END_REF]. We refer the reader to [START_REF] Camps-Valls | Kernel-based methods for hyperspectral image classification[END_REF] and [START_REF] Vapnik | Statistical Learning Theory[END_REF] for details on SVMs. The outputs of this step are the following:

1) classification map, containing class labels for each pixel; 2) probability map, containing probability estimates for each pixel to belong to the assigned class. Two techniques for computing probability estimates for multiclass classification by pairwise coupling are described in [START_REF] Wu | Probability estimates for multi-class classification by pairwise coupling[END_REF]. We propose to use one of these methods, which is implemented in the LIBSVM library [START_REF] Chang | LIBSVM: A Library for Support Vector Machines[END_REF]. The objective is to estimate, for each pixel x, the probabilities to belong to each class of interest p = {p k = p (y = k|x), k = 1, . . . , K} .

(

For this purpose, first, pairwise class probabilities r ij ≈ p(y = i|y = i or j, x) are estimated using an improved implementation [START_REF] Lin | A note on Platt's probabilistic outputs for support vector machines[END_REF] of [START_REF] Platt | Probabilistic outputs for support vector machines and comparison to regularized likelihood methods[END_REF]

r ij ≈ 1 1 + e A f +B (2)
where A and B are estimated by minimizing the negative loglikelihood function using known training data and decision values f . Furthermore, the probabilities in (1) are computed by solving the following optimization problem:

min p K i=1 j:j =i (r ji p i -r ij p j ) 2 subject to K i=1 p i = 1, p i ≥ 0 ∀i. ( 3
)
This problem has a unique solution and can be solved by a simple linear system, as described in [START_REF] Wu | Probability estimates for multi-class classification by pairwise coupling[END_REF]. Finally, a probability map is constructed by assigning to each pixel the maximum probability estimate max(p k ), k = 1, . . . , K.

B. Selection of the Most Reliable Classified Pixels

The aim of this step is to choose the most reliable classified pixels in order to define suitable markers. We propose to use probability estimates obtained as a result of the pixelwise classification for this purpose in order to keep the most reliable classified pixels as markers. A simple way of marker selection consists in thresholding the probability map. In other words, if the probability of the considered pixel belonging to the assigned class k is higher than a given threshold, this pixel is selected to join the markers. In the resulting map of markers, each marker pixel is associated with the class defined by the pixelwise classifier. The marker pixels form connected components in the map of markers so that each connected component represents one marker. The main advantage of this technique of marker selection is its simplicity. However, this method has the following disadvantage: Each marker leads to one region in the segmentation map. Therefore, we need as many markers as the desired number of regions. However, if classes k i and k j are spectrally similar, pixels belonging to one of those classes have a quasi-equal probability to belong to each of them. From here, these classified pixels are not reliable. Therefore, we risk to lose the regions corresponding to either class k i or k j in the final segmentation map. This leads to undersegmentation, which is highly undesired.

To mitigate this problem, we propose the following method of marker selection [see the flowchart in Fig. 3(a)].

1) Perform a connected-component labeling of the pixelwise classification map. For this purpose, a classical connected-component algorithm using the union-find data structure can be used [START_REF] Shapiro | Computer Vision[END_REF].

2) Analyze each connected region as follows.

• If a region is large enough, it should contain a marker, which is determined as P % of the pixels within the connected component with the highest probability estimates. • If a region is small, it should lead to a marker only if it is very reliable; a potential marker is formed by pixels with probability estimates higher than a defined threshold.

The proposed procedure is deducted from the following analysis: Based on the results of our previous studies [START_REF] Tarabalka | Classification of hyperspectral data using support vector machines and adaptive neighborhoods[END_REF], [START_REF] Tarabalka | Segmentation and classification of hyperspectral data using watershed[END_REF], [START_REF] Tarabalka | Spectral-spatial classification of hyperspectral imagery based on partitional clustering techniques[END_REF], it is common that almost no undersegmentation is present in a pixelwise classification map. Therefore, each connected spatial region from the classification map is analyzed if it corresponds most probably to the spatial structure or if it is rather a classification noise [see the illustrative example in Fig. 3(b)]. If the size of the component is large enough to consider it as a relevant region, the most reliable pixels within this region are selected as its marker. If a component contains only a few pixels, it is investigated if these pixels were classified to a particular class with a high probability. If this is the case, the considered connected component represents a small spatial structure. Thus, a marker associated with this region should be defined. Otherwise, the component is the consequence of classification noise, and we tend to eliminate it. Therefore, no marker within this component is selected. When performing labeling of connected components for a pixelwise classification map, we propose to use an eight-neighborhood connectivity.

For the proposed marker selection procedure, the following parameters must be chosen.

1) A parameter M defining if a region is considered as being large or small. We propose to use a number of pixels in the region (i.e., an area of the region) as a criterion of the region size. The threshold of the number of pixels defining if the region is large depends on the resolution of the image and typical sizes of the objects of interest.

For instance, if the image of the volcano is considered (experimental results on the volcano image are illustrated in Section III), where the goal is to classify lavas of different eruption periods, it is known that the lava of different formations consists of large homogeneous regions. Therefore, it can be assumed that the regions representing structures (lavas) in the image scene have a size of at least 10 km 2 . Thus, for an airborne 20-m-resolution image, the threshold of M = 20 pixels for dividing the regions in the groups of large/small ones can be chosen. 2) A parameter P , defining the percentage of pixels within the large region to be used as markers, depends on the previous parameter. Since a marker for the large region must be composed at least of one pixel, the following condition must be fulfilled: P ≥ 100%/M . 3) The last parameter S, which is a threshold of probability estimates defining potential markers for a small region, depends on the probability of the presence of small structures in the image (which also depends on the image resolution and the classes of interest) and the importance of the potential small structures (i.e., what is the cost of losing the small structures in the classification map). For instance, if we are interested in determining regions of different lava formations in the volcano image, the small objects in the image may have no importance for us, and a high value of S can be chosen. However, if the classification aims at determining regions of sick/damaged plants in the field, it may be important not to lose any small region of the damaged species. In this case, the threshold S must be relaxed.

In Section III-D, the dependence of the classification accuracies from the chosen parameters for the marker selection is investigated experimentally. As a conclusion, each connected set of pixels with the same class in the classification map provides either one or zero marker. One should stress that a marker is not necessarily a connected set of pixels: It can spatially be split into several subsets [see Fig. 3(b)].

C. Construction of an MSF

The previous two steps result in a map of markers defining regions of interest in the image. The next step consists in the grouping of all the image pixels into an MSF [START_REF] Stawiaski | Mathematical morphology and graphs: Application to interactive medical image segmentation[END_REF], where each tree is rooted on a classification-derived marker.

For this purpose, each pixel is considered as a vertex v ∈ V of an undirected graph G = (V, E, W ), where V and E are the sets of vertices and edges, respectively, and W is a mapping of the set of edges E into R + . Each edge e i,j ∈ E of this graph connects a couple of vertices i and j corresponding to the neighboring pixels (in the following, we simply call vertices as pixels). Furthermore, a weight w i,j is assigned to each edge e i,j , which indicates the degree of dissimilarity between two pixels connected by this edge. Different dissimilarity measures can be used for computing weights of edges, such as vector norms, Spectral Angle Mapper (SAM), and spectral information divergence (SID) [START_REF] Van Der Meer | The effectiveness of spectral similarity measures for the analysis of hyperspectral imagery[END_REF].

The L1 vector norm between two pixel vectors x i = (x i1 , . . . , x iB ) T and x j = (x j1 , . . . , x jB ) T is given as

L1(x i , x j ) = B b=1 |x ib -x jb |. ( 4
)
The SAM distance between x i and x j determines the spectral similarity between two vectors by computing the angle between them. It is defined as

SAM (x i , x j ) = arccos ⎛ ⎜ ⎜ ⎜ ⎝ B b=1 x ib x jb B b=1 x 2 ib 1/2 B b=1 x 2 jb 1/2 ⎞ ⎟ ⎟ ⎟ ⎠ . (5)
The SID measure [START_REF] Chang | An information theoretic-based approach to spectral variability, similarity and discriminability for hyperspectral image analysis[END_REF] computes the discrepancy of probabilistic behaviors between the spectral signatures of two pixels. It is defined as

SID(x i , x j )= B b=1 q b (x i ) log q b (x i ) q b (x j ) +q b (x j ) log q b (x j ) q b (x i ) (6)
where

q b (x i ) = x ib B l=1 x il . ( 7
)
Furthermore, more complex dissimilarity measures for image segmentation have been proposed in [START_REF] Makrogiannis | A region dissimilarity relation that combines feature-space and spatial information for color image segmentation[END_REF] and [START_REF] Corsini | A fuzzy relational clustering algorithm based on a dissimilarity measure extracted from data[END_REF].

Given a connected graph

G = (V, E), a spanning tree T = (V, E T ) of G is a connected graph without cycles such that E T ⊂ E. A spanning forest F = (V, E F ) of G is a noncon- nected graph without cycles such that E F ⊂ E.
Given a graph G = (V, E, W ), the minimum spanning tree is defined as a spanning tree T * = (V, E T * ) of G such that the sum of the edge weights of T * is minimal

T * ∈ arg min T ∈ST ⎧ ⎨ ⎩ e i,j ∈E T w i,j ⎫ ⎬ ⎭ ( 8
)
where ST is a set of all spanning trees of G.

Given a graph G = (V, E, W ), the MSF rooted on a set of m distinct vertices {t 1 , . . . , t m } consists in finding a spanning forest F * = (V, E F * ) of G, such that each distinct tree of F * is grown from one root t i , and the sum of the edge weights of F * is minimal [START_REF] Stawiaski | Mathematical morphology and graphs: Application to interactive medical image segmentation[END_REF] F * ∈ arg min

F ∈SF ⎧ ⎨ ⎩ e i,j ∈E F w i,j ⎫ ⎬ ⎭ ( 9
)
where SF is a set of all spanning forests of G rooted on {t 1 , . . . , t m }.

In order to obtain the MSF rooted on markers, m additional vertices t i , i = 1, . . . , m, are introduced. Each extra vertex t i is connected by the edge with a null weight to the pixels representing a marker i. Furthermore, an additional root vertex r is added and is connected by the null-weight edges to the vertices t i . The minimum spanning tree of the constructed graph induces an MSF in G, where each tree is grown on a vertex t i ; the MSF is obtained after removing the vertex r. An example of the construction of the MSF rooted on markers is shown in Fig. 4. Prim's algorithm can be used for building the MSF (see Algorithm 1) [START_REF] Prim | Shortest connection networks and some generalizations[END_REF]. The efficient implementation of the algorithm using a binary min heap (for the implementation of a min-priority queue) is possible [START_REF] Cormen | Introduction to Algorithms[END_REF]; the resulting time complexity of the algorithm is O(|E| log |V |).

Algorithm 1 Prim's Algorithm

Require: Connected graph G = (V, E, W ) Ensure: Tree T * = (V * , E * , W * ) V * = {v}, v is an arbitrary vertex from V whileV * = V do Choose edge e i,j ∈ E with minimal weight such that i ∈ V * and j / ∈ V * V * = V * ∪ {j} E * = E * ∪ {e i,j } end while
Each tree in the MSF forms a region in the segmentation map (by mapping the resulting graph onto an image). Finally, a spectral-spatial classification map is obtained by assigning the class of each marker to all the pixels grown from this marker.

Thus, the proposed procedure of the construction of an MSF from region markers is a region growing method, which consists of the following steps: First, seed regions are chosen to belong to the segmentation and classification maps. Then, at each iteration, a new pixel i is added to the segmentation and classification maps so that the dissimilarity criterion between this pixel and one of the pixels j already belonging to the segmentation/classification map is minimal. When including the new pixel to the classification map, a class of the pixel j is assigned to the pixel i.

D. Majority Voting Within Connected Components

Although the most reliable classified pixels are selected as markers, it may happen that a marker is classified to the wrong class. In this case, all the pixels within the region grown from this marker risk to be wrongly classified. In order to make the proposed classification scheme more robust, we propose to postprocess the classification map by applying a simple majority voting technique which has shown good performances for spectral-spatial classification [START_REF] Tarabalka | Segmentation and classification of hyperspectral data using watershed[END_REF], [START_REF] Tarabalka | Spectral-spatial classification of hyperspectral imagery based on partitional clustering techniques[END_REF], [START_REF] Widayati | Application of combined pixel-based and spatial-based approaches for improved mixed vegetation classification using IKONOS[END_REF]. For this purpose, connected-component labeling is applied on the obtained spectral-spatial classification map (using a four-neighborhood connectivity). Furthermore, for every connected component (region), all the pixels are assigned to the most frequent class when analyzing a pixelwise classification map within this region.

Note that an eight-neighborhood connectivity was used for the construction of an MSF, whereas a four-neighborhood connectivity was used for the majority voting. The use of the eightneighborhood connectivity in the first case allows obtaining a more accurate (refined) segmentation map, without rough borders. Since an MSF is built from the set of markers, the number of regions does not depend on the chosen connectivity. When performing the last majority voting step, the use of the four-neighborhood connectivity results in a larger or the same number of connected components as the use of the eightneighborhood connectivity. Therefore, the possible undersegmentation can be corrected in this step. One region from a segmentation map can be split into two connected regions when using the four-neighborhood connectivity. Furthermore, these two regions can be assigned to two different classes by the majority voting procedure.

III. EXPERIMENTAL RESULTS

Three different data sets were used for the experiments, with different contexts (agricultural, volcano, and urban areas) and acquired by different sensors (AVIRIS and ROSIS airborne imaging spectrometers). These data sets and the corresponding results are presented in the next three sections.

A. Classification of the Indiana Image

The Indiana image is of a vegetation area that was recorded by the AVIRIS sensor over the Indian Pine test site in Northwestern Indiana. The image has spatial dimensions of 145 by 145 pixels and a spatial resolution of 20 m/pixel. Twenty water absorption bands have been removed [START_REF] Tadjudin | Covariance estimation with limited training samples[END_REF], and a 200-band image was used for the experiments. Sixteen classes of interest are considered, which are detailed in Table I, with a number of samples for each class in the reference data. A three-band false color image and the reference data are shown in Fig. 5. We have chosen randomly 50 samples for each class from the reference data as training samples, except for classes alfalfa, grass/pasture-mowed, and oats. These classes contain a small number of samples in the reference data. Therefore, only 15 samples for each of these classes were chosen randomly to be used as training samples. The remaining samples comprised the test set.

A pixelwise classification on the 200-band Indiana image was performed, using the multiclass one versus one SVM classifier with the Gaussian radial basis function (RBF) kernel. The optimal parameters C and γ were chosen by fivefold cross validation: C = 128 and γ = 2 -6 . Global and class-specific accuracies are presented in Table I. Fig. 5 shows the obtained classification and probability maps.

Furthermore, a map of markers was created. For this purpose, labeling of connected components on the pixelwise classification map was performed, using the eight-neighborhood connectivity. For each connected component, the following are observed.

1) If it contained more than M = 20 pixels, P = 5% of its pixels with the highest probability estimates were selected as a marker for this component. 2) Otherwise, if a connected component contained pixels with the corresponding probability estimates not lower than the threshold S, these pixels were used as a marker.

In order to define a threshold S, the probability estimates for the whole image were sorted, and S was chosen equal to the lowest probability within the highest T = 2% of all probability estimates. The parameters for marker selection were chosen based on the following analysis: It is known that the image consists of the fields of different types of crops, i.e., large homogeneous regions. In the reference data, the class oats is represented by the smallest field of a size of 20 pixels. Therefore, the classification procedure must be able to recognize the 20-pixel regions. We select M = 20. The parameter P is computed as P = 100%/M = 5%. This means that, for a region of 20 pixels, a one-pixel marker is selected. The last parameter T is chosen to be low since we know that the image does not contain small spatial structures. The correctness and robustness of this theoretical deduction of parameters are proved in Section III-D.

From 2250 connected components in the classification map, 107 markers were selected. Of the marker pixels presented in the reference data, 95% are correctly classified. In the next step, the image pixels were grouped into the MSF, built from the selected markers. We have investigated the use of different dissimilarity measures: the L1 vector norm,2 the SAM, and the SID measures [START_REF] Van Der Meer | The effectiveness of spectral similarity measures for the analysis of hyperspectral imagery[END_REF]. When the class of each marker was assigned to all the pixels of the corresponding tree, the spectralspatial classification maps were obtained. Finally, the obtained classification maps were combined with the pixelwise classifi-cation map, using the majority voting technique, as described in Section II-D.

Table I summarizes the accuracies of the pixelwise SVM and the proposed classification method (before and after the majority voting step). In order to compare performances of the proposed technique with the previously proposed methods, we have included results of a classification using majority vote within the adaptive neighborhoods defined by watershed segmentation (W H + MV ) [START_REF] Tarabalka | Segmentation and classification of hyperspectral data using watershed[END_REF], as well as classification results obtained by performing watershed segmentation3 from the same set of markers (M -W H) [START_REF] Tarabalka | Classification based marker selection for watershed transform of hyperspectral images[END_REF]; these are recently proposed advanced techniques for spectral-spatial classification of hyperspectral images.

First of all, almost no oversegmentation is present in the obtained segmentation map (since one marker led to one region, a segmentation map contains 107 regions). As can be seen from Table I, both the global and most of the class-specific accuracies are improved by the proposed method. The majority voting step additionally improves most of the accuracies (except for the class soybeans-no till). The best global accuracies are achieved by the proposed method when using the SAM dissimilarity measure and including a majority voting step [the corresponding classification map is shown in Fig. 5(f)]. In this case, the overall accuracy is improved by 13.6 percentage points and the average accuracy by 8.3 percentage points when compared to the pixelwise classification. However, the use of other dissimilarity measures also leads to high accuracies; the highest accuracies for 7 of the 16 classes are achieved when using each of the proposed measures.

Furthermore, McNemar's test was performed in order to evaluate the statistical significance of differences in classification accuracies between the most accurate classification map (SAM + MV ) and other classification maps [START_REF] Foody | Thematic map comparison: Evaluating the statistical significance of differences in classification accuracy[END_REF]. According to the results of the test, the SAM + MV classification accuracies are significantly different (here and in the following, we use 1% level of significance when reporting results of McNemar's test) from the accuracies of any other classification method applied for the Indiana image. The improvement of the accuracies after the majority voting step is also significant when using any of the applied dissimilarity measures.

B. Classification of the Hekla Image

The Hekla image was acquired by the AVIRIS sensor over the region surrounding the central volcano Hekla in Iceland [START_REF] Benediktsson | Classification of multisource and hyperspectral data based on decision fusion[END_REF]. The AVIRIS sensor operates in the wavelength range from 0.4 to 2.4 μm and utilizes four spectrometers collecting 224 data channels. During the data collection, spectrometer 4 was not working properly. The 64 data channels recorded by this spectrometer were deleted from the data, along with the first channels for the other three spectrometers (those channels were blank). Therefore, the 157 remaining data channels were used for the experiments. The considered image has spatial dimensions of 560 by 600 pixels. Twelve land cover classes of interest are considered, which are detailed in Table II, with a number of labeled samples for each class. Fig. 6 shows a three-band false color image and the reference data. Fifty samples for each class were randomly chosen from the reference data as training samples, and the rest of the samples were used as the test set.

A multiclass one versus one SVM classification on the original image was performed using the Gaussian RBF kernel. The parameters C = 100 and γ = 0.1 were determined by fivefold cross validation. Table II gives the classification accuracies, and the classification map is shown in Fig. 6(c).

In the next step, a map of markers was created, with the same parameters as for the Indiana image. Furthermore, segmentation and classification of the image were performed by constructing an MSF based on the selected markers. The obtained classification maps were further combined with the pixelwise classification map using the majority voting technique.

Table II gives the accuracies of the proposed classification method. As can be seen, both the global and most of the class-specific accuracies are improved when compared to the pixelwise classification. The majority voting step additionally improves the accuracies. As for the Indiana image, the best global accuracies are achieved when performing the proposed classification with the SAM dissimilarity measure and the majority voting step. Fig. 6(d) shows the corresponding classification map, which is much less noisy than a pixelwise classification map. In this case, the overall accuracy is improved by 10.4 percentage points and the average accuracy by 9.0 percentage points when compared to the pixelwise classification. According to the results of McNemar's test, all the obtained classification maps are significantly different.

C. Classification of the University of Pavia Image

The proposed scheme was also tested on the University of Pavia image of an urban area, acquired by the ROSIS-03 optical sensor. The image is 610 by 340 pixels, with a spatial resolution of 1.3 m/pixel and 103 spectral channels. The reference data contain nine classes of interest. More information about the image, with the number of test and training samples for each class, can be found in [START_REF] Tarabalka | Spectral-spatial classification of hyperspectral imagery based on partitional clustering techniques[END_REF].

Segmentation and classification of the University of Pavia image were performed using the proposed scheme. The parameters for an SVM classification were chosen by fivefold cross validation: C = 128 and γ = 0.125. Marker selection was performed with the same parameters as for the two previous data sets. Table III summarizes the classification accuracies for a pixelwise and spectral-spatial classification. In order to compare the performances of the proposed method with the previously proposed techniques, we have included in the table the accuracies of the classification of the University of Pavia image using an SVM, principal components, and extended morphological profiles; results are taken from [START_REF] Plaza | Recent advances in techniques for hyperspectral image processing[END_REF]. This method has been recently proposed by Benediktsson et al. [START_REF] Benediktsson | Classification of hyperspectral data from urban areas based on extended morphological profiles[END_REF] and is considered as one of the most advanced methods for spectralspatial classification of a multiband datum. Furthermore, the results of the spectral-spatial classification using majority voting within adaptive neighborhoods defined by spatial-based segmentation techniques are included. The following segmentation techniques are used for this purpose (leading to the best classification results among all the spatial-based methods): watershed segmentation (W H + MV ) [START_REF] Tarabalka | Segmentation and classification of hyperspectral data using watershed[END_REF] and recursive hierarchical segmentation (RHSEG), with the possibility of merging only adjacent regions (RHSEG0 + MV ) [START_REF] Tarabalka | Classification of hyperspectral data using support vector machines and adaptive neighborhoods[END_REF].

As can be seen from Table III, both the global and most of the class-specific accuracies are improved by the proposed method. The majority voting step additionally improves most of the accuracies. The best global accuracies are achieved by the proposed method when using the L1 vector norm for measuring dissimilarity between pixels. The corresponding classification map is significantly more accurate than any other obtained classification map, according to the results of McNemar's test. In this case, the overall accuracy is improved by 10.1 percentage points and the average accuracy by 6.5 percentage points when compared to the pixelwise classification. Those accuracies are higher than the ones obtained by the previously proposed techniques given for comparison. The use of the other two measures also led to the high classification accuracies for most of the classes. For instance, the use of the SAM measure led to the best accuracy of classification for the class asphalt when compared to all the previous results found in the literature. However, the global accuracies are not as high as when using the L1 vector norm mainly because of the low accuracy for the class shadows. The SAM distance is actually designed with the purpose that the poorly illuminated and more brightly illuminated pixels from the same class would be mapped to the same spectral angle despite the difference in illumination. It can be an explanation of the fact why the SAM distance led to the assimilation of the shadowed regions with the neighboring structures.

D. Assessment of the Robustness of the Parameter Settings

In Section II-B, the procedure of the choice of parameters for the marker selection procedure was explained. In this section, the dependence of the classification accuracies from the chosen parameters is investigated experimentally for the Indiana and the Hekla images.

First, the choice of the parameter P is analyzed. For this purpose, the other two parameters were fixed as M = 20 and T = 2. Classification using the proposed scheme was performed, with the parameter P varying from 5 to 100. The L1 vector norm and the SAM dissimilarity measures were used. Fig. 7 shows the obtained overall [Fig. 7(a) and (d)] and average [Fig. 7(g) and (j)] classification accuracies for both data sets. As can be seen from the figures, for any value of P , the accuracies are significantly improved when compared to the pixelwise classification. When the value of P is low (a few marker pixels are chosen), the construction of the MSF from the markers gives less accurate classification maps than when it is high. However, the postprocessing majority voting step improves the accuracies significantly. Thus, the complete classification procedure gives the best performances for a low value of P . Then, with the increase of P , the classification accuracies converge to a constant value, for both dissimilarity measures, and the majority step does not additionally increase the accuracies. Results are coherent for both images. As a conclusion, this parameter has no significant influence on the classification accuracies. When a few marker pixels are chosen (for low values of P ), the construction of an MSF using the SAM distance gives better segmentation results (provides more accurate regions) than a pixelwise classification. Therefore, after the additional processing of the corresponding classification maps by majority voting, the best classification results are achieved.

The choice of the parameter T is investigated, by fixing parameters M = 20 and P = 2, varying T from 2 to 100, and performing classification for both data sets. The overall and average classification accuracies are shown in Fig. 7 (second column). As can be seen, the results are coherent for both dissimilarity measures and both data sets. The highest classification accuracies are achieved for the low values of T . These results are coherent with the theoretical analysis given in the previous sections. Since the Indiana and the Hekla images contain large spatial structures (of crop fields and lava formations, respectively), markers for small regions must be selected only in the case if the probability of their correct classification is very high. Therefore, with the increase of T , the probability of selecting a marker for a misclassified region increases, and the classification accuracies decrease. The majority voting step becomes more important for higher values of T , and for the Hekla image, the accuracies for the complete proposed procedure (including the majority voting step) remain almost unchanged, independently of the parameter T .

Furthermore, the choice of the parameter M is investigated, with the other parameters being fixed (P = 20 and T = 5). Fig. 7 (third column) shows the overall and average accuracies of classification when varying the parameter M from 10 to 100. For the Hekla image, the accuracies are slightly lower for M = 10, when compared to other values of this parameter, for which the accuracies remain almost unchanged. This is due to the fact that the image contains mostly large regions of lava fields. Therefore, for any value of M higher than 20, the classification procedure shows a good performance. For the Indiana image, with the increase of the parameter M up to 50, the overall accuracy slightly increases. However, the average accuracy reaches its maximum for M = 20 and then significantly decreases. These results confirm the theoretical analysis: The smallest crop field in the image scene has a size of 20 pixels. When a high value of M for identifying significant regions is chosen, small crop fields risk to be assimilated with the neighboring structures. If this happens, majority voting cannot reconstitute these regions, and they disappear from the final classification map.

In conclusion, the experimental analysis of the parameter choice for the marker selection procedure has confirmed that, by using some a priori information for the image, pa-rameters leading to good classification performances can be deducted.

IV. CONCLUSION

A large number of spectral channels in a hyperspectral image increase the potential of discriminating physical materials and structures in a scene. However, it presents challenges to image analysis because of the huge volume of data that the hyperspectral image usually consists of. Although pixelwise classification techniques have given high classification accuracies when dealing with hyperspectral data, the incorporation of the spatial information into the classifier is needed for further improvement of the classification accuracies.

In this paper, a new spectral-spatial classification scheme for hyperspectral images has been proposed. The method is based on the construction of an MSF, rooted on the markers selected by using pixelwise classification results. Experimental results, presented on the three data sets, have shown that the proposed method improves the classification accuracies, when compared to previously proposed classification schemes, and provides accurate segmentation and classification maps.

Different distances have been investigated for measuring the dissimilarity between pixels when constructing an MSF. It is shown that, in most of the cases, the SAM distance gives the best performances. However, this distance does not discriminate some particular classes from urban areas, such as shadows, and assimilate the pixels belonging to these classes with the neighboring structures.

In conclusion, the proposed classification methodology succeeded in taking advantage of the spatial and the spectral information simultaneously. The method performs well for images representing different scenes: those containing large spatial structures with spectrally confusing classes and those containing small and complex structures. Furthermore, its efficient implementation is possible.

Fig. 1 .

 1 Fig. 1. Structure of a hyperspectral image.

Fig. 2 .

 2 Fig. 2. Flowchart of the proposed segmentation and classification scheme.

Fig. 3 .

 3 Fig. 3. (a) Flowchart of the proposed marker selection procedure. (b) Illustrative example of the marker selection.

Fig. 4 .

 4 Fig. 4. Example of the construction of an MSF rooted on markers. (a) Original image graph G, where colored vertices represent markers 1 and 2; nonmarker pixels are denoted by "0." (b) Addition of extra vertices t 1 , t 2 , and r to the graph. (c) Minimum spanning tree of the graph presented in (b); after removing the vertex r, an MSF is obtained, where each tree grown from the vertex t i forms a region in the segmentation map.

Fig. 5 .

 5 Fig. 5. Indiana image. (a) Three-band color composite (837, 636, and 537 nm). (b) Reference data: . (c) Pixelwise classification map. (d) Probability map (probability estimates for each pixel to belong to the assigned class). (e) Scale of colors to represent the probability estimates in a probability map, from 0% probability at the bottom to 100% probability at the top. (f) Classification map obtained by the proposed scheme, using the SAM dissimilarity measure and including a majority voting step.

Fig. 6 .

 6 Fig. 6. Hekla image. (a) Three-band color composite (1125, 636, and 567 nm). (b) Reference data: , and snow (white). (c) Pixelwise classification map. (d) Classification map obtained by the proposed scheme, using the SAM dissimilarity measure and including a majority voting step.

Fig. 7 .

 7 Fig. 7. Assessment of the robustness of the parameter settings. (a)-(f) Overall and (g)-(l) average classification accuracies as functions of parameters for the marker selection procedure [(a), (d), (g), (j)] P (M = 20, T = 2), [(b), (e), (h), (k)] T (M = 20, P = 20), and [(c), (f), (i), (l)] M (P = 20, T = 5), for the [(a)-(c), (g)-(i)] Indiana and [(d)-(f), (j)-(l)] Hekla images.

TABLE I INFORMATION

 I CLASSES, NUMBER OF LABELED SAMPLES (NO. OF SAMP.), AND CLASSIFICATION ACCURACIES IN PERCENTAGE FOR THE INDIANA IMAGE: OVERALL ACCURACY (OA), AVERAGE ACCURACY (AA), KAPPA COEFFICIENT (κ), AND CLASS-SPECIFIC ACCURACIES; "MV" MEANS INCLUDING A MAJORITY VOTING STEP

TABLE II INFORMATION

 II CLASSES, NUMBER OF LABELED SAMPLES (NO. OF SAMP.), AND CLASSIFICATION ACCURACIES IN PERCENTAGE FOR THE HEKLA IMAGE: OVERALL ACCURACY (OA), AVERAGE ACCURACY (AA), KAPPA COEFFICIENT (κ), AND CLASS-SPECIFIC ACCURACIES; "MV" MEANS INCLUDING A MAJORITY VOTING STEP

TABLE III CLASSIFICATION

 III ACCURACIES IN PERCENTAGE FOR THE UNIVERSITY

OF PAVIA IMAGE: OVERALL ACCURACY (OA), AVERAGE ACCURACY (AA), KAPPA COEFFICIENT (κ), AND CLASS-SPECIFIC ACCURACIES; "MV" MEANS INCLUDING A MAJORITY VOTING STEP

By reference data, we mean manually labeled pixels which are used for training classifiers followed by assessment of classification accuracies.

We have also considered the L2 vector norm as a dissimilarity measure for the construction of the MSF. The corresponding classification accuracies are not given in this paper because of space limitations. These accuracies are mostly nonsignificantly lower than the ones obtained when using the L1 norm.

In[START_REF] Tarabalka | Classification based marker selection for watershed transform of hyperspectral images[END_REF], watershed segmentation is computed using the classical paradigm of the morphological image segmentation[START_REF] Noyel | Filtrage, Réduction de Dimension, Classification et Segmentation Morphologique Hyperspectrale[END_REF]: A gradient of the image is computed; then, a minima imposition technique is applied, followed by the watershed algorithm based on flooding simulations.

ACKNOWLEDGMENT

The authors would like to thank P. Gamba and D. Landgrebe for providing the hyperspectral data.

This work was supported in part by the Marie Curie Research Training Network "Hyper-I-Net." This paper was recommended by Associate Editor D. Goldgof. Y. Tarabalka is with the Grenoble she was a Researcher with the Norwegian Defence Research Establishment, Norway. Her current research work is funded by the "Hyper-I-Net" Marie Curie Research Training Network. Her research interests are in the areas of image processing, pattern recognition, hyperspectral imaging, and development of efficient algorithms.


P E Pakhoova

A V Timoshenko

I N Guterman

G P Zakarchenko

B Petin

Dkhil

I N Leontyev

V E Guterman

E B Pakhomova

P E Timoshenko

A V Guterman

I N Zakharchenko

G P Petin

B Dkhil

electrocatalysts for oxygen reduction

Keywords: platinum alloy, grain size distribution, electrocatalysis, oxygen reduction reaction (ORR), X-ray diffraction (XRD)

XRD and electrochemical investigation of particle size effects in platinum-cobalt cathode electrocatalysts for oxygen reduction

I.N.

Introduction

Proton-exchange membrane fuel cells (PEMFC) have received considerable attention as promising devices for portable and transport applications, due to their high energy density, relatively low operating temperature and minimal corrosion problems. Yet, the commercial viability of the PEMFC's has been still hindered by several problems including the high cost, insufficient stability against degradation, and agglomeration of the Pt nanoparticles. The latter two phenomena are especially intrinsic to the oxygen electrode. They reduce the catalyst's effective surface and hence the activity. The search for more active, cost-effective, and corrosion stable electrocatalysts for the oxygen reduction reaction (ORR) is therefore a priority in fuel cell catalysis research. The most popular strategy toward more active and stable ORR electrocatalysts has been alloying pure Pt with transition metals, such as Co, Ni, etc. It has been suggested [START_REF] Thompsett | Catalysts for the Proton Exchange Membrane Fuel Cell[END_REF][START_REF] Xiong | [END_REF][3][4][5][6] that the activating effect of the alloying elements for the ORR could be associated with (i) modified composition of the surface oxides and improved corrosion resistance of the alloy; (ii) formation of a new electronic structure of the metal; (iii) shortening of the Pt-Pt distance which favors adsorption of oxygen molecules, (iv) formation of a thin Pt shell at the surface of the nanoparticles due to selective dissolution of a second alloying element, and (v) some other effects. One or another mechanism may prevail depending on specific alloy composition and conditions of the reaction process. The positive effect of the second alloying component on the catalyst's aggregation stability seems to result from strengthening of the nanoparticle to carbon carrier adhesion and/or improved corrosion resistance of the carbon surface regions adjacent to the metal nanoparticles [START_REF] Thompsett | Catalysts for the Proton Exchange Membrane Fuel Cell[END_REF]7] . Unfortunately, the second component in such alloys is not as stable as Pt, and the alloy composition may alter owing to corrosion during operation of an electrocatalyst [3,5] . The corrosion effect on the composition and structure of Pt-Me/C catalysts as well as the dependence of the catalyst's stability on their original composition and structure are therefore subjects of great importance.

In reality, carbon carries the nanoparticles of different size, and its metal coverage itself is variable and not always uniform [START_REF] Thompsett | Catalysts for the Proton Exchange Membrane Fuel Cell[END_REF]4,8,9] . Optimum size range of the metal nanoparticles is altogether uncertain and is apparently dependent on a particular electrochemical system, conditions of the reaction process, and the alloy composition. The above considerations demonstrate that control over composition and size of the metal alloy nanoparticles is a real challenge both in science and technology.

The purposes of this work are: (i) to study the influence of water -ethylene glycol solvent composition on structural and micro structural parameters of the Pt3Co/C materials prepared by wet synthesis; (ii) to investigate the particle size effect in the synthesized Pt3Co/C electrocatalists by means of XRD, and (iii) to estimate corrosion stability of the synthesized materials in 1M H2SO4 solution as well as their ORR activity.

Results and Discussion

The XRD patterns of all our Pt-Co/C samples, both asprepared and treated in boiling H2SO4, are presented in Figures 1 and2. One can see the pronounced peaks characteristic of a Pt- Co alloy with the fcc structure. No obvious peaks indicating the presence of free Co or its oxides are found (see Figures 1,2). The peak shapes were described using the pseudo-Voigt function [10] . The X-ray reflections were fitted using the Winplotr from the FullProf software [START_REF] Roisnel | WinPLOTR: Windows tool for powder diffraction patterns analysis[END_REF] . The quality of the fit is shown in Figure 3. It should be noted that our fitting of the reflections from the synthesized samples was made with allowance for reflections from the carbon support. The neglect of this contribution can lead to erroneous determination of the Bragg angle 2 and the full width at half maximum (FWHM), hence underestimation of the particle size (our estimated error is about 0.2 nm for particle sizes close to 3 nm). XRD-pattern of the carbon carrier (Timrex HSAG-300) representing a mixture of the rhombohedral R3m (a=3.6420 Å, =39 0 30) and orthorhombic Fmmm (a = 2.456 Å, b = 4.254 Å, c = 6.696 Å) graphite phases is shown in Figure 1. The (111) reflection has consistently lower FWHM's compared to the other reflections, and the anisotropy increases with increasing particle size. In general, the anisotropic line broadening may be attributed to the three factors: the presence of stacking faults, the presence of dislocations, and nonequivalence of the particle sizes along different crystallographic directions. In our case, it is due to the particle size anisotropy. The presence of stacking faults would provoke a reduced coherent scattering region along the <111> direction (as compared to those for other directions) hence a higher FWHM value. The occurrence of dislocations is hardly probable. It was shown [START_REF] Gryaznov | [END_REF]13] that the particles became dislocation-free below a certain critical size. For instance, dislocation-free particles of iron and nickel have diameters of 23 and 140 nm, respectively [START_REF] Gryaznov | [END_REF] . The same is evident from the high-resolution TEM images of Pt3Co and Pt69Ni31 particles [3,7] .

The average particle size was determined by three separate techniques. The first was the so-called "double Voigt" method [14] . The main relations in this method are For a Voigt size-broadened profile, the size coefficient is given as the Fourier transform

) πL L 2 ( exp L) ( A 2 GS 2 LS S      , where 3 a n L 
is the length of columns of cells along the a3 direction normal to the diffracting planes. The second derivative of the size coefficient,

) (L ]A π 2 ) 2 πL 2 [( L A(L) S 2 GS 2 LS 2 GS 2 2       d d , defines the size distribution function 2 2 V L A(L) L (L) p d d 
. The respective mean values for the volume-weighted grain size are given as

) k ( ) k exp( (L)dL p (L)dL Lp D S GS 2 S 0 V 0 V V erfc       
, where

) /( k GS LS S     .
Determination of the volume-weighted grain size was carried out by means of the D. Balzars program BREADTH [15] .

The second method is based on the assumption that the grain size distribution GSD obeys a Gamma function one, can be found in Ref. [16] . The basic idea is as follows: The average particle size D and its dispersion  were derived from the expressions

M 5 4 FW 2BC  D , M 5 4 FW C 2B   .
The coefficients B and C were found from the expressions

        M 5 4 FW M 5 1 FW 105723 277069 arcctg A , ) A 2101 002237 . 0 ( ctg 00884 0 001555 0 B      . . , A 463695 6515 0 C     .
, where FW1/5M и FW4/5M are the full widths at 1/5 and 4/5 of the peak maximum, respectively. As was shown in Ref. [17] , the grain size distribution determined by this method for strain-free samples is in good agreement with that found from the SEM analysis. For GSD determination by this method we have developed the L&TGSD program [18] The third way applied here for determination of the average particle size is based on the well-known Scherrer equation

) cos H /( K PV  
 D [START_REF] Klug | X-ray Diffraction Procedures from Polycrystalline and Amorphous Materials[END_REF] , where  is the wavelength; D -the volume averaged particle size;  -the Bragg angle, and К = 0.89the Sherrer constant.

The fitting results for the (111) peak were employed for estimation of the average particle size and GSD parameters using the Sherrer equation and the , and the Sherrer methods are listed in Table 1. As follows from Table 1, despite a discrepancy in the particle size values for each individual sample, all the three techniques yield nearly identical variation of the dimension of the as-prepared Pt-Co nanoparticles as a function of ethylene glycol concentration in the solvent, and very similar changes subsequent to the treatment. Thus, the average particle size increases in the sequence PC1> PC3 > PC5 with lowering concentrations of the organic component in the solvent, and the treatment with H2SO4 brings about an additional increase of ca. 0.8-1 nm. method for all three pairs of the asprepared and treated Pt-Co/C samples. The narrowest GSD is found for a 1:5 ratio of water to the nonaqueous component of the solvent. This means that, during synthesis of that material (PC1) the nucleation to growth activation energy ratio Enucl/ Egr was the lowest. In such conditions, the nucleation process prevails over growth of the particles, which corresponds to the instantaneous nucleation model. As the ratio Enucl/ Egr increases with increasing water content (samples PC3, PC5), the growth process becomes more favorable, leading to a larger particle size and GSD broadening (Figure 6).

Grain size distributions calculated by means of the

From comparison of the unit-cell parameters (Table 1) and their dependence on the particle size 111 D (Fig. 7), the following conclusions could be made. (i) The parameters a in all of the synthesized materials are lower than that of pure Pt, (aPt=3.9231Å [START_REF] Downs | [END_REF] ). This fact confirms the formation of a Pt-Co solid solution. (ii)

A nonlinear dependence of the unit cell parameter a on 111 D is observed for the treated samples which have practically identical compositions (within the experimental error). This phenomenon could be explained by a size effect which is due to uncompensated interatomic distances and reduced interplanar spacing near the particle surface. This results in compression of the particles and reduction of the unit cell parameter [21] . The size effect should be more pronounced for smaller nanoparticles where concentration of the surface atoms is essentially higher. A similar effect was observed for nanoparticles of Pd [22] and Ag [23] . A nonlinear dependence of the unit cell parameter on the average particle size observed for the as-prepared samples is a consequence of both the aforesaid size effect and different Co concentrations in the crystallites. (iii) Samples labeled PC4 (the treated PC3) and PC5, although differ essentially in composition, have practically identical unit-cell parameters and particle sizes. It therefore seems that a fraction of Co atoms in the starting (asprepared) samples were not included in the Pt-Co alloy crystallites but were present in an amorphous phase. A similar assumption, concerned with dissolution of only "amorphous" cobalt atoms during corrosion treatment of Pt-Co/C catalysts was made in Ref. [3] .

Cathode chronoamperometric curves for our as-prepared samples demonstrate higher specific currents than those measured for the commercial Pt/C electrocatalysts, TEC10V50E (TKK Co., 46% Pt) or E-TEC (40% Pt). The expected and actually observed enhancement of the ORR activity in the PC5 < PC3 < PC1 series (Fig. 8) may be a result of both the enlargement of the metal surface area and an increase in the intrinsic catalytic activity due to facilitation of dissociative oxygen adsorption through shortening of the Pt -Pt distances, or the unit cell parameter (Fig. 9).

Conclusion

The Pt3Co/C nanoscale materials with average particle sizes of 2.9-4.6 nm and metal loadings of 24-30 wt % were prepared by wet synthesis using water -ethylene glycol matrix solution and NaBH4 as a reducing agent. It was found that the average particle size <D>111 of the synthesized materials decreases progressively with increasing concentration of the organic component (ethylene glycol) in the matrix solution. The GSD dispersion  decreases with decreasing size of the Pt3Co nanoparticles (higher ethylene glycol concentrations in the matrix solution). The narrowest GSD is observed for a H2O -EG ratio of 1:5.

The average particle size increases by 0.8-1 nm, and the grain size distribution becomes broader after treating the Pt3Co/C samples with hot H2SO4 solution.

The unit cell parameter as a function of the particle size shows nonlinear behavior both for the as-prepared samples and those treated with hot H2SO4 solution during 1 hr.

An increase in the anisotropic line broadening with increasing grain size was observed for all of the tested samples. The observed anisotropic line broadening is due to nonequivalent particle sizes along different crystallographic directions.

The mass ORR activity of the prepared Pt3Co/C catalysts in H2SO4 solutions enhances in the order PC5 < PC3 < PC1 (i.e., with decreasing average particle size, unit cell parameter, and GSD dispersion). All of the as-prepared samples show higher catalytic activities than do the commercial Pt/C materials, TEC10V50E (TKK Co., 46% Pt) and E-TEC (40% Pt).

Experimental Section

Preparation of the electrocatalysts. Carbon supported Pt-Co electrocatalysts with nominal Pt:Co atomic ratio of 3:1 were prepared by a low temperature method using sodium borohydride as a reducing agent [24] . A high surface area carbon (Timrex HSAG-300) was impregnated with solutions of chloroplatinic acid (H2PtCl6*6H2O) and cobalt nitrate (Co(NO3)2 *6H2O). The metals were then reduced at room temperature with a sodium borohydride solution which was slowly added to the carbon dispersion at pH 10 under sonication. The water/ethylene glycol mixture was used as a solvent. Water and the nonaqueous component of the solvent were taken in ratios of 1:5, 1:1, and 5:1 for samples labeled PC1, PC3, and PC5, respectively. The resulting material represented 24-30 wt.% metal on the carbon support. All prepared samples were treated in 1M H2SO4 at 100 o C for 1 hr for estimation of the corrosion and aggregate stabilities. The treated samples then received designations PC2, PC4, and PC6, respectively. Metal loadings in the Pt-Co/C materials were determined by differential thermal analysis using a Diamond TG/DTA derivatograph (Perkin Elmer). The Pt:Co atomic ratios in the synthesized catalysts were ascertained by means of an Energy Dispersive X-ray Spectrometry System DX-95 (EDAX, Inc).

Electrochemical measurements. To test the catalytic activity of the prepared Pt3Co/C materials, the rotating disk electrode (RDE) method was used. The glass-carbon electrode's butt-end was soaked with a drop of the catalyst's alcohol suspension containing a small amount of polyvinilidenefluoride. The RDE was rotated at 1000 rpm and stabilized at 0.72 V with an IPC-Pro potentiostat during the current measurements. The electrolyte was a 1M H2SO4 solution saturated with oxygen (p = 1 atm). The potentials cited in this work are referred to that of the reversible hydrogen electrode.

X-ray diffraction (XRD).

Powder diffraction patterns were recorded at the Swiss-Norwegian Beam Lines (SNBL) at the ESRF (=0.72287Å) using a MAR345 image-plate detector. The wavelength, sample-todetector distance (150 mm) and resolution of the setup were calibrated with LaB6 powder (NIST) [25] . The samples were loaded into glass capillaries (Hilgenberg GmbH) having a diameter of 0.3 mm and a wall thickness of 0.01 mm. The data were processed with the Fit2D software [26] . Corrections for the instrumental broadening were made according to a conventional procedure described, e.g., in Ref. [27] .

Figure 1 .

 1 Figure 1. XRD patterns of the carbon-supported Pt-Co/C catalysts (samples PC1, PC2) and of the carbon support itself (Timrex HSAG-300).

Figure 2 .

 2 Figure 2. XRD patterns of the carbon-supported Pt-Co/C catalysts (samples PC3-PC6)

Figure 3 .

 3 Figure 3. Quality of fit for the observed 111 and 200 reflections (open circles), fitted data (solid curve) and the difference (dashed curve).

Figure 4 .

 4 Figure 4. FWHM values vs. 2 for the as-prepared (PC5) and treated (PC6) samples of Pt-Co/C catalyst.



  are the integral breadths of the Lorentz and Gauss functions, and LS breadths of the Lorentz (L) and Gauss (G) functions, corresponding to the size (S) and strain (D) broadening, respectively.

  very close to the conventional lognormal distribution. A detailed description and justification of this method, called the

  and (222) peaks were used for the «double-Voight» method. Values of the average particle size along the (111) direction, 111 D , for the synthesized Pt-Co/C samples estimated using the «double-Voight», the

  Voigt" methods are presented at Figure5for the as-prepared (PC5) and treated (PC6) samples. Since the "double Voigt" method, unlike the equation, takes into account the microstrains, and the two results still coincide very closely, it may be concluded that a contribution of the strains to the observed line broadening is

Figure 5 .

 5 Figure 5. Comparison of grain size distributions calculated by means of the "double Voigt" (curves 1, 3) and M FW 5 4 / 5 1 (curves 2, 4) methods for the asprepared PC5 (left panel) and treated PC6 (right panel) samples of the Pt-Co/C catalyst.

Figure 6 .

 6 Figure 6. Grain size distributions as determined by the M FW 5 4 / 5 1 method.

Figure 7 .

 7 Figure 7. Unit cell parameter a as a function of the particle size D111 along the <111>direction.

Figure 7 .

 7 Figure 7. Room-temperature chronoamperograms of the Pt-Co/C catalysts at 0.72 V in 1M H2SO4 (O2 atmosphere, rotating disk electrode,  = 1000 min -1).

Figure 8 .

 8 Figure 8. Mass activity of electrocatalysts at 0.72 V (t = 200 s) as function of the particle size D111 along the <111>direction, GSD dispersion , and Pt -Pt distance.

Table 1 .

 1 Average particle size, unit cell parameter a, Pt-Pt distance, and alloy composition of the nanostructured Pt-Co/C electrocatalysts.

			Average particle size
	Sample	Sherrer D111, nm	Double-Voit D111, nm	FW D111, 5 1 nm	/	5 4	M , nm	а, Å	Pt-Pt distance, Å	composition EDX
	PC1 PC3	prepared	2.9 3.8	2.5 3.4	3.1 4.0			1.5 2.1	3.881 3.905	2.744 2.761	Pt58Co42 Pt66Co34
	PC5	As	4.6	4.3	4.7			2.6	3.908	2.763	Pt70Co30
	PC2		4.0	3.3	4.2			2.2	3.893	2.765	Pt85Co15
	PC4	Treated	4.7	4.4	4.9			2.6	3.908	2.763	Pt86Co14
	PC6		5.6	5.4	5.7			3.2	3.911	2.752	Pt88Co12

Acknowledgements

The authors wish to thank D. Chernyshov and V. Dmitriev for valuable cooperation and fruitful discussion of the results. The work was supported by The Southern Federal University (internal grant No. 05/6-114) and the Russian Foundation for Basic Research (grant No. 08-08-00869).