Research Artcle Internatonal Journal of Current Engneerng and Technology ISSN 77-46 3 INPRESSCO. All Rghts Reserved. Avalable at http://npressco.com/category/jcet Fuzzy Logc Based RS Image Usng Maxmum Lkelhood and Mahalanobs Dstance Classfers Shvakumar.B.R a*, Pallav.M b a Department of E&C, G.M.I.T, Davanagere, Karnataka, Inda b Department of IT, G.S.S.S.I.E.T.W, Mysore, Karnataka, Inda Accepted 7 March 3, Avalable onlne June 3, Vol.3, No. (June 3) Abstract The conventonal hard clusterng method restrcts each pont of data set to exclusvely just one cluster. As a consequence, wth ths approach the segmentaton results are often very crspy,.e., each pxel of the mage belongs to exactly just one class. However, n many real stuatons, for mages, ssues such as lmted spatal resoluton, poor contrast, overlappng ntenstes, and nose and ntensty n-homogenetes varaton make ths hard (crsp) segmentaton a dffcult task. The fuzzy classfer makes use of spatal features extracted from a multspectral data, and a classfcaton mage s generated usng maxmum lkelhood classfcaton. Fuzzy cluster analyss s performed by allowng gradual membershps, thus offerng the opportunty to deal wth data that belong to more than one cluster at the same tme. Most fuzzy clusterng algorthms are objectve functon based. They determne an optmal classfcaton by mnmzng an objectve functon. In objectve functon based clusterng usually each cluster s represented by a cluster prototype. A case study s presented on dfferent Fuzzy classfcaton methods by varyng the parameters and a comparson s done as to fnd whch method gves hgher accuracy and Kappa value. Two classfcaton methods are used here. They are: Maxmum Lkelhood Classfer and Mahalanobs Dstance Classfer. The data consdered contans both vegetaton and water bodes n equal proporton. The proposed approach decreases the number of msclassfcatons between the Sea Water and Rver Water classes and the number of msclassfcatons between the Hlly Vegetaton and Plan Land Vegetaton classes rasng the overall accuracy to above 8%. Keywords: Fuzzy C-Means (FCM), Fuzzy Supervsed, Maxmum Lkelhood, Mahalanobs Dstance. Introducton Image classfcaton s a complex process that may be affected by many factors. Effectve use of multple features of remotely sensed data and selecton of sutable classfcaton method are sgnfcant for mprovng classfcaton accuracy. Non parametrc classfers such as fuzzy logc, neural network, decson tree classfer and knowledge based classfers have ncreasngly become mportant approaches for multsource data classfcaton. In general mage classfcaton can be grouped nto supervsed and unsupervsed, or parametrc and nonparametrc, or hard and soft (fuzzy) classfcaton, or pxel, subpxel and perfeld. In ths paper, a Fuzzy clusterng based method for mage segmentaton s consdered. Clusterng s a process for classfyng objects or patterns n such a way that samples belongng to same group are more smlar to one another than samples belongng to dfferent regons. Many clusterng strateges *Shvakumar.B.R and Pallav.M are workng as Asst. Prof. have been used, such as the hard clusterng scheme and the fuzzy clusterng scheme. The conventonal hard clusterng method restrcts each pont of data set to exclusvely just one cluster. As a consequence, wth ths approach the segmentaton results are often very crspy,.e., each pxel of the mage belongs to exactly just one class. However, n many real stuatons, for mages, ssues such as lmted spatal resoluton, poor contrast, overlappng ntenstes, and nose and ntensty n-homogenetes varaton make ths hard (crsp) segmentaton a dffcult task. In the other hand, fuzzy clusterng as a soft segmentaton method has been wdely studed and successfully appled n mage segmentaton. Among the fuzzy clusterng methods, fuzzy c-means (FCM) algorthm s the most popular method used n mage segmentaton because t has robust characterstcs for ambguty and can retan much more nformaton than hard segmentaton methods.. Parametrc approach There are many classfer algorthms. In ths paper we 378
Shvakumar.B.R et al Internatonal Journal of Current Engneerng and Technology, Vol.3, No. (June 3) manly consder the followng two classfer algorthms. Maxmum Lkelhood Classfer Mahalanobs Dstance The maxmum lkelhood procedure assumes that the tranng data statstcs for each class n each band are normally dstrbuted (Gaussan). Tranng data wth b- or n-modal hstograms n a sngle band are not deal. In such cases the ndvdual modes probably represent unque classes that should be traned upon ndvdually and labelled as separate tranng classes. Ths should then produce unmodal, Gaussan tranng class statstcs that fulfl the normal dstrbuton requrement. The estmated probablty densty functons for class w (e.g., forest) s computed usng the equaton (). x ˆ pˆ x w exp ˆ ˆ () where, exp [ ] s e (the base of the natural logarthms) rased to the computed power, x s one of the brghtness ˆ values on the x-axs, s the estmated mean of all the values n the tranng class, and ˆ s the estmated varance of all the measurements n ths class. Therefore, we need to store only the mean and varance of each tranng class to compute the probablty functon assocated wth any of the ndvdual brghtness values n t. If our tranng data conssts of multple bands of remote sensor data for the classes of nterest then n that case we compute an n-dmensonal multvarate normal densty functon usng: T p X w where, V V n V exp X M V X M () s the determnant of the covarance matrx, s the nverse of the covarance matrx, and X M T X M s the transpose of the vector. The mean vectors (M ) and covarance matrx (V ) for each class are estmated from the tranng data. Mahalanobs dstance classfcaton s smlar to mnmum dstance classfcaton, except that the covarance matrx s used n the equaton. Varance and covarance are fgured n so that clusters that are hghly vared lead to smlarly vared classes, and vce versa. For example when classfyng urban areas-typcally a class whose pxels vary wdely-correctly classfed pxels may be farther from the mean than those of a class for water, whch s usually not a hghly vared class. The Mahalanobs dstance algorthm assumes that the hstograms of the bands have normal dstrbutons. Formally, the Mahalanobs dstance of a multvarate x ( x, x, x,..., x,) T N vector 3 from a group of values ( wth mean,, 3,...,,) T N and covarance matrx S s defned as: D x x S x T M ( ) ( ) ( ) (3) Mahalanobs dstance (or "generalzed squared nterpont dstance" for ts squared value) can also be defned as a dssmlarty measure between two random vectors and of the same dstrbuton wth the covarance matrx S : d( ) ( ) ( ) (4) 3. Supervsed fuzzy classfcaton Due to the large numbers of spectrally smlar land cover types present n the urban envronment, tradtonal classfcaton approaches such as maxmum lkelhood often result n sgnfcant numbers of msclassfcatons, especally between the Road and Buldng classes, and the Grass and Tree classes. By utlzng spatal features n addton to the spectral nformaton, the Fuzzy pxel-based classfer s able to more accurately classfy hghresoluton magery of urban areas. However, more detal s needed to accurately represent the land cover types present n dense urban areas. A nonroad, non-buldng Impervous Surface class s also needed to represent features such as parkng lots, concrete plazas, etc. To dstngush between these urban land cover classes, an object based classfcaton approach s used to examne features such as object shape and context (neghbourhood) and then classfy the mage objects usng a Fuzzy logc rule base. To facltate object classfcaton, the magery s frst segmented wth a regon mergng segmentaton technque. Several features are extracted from the mage objects and used by the object-based classfer along wth the Fuzzy pxel-based classfcaton. 4. Analyss and results To valdate the applcablty of the proposed method, a case study s presented n ths secton, whch s carred out on IRS-P6/LISS III sample mage wth 3.5m resoluton. The area consdered for analyss purpose s a rectangular area between the ponts 3 o 96 N 74 o 43 E / 3 o 97 N 75 o E as llustrated n Fg.. Fuzzy based mage classfcaton can be carred out n dfferent ways applyng dfferent parametrc rules. In ths case study, two classfcaton methods are manly consdered as parametrc rules. They are: Maxmum lkelhood classfcaton and Mahalanobs dstance classfcaton. The analyss s carred out by varyng the number of classes and also by changng the number of classes per pxel. Dfferent classfcaton methods yelds dfferent results and none of the methods s sutable for varable classes and varable pxels. Dependng upon the nformaton needed about the classfcaton, sutable classes and sutable classes per pxel should be. The selecton of a partcular method s dependent on number of classes and number of classes per pxel. The sutablty of a partcular scheme depends to some extent on the nature of the mage to be classfed. The performance of the methods on the tranng /valdaton 379
Overall Accuracy Kappa Value Shvakumar.B.R et al Internatonal Journal of Current Engneerng and Technology, Vol.3, No. (June 3) data can be used to decde on the best classfer for a gven stuaton. The procedure s repeated for dfferent number of classes and number of classes per pxel. For the dataset consdered, results have been evaluated for: classes and 5 classes per pxel, classes and 8 classes per pxel and classes for classes per pxel. Table II Overall kappa statstcs when the number of classes s and number of classes per pxel s 5. Fg.. 3.5m resoluton mage used for classfcaton study. Table I shows the overall accuracy values for all the set of ponts consdered on the classfed mage for the two classfcaton methods used when the number of classes s and number of classes per pxel s 5. Fg. ndcates the graph of classfcaton accuracy versus the no of ponts on the data. It can be analysed from Fg. that produces hgher accuracy value and shows less varaton n accuracy value compared to the other method. Smlarly, TABLE II shows the Kappa values for classes and 5 classes per pxel for the two classfcaton methods and Fg.3 llustrates ts graph. Table I Overall classfcaton accuracy values when number of classes s and number of classes per pxel s 5. No. Of Ponts Maxmum Lkelhood 9.% 8.% 85.% 7.% 3 83.33% 76.67% 4 8.5% 77.5% 5 8.% 8.% 6 85.% 8.67% 7 8.86% 84.9% 8 8.5% 85.% 5 Mahalanobs Dstance 3 4 5 6 7 8 9 No. of Ponts on data Mahalanobs Dstance Fg.. Graph showng the varaton of accuracy values wth respect to the number of ponts on the data, for Table I. No. of ponts Maxmum Lkelhood.835.743.8.69 3.775.664 4.7565.6648 5.743.78 6.777.78 7.749.753 8.7358.765.5 Mahalanobs Dstance Fg. 3. Graph showng the varaton of Kappa values wth respect to the number of ponts on the data, for Table II. It can be seen from TABLE I and TABLE II that, for classes and 5 classes per pxel, produces best classfcaton results over the data consdered. Table III and Table IV ndcate the Overall Accuracy and Kappa values when the Number of Classes s and Number of Classes per pxel s 8. Table III Overall classfcaton accuracy values when the number of classes s and number of classes per pxel s 8. No. Of Ponts 3 4 5 6 7 8 9 No. of ponts on the data Maxmum Lkelhood Mahalanobs Dstance 9.% 9.% 9.% 85.% 3 9.% 83.33% 4 9.5% 8.5% 5 9.% 86.% 6 88.33% 85.% 7 87.4% 8.43% 8 86.5% 8.% 38
Kappa values Overall Accuracy Overall Accuracy Shvakumar.B.R et al Internatonal Journal of Current Engneerng and Technology, Vol.3, No. (June 3) 5 Fg. 4. Graph showng the varaton of accuracy values wth respect to the number of ponts on the data, for Table III. Table IV Overall kappa statstcs when the number of classes s and number of classes per pxel s 8. No. Of Ponts Maxmum Lkelhood Mahalanobs Dstance.787.88.7633.6875 3.889.673 4.8.6933 5.773.7568 6.753.7339 7.73.6844 8.77.6636.5 3 4 5 6 7 8 9 No. of ponts on the data 3 4 5 6 7 8 9 No. of Ponts on the data Fg. 5. Graph showng the varaton of Kappa values wth respect to the number of ponts on the data, for Table IV. It can be seen from TABLE III and TABLE IV that, for classes and 8 classes per pxel, both the classfer algorthms produce smlar results. But, by takng the average of the classfcaton accuracy, t can be seen that agan produces best classfcaton results over the data consdered. Ths can be more clearly seen n the Graphs llustrated n Fg.4 and Fg.5. Table V and Table VI ndcate the Overall Accuracy and Kappa values when the Number of Classes s and Number of Classes per pxel s. Table V. overall classfcaton accuracy values when the number of classes s and number of classes per pxel s. No. of ponts Maxmum Lkelhood Mahalanobs Dstance 9.% 9.% 8.% 9.% 3 8.% 86.67% 4 8.5% 7.5% 5 8.% 7.% 6 83.33% 75.% 7 85.7% 78.57% 8 85.% 8.% 5 3 4 5 6 7 8 9 Fg. 6. Graph showng the varaton of accuracy values wth respect to the number of ponts on the data, for Table V. Table VI. Overall kappa statstcs when the number of classes s and number of classes per pxel s. No. of ponts No. of ponts on data Maxmum Lkelhood Mahalanobs Dstance.4737.859.598.866 3.679.89 4.746.6565 5.687.6468 6.689.6749 7.73.73 8.733.77 It can be seen from Table V and Table VI that, for classes and classes per pxel agan produces best classfcaton results over the data consdered. Table VII ndcates the summary of all the results that are obtaned for class category ndcatng the average values of both overall classfcaton accuracy and the overall Kappa statstcs. 38
Kappa values Shvakumar.B.R et al Internatonal Journal of Current Engneerng and Technology, Vol.3, No. (June 3) Fg. VI. Graph showng the varaton of Kappa values wth respect to the number of ponts on the data, for TABLE 6. Table VII. Overall classfcaton results for class category. NO. of Classes.5 No. of classes per pxel 5 8 Conclusons 3 4 5 6 7 8 9 No. of ponts on data method used Average of overall classfcato n accuracy (% ) Average of overall kappa statstcs 84.4%.7694 MAHALANOBIS 79.39%.6997 89.77%.7693 MAHALANOBIS 84.575%.738 83.5675%.6598 MAHALANOBIS 8.595%.744 Analyss of the results ndcates that applcaton of Fuzzy Logc makes the RS mage classfcaton more complex. It s because of the type of the data used for classfcaton. Snce we have used a 3.5m resoluton data, whch s consdered as low resoluton data, both methods produce reasonably hgh accuracy value. It s hard to come to a concluson by vsually examnng the classfed mages. Hence accuracy assessment s carred out for numercally fndng whch classfcaton method results n hghest accuracy value. For the case of classes and 5 classes per pxel, produces hghest accuracy value. Agan, as the number of classes per pxel was vared to 8 and, produces best accuracy results. Hence, t can be concluded that, for the data consdered and for classes, Fuzzy based produces best accuracy as compared to Mahalanobs Dstance classfcaton. It should be noted that these results are correct only for the data obtaned. In the study regon, f there s a drastc change such as Industral expanson, human settlement actvty or Deforestaton or Constructon actvty the nature of the data wll change. Then the results defntely wll vary. References James C. Bezdek, James Keller, Raghu Krshnapuram, and Nkhl R. Pal (5), Fuzzy Models and Algorthms for Pattern Recognton and Image Processng, Lbrary of Congress Catalogng-n-Publcaton Data. J. R. Jenson (986), Introductory dgtal mage processng, A remote sensng perspectve, Prentce Hall, New Jersey. John R. Jensen (), Introductory Dgtal Image Processng: A Remote Sensng Perspectve, Prentce Hall Seres. Yan Wang and Mo Jamshd, (4), Fuzzy Logc Appled n Remote Sensng Image, IEEE Internatonal Conference on Systems, Man and Cybernetcs. D.Lu and Q.Weng (March 7), A survey of mage classfcaton methods and technques for mprovng classfcaton performance, Internatonal Journal of Remote Sensng, Vol.8, No.5, 83-87. CONGALTON, R.G. and GREEN, K. (999), Assessng the Accuracy of Remotely Sensed Data: Prncples and practces (Boca Raton, London, New York: Lews Publshers). HUDSON, W.D. and RAMM, C.W (987), Correct formulaton of the Kappa coeffcent of agreement. Photogrammetrc Engneerng and Remote Sensng, 53, pp. 4 4. 38