Software like ILWIS and GRASS GIS can be employed for remote sensing image processing and geographic information systems applications. The modules of the aforementioned image processing software are based on conventional multi-class classifiers/algorithms such as maximumlikelihood classifier. These conventional multi-class classifiers/algorithms are usually written in programming languages such as C, C++, and python. The objective of this research is to experiment the use of a binary classifier/algorithm for multi-class remote sensing task, implemented in MATLAB. MATLAB is a programming language just like C, C++, and python. In this research, the support vector machine binary classifier/algorithm based on a one-against-one approach implemented in MATLAB isapplied to remote sensing multi-class problem. Both simulated and empirical satellite remote sensing data are used to train and test a one-against-one support vector machine classifier. For the purpose ofvalidating the experiment, the resulting classified satellite image is compared with the ground truth data. The polynomial kernel function is used for the modelling. In the simulated application, 25 pixels are usedfor the experiment, out of which 6 pixels are used for training while 19 pixels are used for testing. Out of the 19 tested pixels 18 pixels are correctly classified while only 1 pixel is left unclassified. In the empirical application, 256 and 7182 pixels are unclassified and misclassified respectively out of a total of 62500 pixels; and the computed overall accuracy of the experiment is 88.1%. The satisfactory result of the experiment indicates substantial agreement between the classification result and the reference data

Eyo, E

Eyoh, A

Okwuashi, O

English

Software like ILWIS and GRASS GIS can be employed for remote sensing image processing and geographic information systems applications. The modules of the aforementioned image processing software are based on conventional multi-class classifiers/algorithms such as maximumlikelihood classifier. These conventional multi-class classifiers/algorithms are usually written in programming languages such as C, C++, and python. The objective of this research is to experiment the use of the parametric Gaussian mixture model multi-class classifier/algorithm for multi-class remote sensing task, implemented in MATLAB. MATLAB is a programming language just like C, C++, and python. In this research, a computer program implemented in MATLAB is used to experiment the Gaussian mixture model algorithm. Using the supervised classification technique, both simulated and empirical satellite remote sensing data are used to train and test the Gaussian mixture model algorithm. For the purpose of validating the experiment, the resulting classified satellite image is compared with the ground truth data. For the simulated modelling, twenty-five pixels are used for the modelling, out of which six pixels are used for training while nineteen pixels are used for testing. All the nineteen tested pixels are correctly classified. For the empirical modelling, some of the pixels are wrongly classified; the computed overall accuracy is 85.35%; which indicates substantial agreement between the classificationresult and the reference data

AJOL - African Journals Online

GLOBAL JOURNAL OF ENVIRONMENTAL SCIENCES VOL 10, NO.1&2, 2011: 57-65COPYRIGHT© BACHUDO SCIENCE CO. LTD PRINTED IN NIGERIA. ISSN 1596-6194www.globaljournalseries.com; Email: info@globaljournalseries.comSUPERVISED GAUSSIAN MIXTURE MODEL BASEDREMOTE SENSING IMAGE CLASSIFICATIONONUWA OKWUASHI, ETIM EYO, AND ANIEKAN EYOH(Received 27, June 2011; Revision Accepted 23, August 2011)ABSTRACTSoftware like ILWIS and GRASS GIS can be employed for remote sensing image processingand geographic information systems applications. The modules of the aforementioned imageprocessing software are based on conventional multi-class classifiers/algorithms such as maximumlikelihood classifier. These conventional multi-class classifiers/algorithms are usually written inprogramming languages such as C, C++, and python. The objective of this research is to experiment theuse of the parametric Gaussian mixture model multi-class classifier/algorithm for multi-class remotesensing task, implemented in MATLAB. MATLAB is a programming language just like C, C++, andpython. In this research, a computer program implemented in MATLAB is used to experiment theGaussian mixture model algorithm. Using the supervised classification technique, both simulated andempirical satellite remote sensing data are used to train and test the Gaussian mixture model algorithm.For the purpose of validating the experiment, the resulting classified satellite image is compared with theground truth data. For the simulated modelling, twenty-five pixels are used for the modelling, out ofwhich six pixels are used for training while nineteen pixels are used for testing. All the nineteen testedpixels are correctly classified. For the empirical modelling, some of the pixels are wrongly classified; thecomputed overall accuracy is 85.35%; which indicates substantial agreement between the classificationresult and the reference data.KEY WORDS: Gaussian Mixture Model; Image Classification; Remote SensingPreambleThe process of relating pixels in a satellite image to known land cover is called “imageclassification.” The algorithms used to effect the classification process are called “image classifiers”(Mather, 1987). The extraction of land cover information from satellite images using image classifiershas been the subject of intense interest and research in the remote sensing community (Foody &Mather, 2004). Some of the traditional hard classifiers such as minimum distance to means and the boxclassifiers have been in use in remote sensing studies (Peddle et al., 1994; Rogan et al., 2002; Li et al.,2003; Mahesh & Mather, 2003). Because of the strong desire to maximize the degree of land coverinformation extracted from remotely sensed data research into new methods of classification hascontinued (Foody & Mather, 2004). Recently soft classification algorithms such as artificial neuralnetwork, k nearest neighbour, and Gaussian Mixture Model (GMM) have become part of themainstream classification algorithms. The application of GMM to remote sensing image classificationproblems is uncommon. The objective of this research therefore is to illustrate how the GMM algorithmcan be applied to solving multi-class problems in remote sensing image classification. GMM is aparametric probability density function represented as a weighted sum of Gaussian componentdensities. GMM is commonly used as a parametric model of the probability distribution of continuousmeasurements.57Onuwa Okwuashi, Department of Geoinformatics & Surveying, Faculty of Environmental Studies,University of Uyo, Uyo, NigeriaEtim Eyo, School of Civil Engineering & Geosciences, Newcastle University, Newcastle upon Tyne,United KingdomAniekan Eyoh, Department of Geoinformatics & Surveying, Faculty of Environmental Studies,University of Uyo, Uyo, NigeriaGaussian mixture modelGMM presumes that the patterns ix  originate from a probability density )(xp (Bishop, 1995).This density is a linear combination of Gaussian functions )|( jxp ,     jjTjjcxAcxNjxp21exp1)|( . (1)The normalisation constant jN  is selected such that the integral of )|( jxp  equals one (a necessarycondition for a probability density). The negative exponent is a weighted squared distance (calledMahalanobis distance) between x  and the centre jc ; the corresponding weights are given by thesymmetric matrix jA . The boundary that has a Mahalanobis distance to the centre jc  equal to one is ahyper-ellipsoid. The density )(xp  is a weighted sum of the local densities )|( jxp (Bishop, 1995),mjjxpiPxp1)|()()( . (2)To normalise )(xp , the weights )( jP  must sum to one,   mjjP11)( . Therefore, )( jP  can beinterpreted as the probability that patterns originate from the unit j . It is called “prior probability.” Thegoal of the mixture model is to find the unknown parameters jc , jA , and the priors )( jP  for each unit jsuch that the likelihood, )(1 ini xpL  , to obtain the distribution  ix  given the density )(xp  ismaximal (Bishop, 1995). To solve this optimization problem it is common to use a variant of theexpectation maximization algorithm (Bishop, 1995). It consists of two steps which iterate untilconvergence is reached. In the expectation step, the soft-assignment )|( ixjP  for all j  and i  iscomputed based on a given estimate of the parameters jc , jA , and )( jP ; )|( ixjP  is called“posterior probability.” It is computed using Bayes' theorem1,)()()|()|(iii xpjPjxpxjP  . (3)      In the special case of uniform Gaussians that all have the same width and weight )( jP , is the sameas the Gibbs distribution. In the maximization step, the Gaussian's parameters jc , jA , and )( jP  thatmaximize the likelihood given all )|( ixjP  can be directly computed (Bishop, 1995). The result is thatthe centre jc  is the weighted mean of the set  ix ,1The probability  of observing both  and j  can be written in two ways,; is the probability of  (independent of ),  is theprobability of (independent of ),  is the probability of  under the condition that   is58 ONUWA OKWUASHI, ETIM EYO AND ANIEKAN EYOHgiven, and )|( xjP  is the probability of j  under the condition that x  is given. Reorganizing equationb1 about )|( xjP  yields the Baye’s theorem:)()()|()|(xpjPjxpxjP )|()|(11 ni iini ijxjPxxjPc (4)and the matrix jA  is the inverse of the weighted covariance matrix jC ,)|()|(11 ni ini iijxjPxxjPC . (5)The inverse can be computed by extracting all eigenvectors of jC . Thus, the axes of the mentionedhyper-ellipsoid are the principal components of the local data distribution. The size of this hyper-ellipsoidis given by the eigenvalues lj  from the Principle Component Analysis (PCA) (the semi-axis length ofunit j  in the direction l  equals lj ). Finally, the result for the prior probabilities is (Bishop, 1995),niixjPnjP1)|(1)( . (6)      It can be shown that alternating these expectation and maximization steps increases the likelihoodL  in each iteration step (Bishop, 1995). However, local maxima are not avoided. Further, singleisolated data points (outliers) can make the algorithm unstable (Archambeau et al., 2003). If just onepattern is assigned to a unit (that is, the other patterns have almost zero )|( ixjP ) the variance of thelocal Gaussian collapses to zero.Simulated modellingGiven a simulated ground truth data (Table 1) with a matrix size of 5 x 5, and equivalentsimulated satellite remote sensing multi-spectral data that consist of three spectral bands (see Tables 2,3, and 4), we intend to the classify the satellite data given in Tables 2, 3, & 4 into  three classes: water,undeveloped, and developed. Our objective here is to use the satellite spectral bands given in Tables 2,3, & 4 to derive the ground truth data given in Table 1. All the three spectral bands in Tables 2, 3, and 4contain hypothetical DN1 values.Table 1: Ground truth data (water=1, undeveloped cells=2, and developed cells=3)1 1 1 1 21 1 1 2 23 3 1 2 23 3 2 2 23 3 3 2 21A Digital Number or DN is the value stored within a pixel cell of an image. Typically, the DN of the pixelrepresents the amount of light reflected back to the satellite/sensor. A DN of 0 will appear as black,while a DN value of 255 will appear white.SUPERVISED GAUSSIAN MIXTURE MODEL 59Table 2 Band 11 0 4 2 268 10 9 27 2042 40 7 26 2447 43 22 29 3046 45 50 23 25Table 3 Band 278 73 72 74 10375 70 80 104 101180 190 76 106 108186 182 100 109 107188 184 183 105 110Table 4 Band 330 36 34 37 6633 38 31 67 6390 93 39 68 6297 96 60 65 6192 98 99 66 64      To classify the satellite data given in Tables 2, 3, & 4, a training set has to be randomly selected.The training data (six pixels) consist of elements from the three classes (see Table 5).Table 5: Training dataWater Band 1 (1,2) = 0 Band 2 (1,2) = 73 Band 3 (1,2) = 36Water Band 1 (2,1) = 8 Band 2 (2,1) = 75 Band 3 (2,1) = 33Undeveloped Band 1 (1,5) = 26 Band 2 (1,5) = 103 Band 3 (1,5) = 66Undeveloped Band 1 (2,4) = 27 Band 2 (2,4) = 104 Band 3 (2,4) = 67Developed Band 1 (3,1) = 42 Band 2 (3,1) = 180 Band 3 (3,1) = 90Developed Band 1 (4,2) = 43 Band 2 (4,2) = 182 Band 3 (4,2) = 96For modelling convenience let the remainingnineteen cells that were not used for training theclassifier (see Table 6) represent the test set.Conventionally the size of the test set is usuallysmaller than that of the training set in machinelearning. But for the purpose of illustration, let theremaining nineteen cells serve as the test set.60 ONUWA OKWUASHI, ETIM EYO AND ANIEKAN EYOHTable 6: Test dataBand 1 (1,1) = 1 Band 2 (1,1) = 78 Band 3 (1,1) = 30Band 1 (4,1) =47Band 2 (4,1) = 186 Band 3 (4,1) = 97Band 1 (5,1) =46Band 2 (5,1) = 188 Band 3 (5,1) = 92Band 1 (2,2) =10Band 2 (2,2) = 70 Band 3 (2,2) = 38Band 1 (3,2) =40Band 2 (3,2) = 190 Band 3 (3,2) = 93Band 1 (5,2) =45Band 2 (5,2) = 184 Band 3 (5,2) = 98Band 1 (1,3) = 4 Band 2 (1,3) = 72 Band 3 (1,3) = 34Band 1 (2,3) = 9 Band 2 (2,3) = 80 Band 3 (2,3) = 31Band 1 (3,3) = 7 Band 2 (3,3) = 76 Band 3 (3,3) = 39Band 1 (4,3) =22Band 2 (4,3) = 100 Band 3 (4,3) = 60Band 1 (5,3) =50Band 2 (5,3) = 183 Band 3 (5,3) = 99Band 1 (1,4) = 2 Band 2 (1,4) = 74 Band 3 (1,4) = 37Band 1 (3,4) =26Band 2 (3,4) = 106 Band 3 (3,4) = 68Band 1 (4,4) =29Band 2 (4,4) = 109 Band 3 (4,4) = 65Band 1 (5,4) =23Band 2 (5,4) = 105 Band 3 (5,4) = 66Band 1 (2,5) =20Band 2 (2,5) = 101 Band 3 (2,5) = 63Band 1 (3,5) =24Band 2 (3,5) = 108 Band 3 (3,5) = 62Band 1 (4,5) =30Band 2 (4,5) = 107 Band 3 (4,5) = 61Band 1 (5,5) =25Band 2 (5,5) = 110 Band 3 (5,5) = 64      The computer program used to model theGMM algorithm was implemented in MATLAB. Totrain the GMM classifier the means of each classwas computed using the training data given inTable 5. The variance of each class was alsocomputed. An a priori probability for each classwas chosen such that the a priori probabilityfulfils:  0<a priori<1; 0.5 was chosen for eachclass. Then a posteriori probabilities werecomputed for each test point (see Table 8). Foreach pixel, based on the maximum likelihoodprinciple, the class with the highest a posterioriprobability was assigned to that pixel. The modelalso computes the mixing proportion for eachclass (see Table 7). The training and test resultsare display in Tables 7 and 8 respectively.SUPERVISED GAUSSIAN MIXTURE MODEL 61Table 7: Training resultGaussian mixture distribution with 3 components in 3 dimensionsComponent 1: WaterMixing proportion: 0.333333Mean:     4.0000   74.0000   34.5000Component 2: UndevelopedMixing proportion: 0.333333Mean:    27.5000 103.5000   66.5000Component 3: DevelopedMixing proportion: 0.333333Mean:    42.5000 181.0000   93.0000Variances of components 1, 2, & 3 respectively1.0e+003 * [0.3079    2.4443    0.6911]Table 8: Test result (water =1, undeveloped =2, and developed =3)Cell Posterior probability Class RemarkWater Undeveloped Developed1 0.9004 0.0993 0.0004 1 Correct2 0.0002 0.0670 0.9328 3 ,,3 0.0003 0.0790 0.9207 3 ,,4 0.7752 0.2234 0.0013 1 ,,5 0.0006 0.0939 0.9054 3 ,,6 0.0003 0.0751 0.9246 3 ,,7 0.8652 0.1343 0.0006 1 ,,8 0.8202 0.1787 0.0011 1 ,,9 0.7938 0.2049 0.0013 1 ,,10 0.2468 0.7071 0.0461 2 ,,11 0.0001 0.0595 0.9404 3 ,,12 0.8639 0.1355 0.0006 1 ,,13 0.1275 0.772 0.1005 2 ,,14 0.1125 0.7732 0.1142 2 ,,15 0.1732 0.751 0.0758 2 ,,16 0.2465 0.7052 0.0483 2 ,,17 0.1839 0.7419 0.0742 2 ,,18 0.1288 0.7745 0.0967 2 ,,19 0.1542 0.7546 0.0911 2 ,,62 ONUWA OKWUASHI, ETIM EYO AND ANIEKAN EYOHTable 9: Confusion matrix for GMM classificationReference dataWater Undeveloped Developed UnclassifiedPredicted dataWater 8 0 0 0Undeveloped 0 10 0 0Developed 0 0 7 0Unclassified 0 0 0 0It can be discerned from Table 8 that all the test points were correctly classified by the GMM algorithm.Using the confusion matrix visualisation (Table 9), the overall accuracy can be computed as the sum ofthe diagonal elements in the matrix divided by all the elements in the matrix. Therefore, overall accuracy= 25/25 = 100%.Empirical modellingA multispectral Landsat 7 ETM image of Porirua, New Zealand, acquired in 2006 was used forthe experiment (see Figure 3). The Landsat image consists of seven spectral bands, and has a cell sizeof 25m x 25m. The original satellite data were first reviewed in GIS (ArcGIS software); and all sevenbands were extracted using the layer properties tool and visualised in MATLAB (see Figure 3). Beforeimporting the data into MATLAB, they were first converted from raster to ASCII data using the ArcGISconversion tool. MATLAB cannot read raster files; hence the data must be in ASCII format for onwardprocessing in MATLAB. In MATLAB the final study area was extracted from the original satellite image.Some regions of the satellite image were affected by cloud, which was why the final study area did notinclude those regions affected by cloud. All the seven bands were used for the classification experiment.The stratified random sampling was used to select the training data. The classified image was visualisedin the GIS.SUPERVISED GAUSSIAN MIXTURE MODEL 63The results of the GMM experiment are given in Figure 1 and Table 10. The confusion matrixgiven in Table 10 was computed by comparing the result of the GMM classification and the referencedata given in Figure 2. Using the confusion matrix given in Table 10, the computed overall accuracy was85.35%.50 100 150 200 25050100150200250 50 100 150 200 2505010015020025050 100 150 200 2505010015020025050 100 150 200 2505010015020025050 100 150 200 2505010015020025050 100 150 200 2505010015020025050 100 150 200 25050100150200250Band 1                                       Band 2                  Band 3                                      Band 4Band 5                                        Band 6                                      Band 7                                   Satellite imageFigure 1 Extracted bands 1 - 7 of Landsat image of Porirua and original Landsat image of Porirua, New ZealandLegendUnclassifiedDevelopedUndevelopedWater Reference data GMMFigure 2 Classification result for GMM64 ONUWA OKWUASHI, ETIM EYO AND ANIEKAN EYOHTable 10: Confusion matrix for GMMReference dataDeveloped Undeveloped Water UnclassifiedPredicted dataDeveloped 9411 46 0 0Undeveloped 7686 37117 0 0Water 190 1233 6817 0Unclassified 0 0 0 0CONCLUSIONThis study illustrated basically how theGMM algorithm can be applied to theclassification of satellite remote sensing data.The essence of first illustrating the experimentusing simulated data was to help explain how theempirical experiment was implemented. In thesimulated modelling, from Table 9, no water,undeveloped, and developed cells was wronglypredicted.  In the empirical modelling, from Table10, 46 undeveloped cells were wrongly predictedas developed; 7686 developed cells werewrongly predicted as undeveloped; 190 and 1233developed and undeveloped cells wererespectively wrongly predicted as water; and nocell was left unclassified. . From Tables 9 and 10,note that, the diagonal elements are the correctlyclassified pixels. The high computed overallaccuracy espouses previous findings thatadjudge the Gaussian mixture model as one ofthe most robust parametric classifiers.REFERENCESArchambeau, C., Lee, J. A., and Verleysen, M.,2003. On convergence problems of the EMalgorithm for finite gaussian mixtures. InVerleysen, M., (Ed.), Proceedings of theEuropean Symposium on Artificial NeuralNetworks (ESANN 2003) (99-106),Belgium: D-side.Bishop, C. M., 1995. Neural Networks for PatternRecognition. Oxford University Press, UK.Foody, M. G. and Mather, A., 2004. TowardIntelligent Training of Supervised ImageClassifications: Directing Training DataAcquisition for SVM Classification.Remote Sensing of Environment, 93, 107- 117.Li, T. S., Chen, C. Y., and Su, C. T., 2003.Comparison of neural and statisticalalgorithms for supervised classification ofmulti-dimensional data. Int. J. Indus.Eng.—Theory Appl. Pract., 10, 73–81.Mahesh P. and Mather, P. M., 2003. Anassessment of the effectiveness ofdecision tree methods for land coverclassification. Remote Sens. Environ., vol.86, 554–565.Mather, P., 1987. Computer Processing ofRemotely Sensed Images – AnIntroduction. New York: John Wiley andsons.Peddle D.R., Foody, G. M., Zhang, A., Franklin, S.E., and LeDrew, E. F., 1994. Multisource imageclassification II: An empirical comparisonof evidential reasoning and neuralnetwork approaches. Canadian Journalof Remote Sensing, 20, 396 – 407.Rogan, J., Franklin, J., and Roberts, D. A., 2002.A comparison of methods for monitoringmultitemporal vegetation change usingThematic Mapper imagery. Remote Sens.Environ., 80, 143–156.SUPERVISED GAUSSIAN MIXTURE MODEL 65

Supervised Gaussian mixture model based remote sensing image classification

Supervised remote sensing image classification: An example of a one-against-one multi-class polynomial kernel based support vector machine

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Supervised remote sensing image classification: An example of a one-against-one multi-class polynomial kernel based support vector machine

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