A simulated Linear Mixture Model to Improve Classification Accuracy of Satellite. Data Utilizing Degradation of Atmospheric Effect

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1 A simulated Linear Mixture Model to Imrove Classification Accuracy of Satellite Data Utilizing Degradation of Atmosheric Effect W.M Elmahboub Mathematics Deartment, School of Science, Hamton University Hamton, Virginia 3668, USA ABSTRACT Researchers in remote sensing have attemted to increase the accuracy of land cover information extracted from remotely sensed imagery. Factors that influence the suervised and unsuervised classification accuracy are the resence of atmosheric effect and mixed ixel information. A linear mixture simulated model exeriment is generated to simulate real world data with known end member sectral sets and class cover roortions (CCP). The CCP were initially generated by a random number generator and normalized to make the sum of the class roortions equal to.0 using MATLAB rogram. Random noise was intentionally added to ixel values using different combinations of noise levels to simulate a real world data set. The atmosheric ttering error is comuted for each ixel value for three generated images with SPOT data. Accuracy can either be classified or misclassified. Results ortrayed great imrovement in classified accuracy, for examle, in image, misclassified ixels due to atmosheric noise is 4 %. Subsequent to the degradation of atmosheric effect, the misclassified ixels were reduced to 4 %. We can conclude that accuracy of classification can be imroved by degradation of atmosheric noise. Keywords: Simulation and modeling, remote sensing data.. INTRODUCTION The value of the land cover classification deends on its accuracy. Low classification accuracy of remote sensing data remains the area of growing concern in scientific community. Therefore researchers in remote sensing have attemted to increase the accuracy of the land cover information extracted from remotely sensed imagery. Factors that influence the classification accuracy are the resence of atmosheric effect and mixed ixel information []. Natural aerosols such as dust articles and water drolet are the main causes of atmosheric noise in satellite imagery [4]. The atmosheric ttered noise error varies with zenith angle, article size distribution, and ttering coefficient and increases for zenith angle exceeds 60 o [3]. The atmosheric error varies also with land cover tye. The error that is distributed within the whole image will lead to misclassification of ixels. A linearly modeled simulated image with atmosheric noise and mixed ixel information (class cover roortion) reresenting a real world data set using SPOT data was generated, however, the focus will be on correcting the atmosheric ttered noise to imrove the image classification accuracy. The most imortant requirements for generation of the linear model are estimation of end member sectra (ure ixel information) and class cover roortion (CCP). In general, the end member sectra (EMS) can be obtained by carefully selecting the ure ixel values from a erfectly homogeneous area of the imagery. Multile member sectra collected from several areas of the imagery should be otimized into a single reresentative EMS, since collected multile sectra include sectral variation due to atmosheric effects and imerfect calibration []. For the estimation of the EMS and cover class roortions the least squares method is used. Constraining methods, including Lagrangian-Least Square- Cover Class Proortions (L-LS-CCP), Weighted-Least Squares- Cover Class Proortions (W-LS-CCP), and Quadratic rogramming constraining method-cover class roortions (Q- CCP) are used to make the sum of CCP equal to.0 []. Random and atmosheric noises are added to simulate real world data sets. The accuracy of classification can be evaluated by comaring classified or misclassified of the corrected image () and the simulated noisy image (). In section.,., and.3, we discuss the rinciles of the linear mixture model, normalized least squares method, and the linear mixture model noise resectively.. Princiles of the Linear Mixture Model According to the linear mixture model, we can write the following: X i = M ij f j + e i, () Where X i reresents the ixel value, M ij is the EMS, f j is cover class roortions, e i is a noise term. M ij is indeendent of f j. In matrix notation, this is: X = Mf + e = µ f + µ f µ c f c + e, () The vector µ i denotes the columns of M []. For least squares estimation of cover class roortion, we assume that all errors are confined to E, and then equation () of the linear mixture model can be modified in the following: X = MF ˆ + E (3) Now the goal of least squares is to otimize the n c EMS matrix Mˆ so that the term X MF is minimized. Using the least squares method, the solution can be decided such that: ISSN: SYSTEMICS, CYBERNETICS AND INFORMATICS VOLUME 3 - NUMBER 5

2 ˆ + T M = X ( F ls ) = X ( F ) [ F ( F )] (4) + (F ) reresents a seudo inverse matrix of F []. The least squares otimization will be used in the data generation exeriment in section.. Normalized Least Squares Method MATLAB normal random generator is used to estimate the CCP. If an estimated vector F $ LS included negative elements, it will be set to zero. For examle, if the vector of the estimated CCP FLS $ is [ ], then the negative roortions and will first be set to zero and the new $F LS vector will be reresented by [ ]. Secondly, each roortion will be multilied by [ / (sum of element)] i.e., [/( )] to yield $ FNLS = [4/ 0 7/ 0] []..3 Linear Mixture Model Noise The ixel values of the simulated image can be calculated based on the linear mixture, equation (). Atmosheric noise is added to the model to simulate the real world data set. The atmosheric noise is derived using the following equations: = n n = ii 0 i ( ) x i ( i!) i ξ (5) 8 3 m m + Q 4 = x [ ] (6) C 0 0 = Q ( θ ) sin φ cos ϕdφ (7) r r 4.5 n ( r) = C ( ) (8) min µ = * C*( ) [ r Q r Q ]*ex( Z/ H)* secθ (.5) n n r min σ ( + A) µ = (( + A) K κ γ η Z Z γ η + ) + (( L L ) / Q min max min max (9) (0) κ = L () η γ = ex( K Z ( + ) cos( θ ) () = cos( θ ) + ( cos( θ ) ) (3) Where Equation (5) reresents Bessel function that is needed to derive the ttering efficiency er single article; Equation (6) reresents the article ttering efficiency; Equation (7) reresents the ttering coefficient of the medium surrounding the article; Equation (8) reresents the size distribution; Equation (9) reresents the ttering coefficient er unit volume; and Equation (0) reresents the ttering noise er ixel. rmin r rmax, r is article size, r min = 0.µ m, r max = 0µm, and C is the unknown constant reresenting the highest concentration of articles in a unit volume. Z is altitude, x is the arameter size H is the le height, m is the comlex index of refraction and H = 0.8 in a clear sky conditions. Q, Q, Qn are the ttering efficiencies for different article sizes ( r, r, r n ) at each image bandwidth assuming that the article sizes are arbitrary ( µ mfor band ; µ m for band ; µ m for band 3). In equation (6), σ reresents an error assuming that a fraction of noise of the ttered radiation is assumed to be transmitted to the sensor and can be converted back from radiances to digital numbers using Equation () [4] A is the ixel area, κ is the ixel value converted to radiances, θ is the zenith angle, Lmin is the minimum ixel value, Lmax is the maximum ixel value, and Qmax is 55 within the image [5]. The noise error for each ixel varies with the zenith angle, size distribution, ttering coefficient, and ixel value. Using a sequence of iterations in addition to emloying randomly collected training sets, we can determine the unknown constant C in Equation (9). To remove the noise, subtraction of the error is essential. Subtraction technique relies on the following exression: Y ij = X ij σ. (0) Where X reresents the inut ixel value at line i (row) and ij samle j (column). The errorσ reresents the noise er ixel as in Equation (0). If deriving the constant C and removing the noise led to reduction in the error matrix (confusion matrix of the classification result) elements that are located off the major diagonal (misclassified ixels), then the overall accuracy reresented by the major diagonal elements would exhibit imrovement. The final ste is the sequence of classifications and evaluations using indeendent training sets of known ground truth locations, error matrices, and KHAT statistics [4]. In section, we discuss the exeriment of the linear mixture model data generation.. DATA GENERATION EXPERIMENTS The generation (6) of the exerimental data sets requires creating end member s sectra and the CCP values according to equation (). Each known EMS data set reresents real world ixel values, for examle, combinations of grass, roads, buildings, dee water, and shallow water were manually extracted from actual SPOT (band, band, band 3) as shown in figures 3, 4, and 5. The EMS was otimized as shown in equation (4). MATLAB random number generator initially generated the simulated CCP values for each class. The different combinations of CCP, L-LS-CCP, W-LS-CCP, and Q-CCP are used as constraining methods to normalize the CCP and make the sum of three roortions equal to. The Q-CCP roved to be the best method. Figures and indicate that this method 6 SYSTEMICS, CYBERNETICS AND INFORMATICS VOLUME 3 - NUMBER ISSN:

3 roduced better results because of a lower RMSE that does not change with samle size. Random noise was intentionally added to ixel values and CCP by different combinations of noise levels to simulate a real world data set using MATLAB rogram. The atmosheric ttering error that is derived in Equation (0) has been comuted and added for each ixel value. The outut image can be dislayed and classified using IRDAS IMAGINE (commercial remote sensing software). The simulated image is also classified following the correction of atmosheric noise. 3. RESULTS The Linear Mixture Model is tested using statistical tests to determine the reliability of the model. The first test indicates that the model is aroriate at 99 % confidence level. The second test deicts that the regression model is significant at 90 % confidence level. The ost-rocessing was erformed as the final ste to test the results by comaring misclassified of the corrected image () and the noisy image (). Higher misclassified indicate low accuracy. The accuracy assessments and results of the linear mixture model are resented in Tables,, and 3. In Table, the total reference are 5700, total misclassification ercent error of is 4 %, and total misclassification ercent error of is 4 %. error due to atmosheric noise is 37 % for dee and shallow water. In Table, the total are 36000, total misclassification ercent error of is %, and total misclassification ercent error of is 5 %. error due to atmosheric noise for grass and trees is 30 %. In Table 3, the total are 36000, total misclassification ercent error of is 7 %, and total misclassification ercent error of is 47 %. error due to atmosheric noise for road and buildings is 40 %. Therefore the atmosheric error is significant, which resulted in low classification accuracy that led to higher misclassified ixels. Image, Image, and Image 3 are integrated into single image. The classification for the integrated image was erformed and the result is shown in Table 4. for roads on the lower art of the image. The total error due to atmosheric noise of image 3 is 40 % and there are 7 % total random error, due to comutations, truncations, and mixed ixel information. These simulation-testing results from images,, and 3 were investigated for the same hyothesis; we can conclude that the linear mixture model exeriments show significant reduction in the misclassified ixels when comaring with ; therefore there is significant imrovement in classification accuracy when the atmosheric error is removed including all the simulated images. 5. REFERENCES [] G. M., Foody, D.P., Cox, Subixel Land Cover Comosition Estimation Using a Linear Mixture Model and Fuzzy Membershi Functions, International Journal of Remote Sensing, Vol. 5, No. 3, 994, [] J.J., Settle, N. A., Drake, Linear Mixing and the Estimation of Ground Cover Proortions, International Journal of Remote Sensing, Vol. 4, No. 6, 993, [3] S. M., Singh, Lowest Order Correction for Solar Zenith Angle to Global Vegetation Index (GVI) data, Intentional Journal of Remote Sensing, Vol. P, No. 0 and, 988, [4] W.M. Elmahboub, An Integrated Atmosheric Correction and Classification Accuracy, Ph.D. Dissertation, University of Wisconsin Madison, Madison WI, 000,. 50. [5] W.M. Elmahboub, F. Scarace, B. Smith, An Integrated Methodology to Imrove Classification Accuracy of Remote Sensing Data, IEEE International Geosciences and Remote Sensing Symosium Proceedings, Vol. IV, 003, [6] W.M. Elmahboub and E. Yankey, Sectral Analysis for Mars Surface Minerals using Hubble Telescoe Digital, SIP 005, DISCUSSIONS and CONCLUSION The main urose for adoting atmosheric correction in the linear mixture model is to investigate its imact on the accuracy of classification. After erforming all the necessary exeriments, Table 3 shows great imrovement in classification accuracy. For image, the shows an error of.6% of misclassified ixels (dee water) at the to of the image comared to an error of 7 % of the. There is an error of 0. % of the, comared to an error of 3 % of the for misclassified ixels of shallow water. There is also an error of % of comared to an error of % of misclassified ixels of dee water. The classification results erformed with higher accuracy. For image there is % error of misclassified ixels comared to % error of the misclassified ixels of grass at the uer art of the image. There is also 6 % error of comared to 7 % error of for misclassified ixels of trees, and 4 % error of comared to 3 % error of for misclassified ixels of grass on the lower art of the image. For image 3.There is 4 % error of comared to 5 % error of misclassified ixels of roads on the uer art of the image. There is.5% error of comared to 9 % error of misclassified ixels of buildings, and.34 % error of comared to a larger 3 % error of 6. FUTURE RECOMMENDATIONS The simulated linear mixture model shows romising results for imroving classification accuracy through degradation of atmosheric ttering noise of satellite data. The accuracy can be significant for a large scene with zenith angle exceeding 60 o where the noise caused by aerosol ttering varies significantly across the scene. ISSN: SYSTEMICS, CYBERNETICS AND INFORMATICS VOLUME 3 - NUMBER 7

4 RMSE Random noise level vs RMSE Shallow water Noise level Figure RMSE of CCP estimation and constraining methods. Series reresents QCCP; series reresents L, W-LS-CCP. Figure 3 Simulation of Image RMSE VS Samle Size Trees 300 RMSE Figure 4 Simulation of Image Samle size 300 Figure RMSE of CCP estimation and constraining methods by changing samle sizes. 300 Figure 5 Simulation of Image 3 8 SYSTEMICS, CYBERNETICS AND INFORMATICS VOLUME 3 - NUMBER ISSN:

5 Class Ref. Mis. Mis. % % Shallow water 490 Figure Trees The integrated simulated image Pixels Pixels Of Of Of Of Building s re 6.6 Table. Comarison between misclassified of and for image. Ref. Mis- Mis- % % Class of of Dee water Shallow water Dee water Table. Comarison between misclassified of and for image. Class Ref. Mis. Mis. % % Table 4 Accuracy assessment for the integrated image Class tye of of Acc Of Acc of Unknown Shallow water Trees % Of of Trees Table 3. Comarison between misclassified of and for image. ISSN: SYSTEMICS, CYBERNETICS AND INFORMATICS VOLUME 3 - NUMBER 9

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