An information fusion approach for glacier ... - Semantic Scholar
An information fusion approach for glacier mapping using multi-source remote sensing data Ahmed Guermazi, Lionel Valet, Philippe Bolon LISTIC, Universit´e de Savoie 74944 Annecy le Vieux FRANCE Email: {Ahmed.Guermazi, Lionel.Valet, Philippe.Bolon}@univ-savoie.fr Abstract—Semi-automatic developed techniques for mapping glaciers are essentially based on handling each source of information separately. These sources of information, formed often by satellite images and DEM (Digital Elevation Model), are acquired from different sensors at different dates and usually do not have the same spatial resolution. This aspect has been considered in this remote sensing based study to distinguish between three regions (glaciers, moraines and lakes) in a test area situated into the Alps mountains. A semi-automatic multisource approach for the glacier detection is used which integrates the inputs from SPOT satellite images and DEM into a common space representation. Information extracted from these sources is aggregated using the belief function theory in order to take into account uncertainty and imprecision of the inputs.
I. I NTRODUCTION The observed global warming on the earth surface is the cause of many natural phenomena that appear at a large scale: the increase of the mean sea level, the widespread ice melting and the precipitation decreasing. Warming is also associated with the continuous retreat of glaciers [1]. This retreat is becoming increasingly rapid in such a way that some glaciers have entirely disappeared, and the existence of a large number of glaciers is threatened. The monitoring of the mass balance of glaciers is the common way to infer climatic change [2]. Glaciers are thus key indicators used to assess change in remote mountain areas where climatic stations are very rare or not-existent [3]. The continuous decline of glaciers will have a number of different impacts giving rise to unstable areas. When a glacier has a rapid melting cycle, the terminal moraine may not be strong enough to keep the rising waters behind it, leading to massive flooding. These phenomena might have large economic and societal impacts, for example on the hydrologic regime, tourism and natural hazards. The Alps with the most density populated high-mountain region in the world, are affected by this problem [4]. There is a growing risk due to the creation and expansion of the glacial lakes resulting from the melting of glaciers. For this reason the detection of potential hazards in a glacier area is a new challenge. The handling of regions of interest requires a mapping of the large glacier zones and also detection changes by updating the glacier outlines. Moreover, the manual glacier mapping achieved by geological and geophysical experts is too laborious and this is also accentuated by the difficult access
to the areas. The aim of this study is to develop a semi-automatic method suitable for mapping and updating glaciers in alpine areas with remote sensing data. Thanks to optical images and the Digital Elevation Model (DEM), the challenge of this application is to manage the different spatial and spectral resolution of the available data to take into account their imperfections. Indeed, the complex land topography of glacier areas and the overlapping borders of the geomorphologic regions make a context where uncertainty and unreliability are omnipresent. This paper proposes a complete information treatment chain based on an information fusion approach for glacier cartography. Firstly, some surface attributes are extracted from an optical image and a Digital Elevation Model. Secondly, this available dataset is represented using a triangulated graph that provides an interesting common space of multi-source data. The last stage concerns the classification of each facet into three classes representing the regions of interest (glacier, moraine and lake). Two classification approaches are applied within this paper: the first one is the classical k-nearest neighbours (k-NN) [5] and the second one is the credal k-NN [6]. The results obtained with these methods are then analysed. The paper is organized in the following way: section 2 presents the studied area, the data sources and the previous research on the topic. Section 3 focusses on the processing chain. Finally, the first results obtained by the two based kNN classifiers are discussed in section 4. II. A LPINE GLACIER MAPPING A. Problematic The glacier cartography problem consists of mapping the land-cover surface by distinguishing some regions from the others. The three regions retained for this study are glacier, lake and moraine. Obviously, these are correlated together and they correspond to the main regions researched by geologists to understand their organisation and to control their evolution. Generally, dissimilarities between glaciated and unglaciated terrain render them distinguishable within remote sensing data. The objective is to develop a processing chain able to detect these regions using optical images to facilitate the evolution follow-up of the glacier areas. The geographic area concerned is the occidental Alps where global warming has had a strong
1497
Fig. 1. Source de l’Arc and Mulinet glaciers located in the Vanoise massif Alps mountains).
impact on the glaciers. Only a smaller area called source de l’Arc (Fig. 1) is used in the proposed processing chain. B. Previous works Previous studies for mapping glaciers have applied various remote sensing techniques for image classification. They could be grouped into three categories: 1) Multi-spectral classification: an algorithm for deriving glacier boundaries from multi-spectral imagery has been tested in [7], [8], and [9]. The algorithm is based on segmentation of a TM4/TM5 and TM3/TM5 ratio (Thematic Mapper band 3, 4 and 5 of the Landsat image). For each pixel of the image, the spectral ratio between different spectral bands of the Landsat image is calculated. Classification is then achieved by a supervised approach based on an empirical threshold. 2) Geomorphometric classification: an algorithm proposed by Bonk [10] which was based on a geomorphometric approach was used in order to differentiate the glacier from surrounding landforms. A morphometric terrain analysis using high resolution DEM was used to delineate glacier area. Different attributes (slope, profile curvature and tangential curvature) are calculated for each pixel of the DEM image. An unsupervised classification approach based on the ISODATA clustering algorithm was used for glacier mapping. 3) Multi-spectral and geomorphometric approach: the principal aim of this kind of approach is to exploit simultaneously the advantages of multi-spectral information from satellite images and information derived from DEM. These multi-source approaches use a sequential processing technique and simple rules for pixel-based classification [11], [12], [13]. C. Data sources The data available for this study comprises mainly of an orthorectified and georeferenced image from SPOT5 satellitesensor (Fig. 2(a)) and a DEM (Fig. 2(b)). The SPOT image was
acquired in 2009 with 4 spectral bands and spatial resolution of 10m. The bands are: Band 1: green, 0.50-0.59 µ m. Band 2: red, 0.61-0.68 µ m. Band 3: NIR (Near Infrared), 0.78-0.89 µ m. Band 4: SWIR (Short Wave Infrared), 1.58-1.75 µ m. The DEM was acquired in 2001 and it has a lower spatial resolution (50 m). A sequence of preprocessing steps (orthorectification, georeferencing and projection transformation) has been applied on raw data. It aims at ensuring that the geographic position of the SPOT and DEM images are consistent with the true spatial position and not significantly affected by the artefacts of the acquisition measurement (missing data, fuzzy appearance and visibility). However, the transformation maintains and sometime increases the imprecision and the uncertainty that are inherent to this kind of data. The third source of information includes a crisp topographic glacier map achieved manually by the experts and completed by terrain measurements taken in 2011 (Fig. 2(c)). However, this manual mapping is also uncertain. Indeed, in this application, the real frontiers between the regions are fuzzy. The regions may completely or partially overlapped and thus make it more difficult to distinguish. III. M ETHODOLOGY In this research, a methodology framework has been developed to test the efficiency of using a fusion approach based on the belief function for geomorphological mapping of glaciers. The processing steps presented in Fig. 3 are described below. A. Terrain attribute extraction The first processing step in the proposed methodology consists of feature extraction. The basic idea behind the extraction stage is to describe the surface of the landforms. Terrain attributes are good predictors for glacier detection [14]. These attributes can be divided into two categories: radiometric attributes and morphometric attributes. Morphometric features are calculated from elevation data while radiometric features are extracted from optical images. In our case, the radiometric attributes include the Normalized Difference Vegetation Index (NDVI) and the Normalized Difference Snow Index (NDSI) and they are computed from SPOT5 image (Fig. 3, step 2). DEM is used to produce morphometric attributes (Fig. 3, step 1), they comprise first and second order derivative of the elevation field such as slope and curvature. The mathematical representation of these two attributes and the methods for calculating them can be found in [15]. Slope and curvature are the most important features to differentiate glacier from surrounding landforms [10] [16] and to detect the moraine boundaries [12] [3]. NDVI is defined as a difference of reflectance in the NIR band and the red band divided by the sum of the two reflectance. NDSI is the difference between the green band and the SWIR band divided by the sum of the two bands of the Spot image. Further, NDVI is found to be a good attribute to distinguish lake areas [3], whereas, NDSI is a significant measurement to detect snow covered regions such as snow based glaciers [17]. Four attribute images result
1498
(a) SPOT image
(b) DEM Fig. 2.
Fig. 3.
(c) The expert references
Data sources of the source de l’Arc glacier
The proposed processing chain for glaciers mapping.
from the feature extraction step: slope, curvature, NDVI and NDSI images as can be seen in Fig. 3. Hence, the attribute images have the same spatial resolution that the initial images from which they were extracted. Therefore, the attribute images keep the geographic transformations process applied to the Spot and DEM images (orthorectification, georeferencing and projection transformation) and thus the measurement distortions are propagated to these images. B. Graph construction An attribute taken separately is not able to accurately differentiate between the three geomorphological elements (glacier, moraine and lake) thus the combination of all the
attributes becomes necessary. On the other hand, these images, which are calculated at different resolution scales, require correspondence resolution transformation [18]. A common representation is thus needed to support these dissimilarities and to express the attributes measurements into a common information space. 1) Selection of the interesting pixels: The chosen strategy is to select some interesting pixels from each computed attribute by a neighbourhood analysis. The objective of this analysis is to identify the unstable pixels which have intensity variation with their neighbourhood pixels according to their attribute values. At the begin, the attribute variation is computed between each pixels and their neighbours. The neighbours is
1499
NDVI 0.03
NDSI 0.13
Slope 2.3 (Degrees)
Curvature 0.18 (rad/m)
TABLE I S TABILITY THRESHOLD OF THE ATTRIBUTE VARIATIONS .
defined as the eight adjacent pixels expressed with the discrete coordinate represented by row and column position in the image. Only the largest attribute variation value between a pixel and their neighbours is retained. A selection criteria of these pixels is applied through a stability threshold. As the attribute values are recognized in different variable spacing, four thresholds si are used for this study that correspond to the NDVI, NDSI, Slope and Curvature attribute. These attributes are currently used in the literature and several interpretations have been yet proposed. In [3] and [17], a spectral analysis of the NDVI and NDSI is used to distinguish between lake and glacier areas. In [19], thresholds are proposed to detect moraine areas using the slope and the curvature. The thresholds used in this study are given in Tab. I. Therefore, a pixel is selected when its largest attribute variation with its neighbours is greater than the threshold. The stability threshold can be seen as the smallest attribute variation level of the selected pixels. More the threshold is small, more pixels are chosen. Once the interesting pixels are selected, their discrete coordinates are projected to the continuous space using the longitude and latitude coordinates of the center of the pixels to form the support points. Figure 4 shows the process leading to the selection of the support points. 2) Triangular graph modelling: In order to establish a model which represents the stable areas, a Delaunay triangulation algorithm is applied on the support points (Fig. 4). This method ensures that the circle passing through the three vertices encompasses no other points. Because the points represent unstable sites in the way of at least one attribute, the obtained facets can be considered as stable areas. The great advantage of using graph facets is the possibility of adapting the facets shape to fit variation coming from the attributes space. More data points can be used in regions where there is a lot of attributes stability change, and fewer points in regions where the attributes stability hardly changes. Consequently, a graph can approximate any attributes stability at any desired tolerance with a minimal number of facets. The last stage consists in evaluating the attribute values for each facet. The average of the attribute values situated into the facet is computed. This average is weighted by the intersection rate of the facet with the pixels (Fig. 5). A vector composed of all attributes is thus obtained. It characterizes the facet and it will be used for the classification stage. C. Facets classification Facets classification is based on a supervised approach. The references provided by geophysicists represent ground truth
Fig. 5.
Computation method of the vector of attributes.
delineation of the three regions. They are used to determine the output classes of each input facet to be classified. For this, the references are first transformed into facets to be comparable to the input one. Determination of the reference facets is based on a coverage analysis between graph facets and the expert references. Facets that are completely covered by a reference are labelled to the corresponding regions and they form the learning set of facets. IV. C LASSIC AND CREDAL K NN
CLASSIFICATION
A. kNN classifiers Two classifiers based on the k-NN rule are implemented to classify the graph facets. Given a set of n labelled examples → → → Tn = {(X1 ,Y1 ), (X2 ,Y2 ), ..., (Xn ,Yn )} with input vectors Xi and class labels Yi , the k-NN rule classifies a new incoming sample → X to the most represented class in its neighbourhood. The neighbourhood is determined from the training set Tn . To identify the nearest neighbours, the classical k-NN uses a measure of similarity between the samples. For the following study, the euclidean distance is used. The second approach used the credal k-NN algorithm based on Dempster-Shafer theory [6]. The frame of discernment contains the three researched classes C1 for glacier, C2 for lake and C3 for moraine Ω = {C1 ,C2 ,C3 }. In this approach, each neighbour of a facet to be classified is considered as an item of evidence supporting certain hypotheses about the class membership of that facet. The contribution of evidence to the credibility of different hypotheses is described by a basic probability assignment (BPA) function m. The BPAs are calculated for each k nearest neighbours using the optimisation procedure proposed in [20] and they are aggregated using the Dempsters rule of combination. With this approach, the BPAs have non null values only for the singleton subsets Ci and for the entire set of Ω.
1500
Fig. 4.
Points selection for the graph construction.
B. The reject class In this application, the objective is also to detect the area situated outside of the expert references (region different to glacier, lake and moraine). The idea is to be able to classify the incoming samples to a different class that is not represented in the training set. The credal and classic k-NN based method don’t include the class reject option. The reject class for the classic k-NN approach is based on the distance of the incoming facet to the samples. When this distance is too important, the facet is classified to the reject class called “other area”. The decision rule of credal k-NN based on BPA can be modified to include a distance-reject option in the classification process [20]. The distance-reject is applied by imposing threshold value c on the final obtained credibility. The sample xs will be distance-rejected if ms (Ci ) < c,Ci ∈ {C1 ,C2 ,C3 }. When the sample xs to be classified is far away from any previously recorded samples, it is therefore suspected to be classified as a class that is not represented in the training set. As a consequence, a new class is added to the samples, in our case xs will be assigned to other area class. C. Results and discussion The comparison of the two classification procedures are now presented. At the beginning, stability thresholds are imposed for each attribute image dataset and therefore a graph of facets is constructed (19389 facets for glaciers, 565 facets for lakes and 4164 facets for moraines). Classic and credal k-NN are experimented using n-fold cross validation method. The first experiment illustrates the classification rate evolution according to the number of neighbour k (Fig. 6).
The glacier detection performance is constant for the both methods, contrary to the degradation of the accuracy of lakes when smaller training sample are used. Glacier classification is less sensitive to the number of neighbours. Furthermore, by increasing the number of neighbours, the surface rate of moraine and lake becomes constant for classic k-NN and credal k-NNs. Two parts can be observed from figure 6: the first part of the plot where moraine and lake classification decreases for the credal k-NN rule and increases for the classic k-NN and the second part of the plot where surface rate of moraine and lake tend for the same value for both classification methods. This means that the credal k-NN method is more robust when little neighbours are taken into account. The method has better management of the contradiction between the samples concerned. Figure 7 presents the classification rate attached to the variation of the sets number used for the n-fold cross validation. It can be observed that credal k-NN method performs better than classic k-NN when n is increased. The detection rate for the glacier did not change much with different values of n. The highest detection rate for both methods is obtained when the number of n-fold is between 20 and 50. Further experiments show that performance of credal and classic k-NN is constant when n > 50. Finally, the comparison between the best distance-reject classification of classic and credal k-NN is presented in Tab. II. Results show that the detection rate of the credal k-NN are higher than the rates of the classic k-NN. Distances between samples appear to be less sensitive for the credal k-NN. The distance-reject based classifications are shown in Fig. 8. The
1501
Fig. 6. Mean surface ratio evolution according to k (n = 20). Solid line represent the classic k-NN classification and alternating dots represent credal k-NN classification.
Fig. 7. Mean surface ratio evolution accordint to n (k = 25). Solid line represent the classic k-NN classification and alternating dots represent credal k-NN classification.
comparison between expert references and the classification mapping indicate that glaciers are fairly well captured by the two algorithms. However, classic k-NN is more sensitive for moraine and lake classification than credal k-NN. There is also misclassified detections that appear out of the researched regions.
Glacier Lake Moraine
Credal k-NN % 95.7 87.4 66.2
Classic k-NN % 93.7 32.6 44
TABLE II FACETS SURFACE RATIO
OF THE BEST DISTANCE - REJECT CLASSIFICATION OF CREDAL AND CLASSIC k-NN.
V. C ONCLUSION The approach presented to map the glacier at the source de l’Arc area of the Alpine region based on SPOT imagery and DEM provided promising results. The developed method
based on morphometric and radiometric parameters derived from the sources of data have been represented in common
1502
(a) Distance-reject classification with credal k-NN Fig. 8.
(b) Distance-reject classification with classic k-NN
Comparison between expert references and the best distance-reject classification results obtained by credal and classic k-NN.
space. Using a graph, they are fused by belief function theory to delineate glacier, moraines and lakes. Results show that the credal k-NN approach gives robust results than classic k-NN approach. Further improvements are planned such as the use of another method to determine the neighbourhood in kNN algorithm. Moreover, the graph resolution fixed by the attribute variation thresholding could also has an impact on the detection rates. The methodology proposed in this paper is suitable for better exploiting the uncertainty between the regions. In a future work, the mass functions will be updating for all the subset of Ω (and not only for the singleton) with a better managing of the references given by the experts. ACKNOWLEDGMENT This work was supported by the European Regional Development Fund (FEDER) through the GlaRiskAlp project (projet simple Alcotra no 56), a European Territorial Cooperation Program (Alcotra France-Italy 2007-2013). R EFERENCES [1] J. Lu, G. A. Vecchi, and T. Reichler, “Expansion of the hadley cell under global warming,” Geophysical Research Letters, vol. 34, L06805, 2007. [2] J. Oerlemans, “Quantifying global warming from the retreat of glaciers,” Science, vol. 264, p. 243245, 1994. [3] T. Bolch, M. Buchroithner, A. Kunert, and U. Kamp, “Automated delineation of debris-covered glaciers based on aster data,” in Geoinformation in Europe (Proc. of 27th EARSel Symposium, 04-07 June 2007), Bozen, Italy, 2007, pp. 403–410. [4] W. Haeberli and M. Beniston, “Climate change and its impacts on glaciers and permafrost in the alps,” Ambio, vol. 27, pp. 258–265, 1998. [5] E. Fix and J. Hodges, “Nonparametric discrimination: consistency properties,” USAF School Aviation Medicine Randolph Field, TX, no. 4, 1951. [6] T. Denoeux, “A k-nearest neighbor classification rule based on dempstershafer theory,” IEEE Transactions on Systems, Man and Cybernetics, vol. 25, pp. 804–813, 1995. [7] F. Paul, “Evaluation of different methods for glacier mapping using landsat tm,” Proceedings of EARSeL-SIG-Workshop Land Ice and Snow, vol. 1, pp. 239–245, 2000. [8] F. Paul, A. Kb, M. Maisch, T. Kellenberger, and W. Haeberli, “The new remote-sensing-derived swiss glacier inventory: I. methods,” Annals of Glaciology, vol. 34, no. 1, pp. 355–361, 2002.
[9] F. Paul, C. Huggel, A. Kb, T. Kellenberger, and M. Maisch, “Comparison of tm-derived glacier areas with higher resolution data sets,” in Proceedings of EARSeL-LISSIG-Workshop Observing our Cryosphere from Space, vol. 16, no. 2, 2002, pp. 15–21. [10] R. Bonk, “Scale-dependent geomorphometric analysis for glacier mapping at nanga parbat: Grass gis approach,” in Proceedings of the Open source GIS-GRASS users conference. Citeseer, 2002, pp. 1–4. [11] D. J. Gratton, P. J. Howarth, and D. J. Marceau, “Combining dem parameters with landsat mss and tm imagery in a gis for mountain glacier characterization,” IEEE Transactions on Geoscience and Remote Sensing, vol. 28, no. 4, pp. 766 – 769, 1990. [12] F. Paul, C. Huggel, and A. Kb, “Combining satellite multispectral image data and a digital elevation model for mapping debris-covered glaciers,” Remote Sensing of Environment, vol. 89, no. 4, pp. 510–518, 2004. [13] A. K¨aa¨ b, “Combination of srtm3 and repeat aster data for deriving alpine glacier flow velocities in the bhutan himalaya,” Remote Sensing of Environment, vol. 94, p. 463474, 2005. [14] A. Brenning and D. Trombotto, “Logistic regression modeling of rock glacier and glacier distribution: Topographic and climatic controls in the semi-arid andes,” Geomorphology, vol. 81, no. 1-2, pp. 141–154, 2006. [15] J. Wilson and J. Gallant, Terrain Analysis: Principles and Applications. Wiley New York, 2000. [16] T. Bolch and U. Kamp, “Glacier mapping in high mountains using dems, landsat and aster data,” Grazer Schriften der Geographie und Raumforschung, vol. 41, pp. 37–48, 2006. [17] V. Salomonson and I. Appel, “Estimating fractional snow cover from modis using the normalized difference snow index,” Remote Sensing of Environment, vol. 89, no. 3, pp. 351–360, 2004. [18] G. Macchiavello, G. Moser, G. Boni, and S. Serpico, “Automatic unsupervised classification of snow-covered areas by decision-tree classification and minimum-error thresholding,” in Geoscience and Remote Sensing Symposium, IEEE International, IGARSS 2009., vol. 2. IEEE, 2010, pp. 1000 –1003. [19] L. Zevenbergen and C. Thorne, “Quantitative analysis of land surface topography,” Earth Surface Processes and Landforms, vol. 12, pp. 47– 56, 1987. [20] T. Denoeux and L. M. Zouhal, “An evidence-theoretic k-nn rule with parameter optimization,” IEEE Transactions on Systems, Man and Cybernetics, pp. 1–7, 1998.
1503
I. I NTRODUCTION The observed global warming on the earth surface is the cause of many natural phenomena that appear at a large scale: the increase of the mean sea level, the widespread ice melting and the precipitation decreasing. Warming is also associated with the continuous retreat of glaciers [1]. This retreat is becoming increasingly rapid in such a way that some glaciers have entirely disappeared, and the existence of a large number of glaciers is threatened. The monitoring of the mass balance of glaciers is the common way to infer climatic change [2]. Glaciers are thus key indicators used to assess change in remote mountain areas where climatic stations are very rare or not-existent [3]. The continuous decline of glaciers will have a number of different impacts giving rise to unstable areas. When a glacier has a rapid melting cycle, the terminal moraine may not be strong enough to keep the rising waters behind it, leading to massive flooding. These phenomena might have large economic and societal impacts, for example on the hydrologic regime, tourism and natural hazards. The Alps with the most density populated high-mountain region in the world, are affected by this problem [4]. There is a growing risk due to the creation and expansion of the glacial lakes resulting from the melting of glaciers. For this reason the detection of potential hazards in a glacier area is a new challenge. The handling of regions of interest requires a mapping of the large glacier zones and also detection changes by updating the glacier outlines. Moreover, the manual glacier mapping achieved by geological and geophysical experts is too laborious and this is also accentuated by the difficult access
to the areas. The aim of this study is to develop a semi-automatic method suitable for mapping and updating glaciers in alpine areas with remote sensing data. Thanks to optical images and the Digital Elevation Model (DEM), the challenge of this application is to manage the different spatial and spectral resolution of the available data to take into account their imperfections. Indeed, the complex land topography of glacier areas and the overlapping borders of the geomorphologic regions make a context where uncertainty and unreliability are omnipresent. This paper proposes a complete information treatment chain based on an information fusion approach for glacier cartography. Firstly, some surface attributes are extracted from an optical image and a Digital Elevation Model. Secondly, this available dataset is represented using a triangulated graph that provides an interesting common space of multi-source data. The last stage concerns the classification of each facet into three classes representing the regions of interest (glacier, moraine and lake). Two classification approaches are applied within this paper: the first one is the classical k-nearest neighbours (k-NN) [5] and the second one is the credal k-NN [6]. The results obtained with these methods are then analysed. The paper is organized in the following way: section 2 presents the studied area, the data sources and the previous research on the topic. Section 3 focusses on the processing chain. Finally, the first results obtained by the two based kNN classifiers are discussed in section 4. II. A LPINE GLACIER MAPPING A. Problematic The glacier cartography problem consists of mapping the land-cover surface by distinguishing some regions from the others. The three regions retained for this study are glacier, lake and moraine. Obviously, these are correlated together and they correspond to the main regions researched by geologists to understand their organisation and to control their evolution. Generally, dissimilarities between glaciated and unglaciated terrain render them distinguishable within remote sensing data. The objective is to develop a processing chain able to detect these regions using optical images to facilitate the evolution follow-up of the glacier areas. The geographic area concerned is the occidental Alps where global warming has had a strong
1497
Fig. 1. Source de l’Arc and Mulinet glaciers located in the Vanoise massif Alps mountains).
impact on the glaciers. Only a smaller area called source de l’Arc (Fig. 1) is used in the proposed processing chain. B. Previous works Previous studies for mapping glaciers have applied various remote sensing techniques for image classification. They could be grouped into three categories: 1) Multi-spectral classification: an algorithm for deriving glacier boundaries from multi-spectral imagery has been tested in [7], [8], and [9]. The algorithm is based on segmentation of a TM4/TM5 and TM3/TM5 ratio (Thematic Mapper band 3, 4 and 5 of the Landsat image). For each pixel of the image, the spectral ratio between different spectral bands of the Landsat image is calculated. Classification is then achieved by a supervised approach based on an empirical threshold. 2) Geomorphometric classification: an algorithm proposed by Bonk [10] which was based on a geomorphometric approach was used in order to differentiate the glacier from surrounding landforms. A morphometric terrain analysis using high resolution DEM was used to delineate glacier area. Different attributes (slope, profile curvature and tangential curvature) are calculated for each pixel of the DEM image. An unsupervised classification approach based on the ISODATA clustering algorithm was used for glacier mapping. 3) Multi-spectral and geomorphometric approach: the principal aim of this kind of approach is to exploit simultaneously the advantages of multi-spectral information from satellite images and information derived from DEM. These multi-source approaches use a sequential processing technique and simple rules for pixel-based classification [11], [12], [13]. C. Data sources The data available for this study comprises mainly of an orthorectified and georeferenced image from SPOT5 satellitesensor (Fig. 2(a)) and a DEM (Fig. 2(b)). The SPOT image was
acquired in 2009 with 4 spectral bands and spatial resolution of 10m. The bands are: Band 1: green, 0.50-0.59 µ m. Band 2: red, 0.61-0.68 µ m. Band 3: NIR (Near Infrared), 0.78-0.89 µ m. Band 4: SWIR (Short Wave Infrared), 1.58-1.75 µ m. The DEM was acquired in 2001 and it has a lower spatial resolution (50 m). A sequence of preprocessing steps (orthorectification, georeferencing and projection transformation) has been applied on raw data. It aims at ensuring that the geographic position of the SPOT and DEM images are consistent with the true spatial position and not significantly affected by the artefacts of the acquisition measurement (missing data, fuzzy appearance and visibility). However, the transformation maintains and sometime increases the imprecision and the uncertainty that are inherent to this kind of data. The third source of information includes a crisp topographic glacier map achieved manually by the experts and completed by terrain measurements taken in 2011 (Fig. 2(c)). However, this manual mapping is also uncertain. Indeed, in this application, the real frontiers between the regions are fuzzy. The regions may completely or partially overlapped and thus make it more difficult to distinguish. III. M ETHODOLOGY In this research, a methodology framework has been developed to test the efficiency of using a fusion approach based on the belief function for geomorphological mapping of glaciers. The processing steps presented in Fig. 3 are described below. A. Terrain attribute extraction The first processing step in the proposed methodology consists of feature extraction. The basic idea behind the extraction stage is to describe the surface of the landforms. Terrain attributes are good predictors for glacier detection [14]. These attributes can be divided into two categories: radiometric attributes and morphometric attributes. Morphometric features are calculated from elevation data while radiometric features are extracted from optical images. In our case, the radiometric attributes include the Normalized Difference Vegetation Index (NDVI) and the Normalized Difference Snow Index (NDSI) and they are computed from SPOT5 image (Fig. 3, step 2). DEM is used to produce morphometric attributes (Fig. 3, step 1), they comprise first and second order derivative of the elevation field such as slope and curvature. The mathematical representation of these two attributes and the methods for calculating them can be found in [15]. Slope and curvature are the most important features to differentiate glacier from surrounding landforms [10] [16] and to detect the moraine boundaries [12] [3]. NDVI is defined as a difference of reflectance in the NIR band and the red band divided by the sum of the two reflectance. NDSI is the difference between the green band and the SWIR band divided by the sum of the two bands of the Spot image. Further, NDVI is found to be a good attribute to distinguish lake areas [3], whereas, NDSI is a significant measurement to detect snow covered regions such as snow based glaciers [17]. Four attribute images result
1498
(a) SPOT image
(b) DEM Fig. 2.
Fig. 3.
(c) The expert references
Data sources of the source de l’Arc glacier
The proposed processing chain for glaciers mapping.
from the feature extraction step: slope, curvature, NDVI and NDSI images as can be seen in Fig. 3. Hence, the attribute images have the same spatial resolution that the initial images from which they were extracted. Therefore, the attribute images keep the geographic transformations process applied to the Spot and DEM images (orthorectification, georeferencing and projection transformation) and thus the measurement distortions are propagated to these images. B. Graph construction An attribute taken separately is not able to accurately differentiate between the three geomorphological elements (glacier, moraine and lake) thus the combination of all the
attributes becomes necessary. On the other hand, these images, which are calculated at different resolution scales, require correspondence resolution transformation [18]. A common representation is thus needed to support these dissimilarities and to express the attributes measurements into a common information space. 1) Selection of the interesting pixels: The chosen strategy is to select some interesting pixels from each computed attribute by a neighbourhood analysis. The objective of this analysis is to identify the unstable pixels which have intensity variation with their neighbourhood pixels according to their attribute values. At the begin, the attribute variation is computed between each pixels and their neighbours. The neighbours is
1499
NDVI 0.03
NDSI 0.13
Slope 2.3 (Degrees)
Curvature 0.18 (rad/m)
TABLE I S TABILITY THRESHOLD OF THE ATTRIBUTE VARIATIONS .
defined as the eight adjacent pixels expressed with the discrete coordinate represented by row and column position in the image. Only the largest attribute variation value between a pixel and their neighbours is retained. A selection criteria of these pixels is applied through a stability threshold. As the attribute values are recognized in different variable spacing, four thresholds si are used for this study that correspond to the NDVI, NDSI, Slope and Curvature attribute. These attributes are currently used in the literature and several interpretations have been yet proposed. In [3] and [17], a spectral analysis of the NDVI and NDSI is used to distinguish between lake and glacier areas. In [19], thresholds are proposed to detect moraine areas using the slope and the curvature. The thresholds used in this study are given in Tab. I. Therefore, a pixel is selected when its largest attribute variation with its neighbours is greater than the threshold. The stability threshold can be seen as the smallest attribute variation level of the selected pixels. More the threshold is small, more pixels are chosen. Once the interesting pixels are selected, their discrete coordinates are projected to the continuous space using the longitude and latitude coordinates of the center of the pixels to form the support points. Figure 4 shows the process leading to the selection of the support points. 2) Triangular graph modelling: In order to establish a model which represents the stable areas, a Delaunay triangulation algorithm is applied on the support points (Fig. 4). This method ensures that the circle passing through the three vertices encompasses no other points. Because the points represent unstable sites in the way of at least one attribute, the obtained facets can be considered as stable areas. The great advantage of using graph facets is the possibility of adapting the facets shape to fit variation coming from the attributes space. More data points can be used in regions where there is a lot of attributes stability change, and fewer points in regions where the attributes stability hardly changes. Consequently, a graph can approximate any attributes stability at any desired tolerance with a minimal number of facets. The last stage consists in evaluating the attribute values for each facet. The average of the attribute values situated into the facet is computed. This average is weighted by the intersection rate of the facet with the pixels (Fig. 5). A vector composed of all attributes is thus obtained. It characterizes the facet and it will be used for the classification stage. C. Facets classification Facets classification is based on a supervised approach. The references provided by geophysicists represent ground truth
Fig. 5.
Computation method of the vector of attributes.
delineation of the three regions. They are used to determine the output classes of each input facet to be classified. For this, the references are first transformed into facets to be comparable to the input one. Determination of the reference facets is based on a coverage analysis between graph facets and the expert references. Facets that are completely covered by a reference are labelled to the corresponding regions and they form the learning set of facets. IV. C LASSIC AND CREDAL K NN
CLASSIFICATION
A. kNN classifiers Two classifiers based on the k-NN rule are implemented to classify the graph facets. Given a set of n labelled examples → → → Tn = {(X1 ,Y1 ), (X2 ,Y2 ), ..., (Xn ,Yn )} with input vectors Xi and class labels Yi , the k-NN rule classifies a new incoming sample → X to the most represented class in its neighbourhood. The neighbourhood is determined from the training set Tn . To identify the nearest neighbours, the classical k-NN uses a measure of similarity between the samples. For the following study, the euclidean distance is used. The second approach used the credal k-NN algorithm based on Dempster-Shafer theory [6]. The frame of discernment contains the three researched classes C1 for glacier, C2 for lake and C3 for moraine Ω = {C1 ,C2 ,C3 }. In this approach, each neighbour of a facet to be classified is considered as an item of evidence supporting certain hypotheses about the class membership of that facet. The contribution of evidence to the credibility of different hypotheses is described by a basic probability assignment (BPA) function m. The BPAs are calculated for each k nearest neighbours using the optimisation procedure proposed in [20] and they are aggregated using the Dempsters rule of combination. With this approach, the BPAs have non null values only for the singleton subsets Ci and for the entire set of Ω.
1500
Fig. 4.
Points selection for the graph construction.
B. The reject class In this application, the objective is also to detect the area situated outside of the expert references (region different to glacier, lake and moraine). The idea is to be able to classify the incoming samples to a different class that is not represented in the training set. The credal and classic k-NN based method don’t include the class reject option. The reject class for the classic k-NN approach is based on the distance of the incoming facet to the samples. When this distance is too important, the facet is classified to the reject class called “other area”. The decision rule of credal k-NN based on BPA can be modified to include a distance-reject option in the classification process [20]. The distance-reject is applied by imposing threshold value c on the final obtained credibility. The sample xs will be distance-rejected if ms (Ci ) < c,Ci ∈ {C1 ,C2 ,C3 }. When the sample xs to be classified is far away from any previously recorded samples, it is therefore suspected to be classified as a class that is not represented in the training set. As a consequence, a new class is added to the samples, in our case xs will be assigned to other area class. C. Results and discussion The comparison of the two classification procedures are now presented. At the beginning, stability thresholds are imposed for each attribute image dataset and therefore a graph of facets is constructed (19389 facets for glaciers, 565 facets for lakes and 4164 facets for moraines). Classic and credal k-NN are experimented using n-fold cross validation method. The first experiment illustrates the classification rate evolution according to the number of neighbour k (Fig. 6).
The glacier detection performance is constant for the both methods, contrary to the degradation of the accuracy of lakes when smaller training sample are used. Glacier classification is less sensitive to the number of neighbours. Furthermore, by increasing the number of neighbours, the surface rate of moraine and lake becomes constant for classic k-NN and credal k-NNs. Two parts can be observed from figure 6: the first part of the plot where moraine and lake classification decreases for the credal k-NN rule and increases for the classic k-NN and the second part of the plot where surface rate of moraine and lake tend for the same value for both classification methods. This means that the credal k-NN method is more robust when little neighbours are taken into account. The method has better management of the contradiction between the samples concerned. Figure 7 presents the classification rate attached to the variation of the sets number used for the n-fold cross validation. It can be observed that credal k-NN method performs better than classic k-NN when n is increased. The detection rate for the glacier did not change much with different values of n. The highest detection rate for both methods is obtained when the number of n-fold is between 20 and 50. Further experiments show that performance of credal and classic k-NN is constant when n > 50. Finally, the comparison between the best distance-reject classification of classic and credal k-NN is presented in Tab. II. Results show that the detection rate of the credal k-NN are higher than the rates of the classic k-NN. Distances between samples appear to be less sensitive for the credal k-NN. The distance-reject based classifications are shown in Fig. 8. The
1501
Fig. 6. Mean surface ratio evolution according to k (n = 20). Solid line represent the classic k-NN classification and alternating dots represent credal k-NN classification.
Fig. 7. Mean surface ratio evolution accordint to n (k = 25). Solid line represent the classic k-NN classification and alternating dots represent credal k-NN classification.
comparison between expert references and the classification mapping indicate that glaciers are fairly well captured by the two algorithms. However, classic k-NN is more sensitive for moraine and lake classification than credal k-NN. There is also misclassified detections that appear out of the researched regions.
Glacier Lake Moraine
Credal k-NN % 95.7 87.4 66.2
Classic k-NN % 93.7 32.6 44
TABLE II FACETS SURFACE RATIO
OF THE BEST DISTANCE - REJECT CLASSIFICATION OF CREDAL AND CLASSIC k-NN.
V. C ONCLUSION The approach presented to map the glacier at the source de l’Arc area of the Alpine region based on SPOT imagery and DEM provided promising results. The developed method
based on morphometric and radiometric parameters derived from the sources of data have been represented in common
1502
(a) Distance-reject classification with credal k-NN Fig. 8.
(b) Distance-reject classification with classic k-NN
Comparison between expert references and the best distance-reject classification results obtained by credal and classic k-NN.
space. Using a graph, they are fused by belief function theory to delineate glacier, moraines and lakes. Results show that the credal k-NN approach gives robust results than classic k-NN approach. Further improvements are planned such as the use of another method to determine the neighbourhood in kNN algorithm. Moreover, the graph resolution fixed by the attribute variation thresholding could also has an impact on the detection rates. The methodology proposed in this paper is suitable for better exploiting the uncertainty between the regions. In a future work, the mass functions will be updating for all the subset of Ω (and not only for the singleton) with a better managing of the references given by the experts. ACKNOWLEDGMENT This work was supported by the European Regional Development Fund (FEDER) through the GlaRiskAlp project (projet simple Alcotra no 56), a European Territorial Cooperation Program (Alcotra France-Italy 2007-2013). R EFERENCES [1] J. Lu, G. A. Vecchi, and T. Reichler, “Expansion of the hadley cell under global warming,” Geophysical Research Letters, vol. 34, L06805, 2007. [2] J. Oerlemans, “Quantifying global warming from the retreat of glaciers,” Science, vol. 264, p. 243245, 1994. [3] T. Bolch, M. Buchroithner, A. Kunert, and U. Kamp, “Automated delineation of debris-covered glaciers based on aster data,” in Geoinformation in Europe (Proc. of 27th EARSel Symposium, 04-07 June 2007), Bozen, Italy, 2007, pp. 403–410. [4] W. Haeberli and M. Beniston, “Climate change and its impacts on glaciers and permafrost in the alps,” Ambio, vol. 27, pp. 258–265, 1998. [5] E. Fix and J. Hodges, “Nonparametric discrimination: consistency properties,” USAF School Aviation Medicine Randolph Field, TX, no. 4, 1951. [6] T. Denoeux, “A k-nearest neighbor classification rule based on dempstershafer theory,” IEEE Transactions on Systems, Man and Cybernetics, vol. 25, pp. 804–813, 1995. [7] F. Paul, “Evaluation of different methods for glacier mapping using landsat tm,” Proceedings of EARSeL-SIG-Workshop Land Ice and Snow, vol. 1, pp. 239–245, 2000. [8] F. Paul, A. Kb, M. Maisch, T. Kellenberger, and W. Haeberli, “The new remote-sensing-derived swiss glacier inventory: I. methods,” Annals of Glaciology, vol. 34, no. 1, pp. 355–361, 2002.
[9] F. Paul, C. Huggel, A. Kb, T. Kellenberger, and M. Maisch, “Comparison of tm-derived glacier areas with higher resolution data sets,” in Proceedings of EARSeL-LISSIG-Workshop Observing our Cryosphere from Space, vol. 16, no. 2, 2002, pp. 15–21. [10] R. Bonk, “Scale-dependent geomorphometric analysis for glacier mapping at nanga parbat: Grass gis approach,” in Proceedings of the Open source GIS-GRASS users conference. Citeseer, 2002, pp. 1–4. [11] D. J. Gratton, P. J. Howarth, and D. J. Marceau, “Combining dem parameters with landsat mss and tm imagery in a gis for mountain glacier characterization,” IEEE Transactions on Geoscience and Remote Sensing, vol. 28, no. 4, pp. 766 – 769, 1990. [12] F. Paul, C. Huggel, and A. Kb, “Combining satellite multispectral image data and a digital elevation model for mapping debris-covered glaciers,” Remote Sensing of Environment, vol. 89, no. 4, pp. 510–518, 2004. [13] A. K¨aa¨ b, “Combination of srtm3 and repeat aster data for deriving alpine glacier flow velocities in the bhutan himalaya,” Remote Sensing of Environment, vol. 94, p. 463474, 2005. [14] A. Brenning and D. Trombotto, “Logistic regression modeling of rock glacier and glacier distribution: Topographic and climatic controls in the semi-arid andes,” Geomorphology, vol. 81, no. 1-2, pp. 141–154, 2006. [15] J. Wilson and J. Gallant, Terrain Analysis: Principles and Applications. Wiley New York, 2000. [16] T. Bolch and U. Kamp, “Glacier mapping in high mountains using dems, landsat and aster data,” Grazer Schriften der Geographie und Raumforschung, vol. 41, pp. 37–48, 2006. [17] V. Salomonson and I. Appel, “Estimating fractional snow cover from modis using the normalized difference snow index,” Remote Sensing of Environment, vol. 89, no. 3, pp. 351–360, 2004. [18] G. Macchiavello, G. Moser, G. Boni, and S. Serpico, “Automatic unsupervised classification of snow-covered areas by decision-tree classification and minimum-error thresholding,” in Geoscience and Remote Sensing Symposium, IEEE International, IGARSS 2009., vol. 2. IEEE, 2010, pp. 1000 –1003. [19] L. Zevenbergen and C. Thorne, “Quantitative analysis of land surface topography,” Earth Surface Processes and Landforms, vol. 12, pp. 47– 56, 1987. [20] T. Denoeux and L. M. Zouhal, “An evidence-theoretic k-nn rule with parameter optimization,” IEEE Transactions on Systems, Man and Cybernetics, pp. 1–7, 1998.
1503
