A Land Cover Mapping Algorithm Based on a Level Set Method

Transcription

1 Kasetsart J. (Nat. Sci.) 47 : (03) A Land Cover Mapping Agorithm Based on a Leve Set Method eerasit Kasetkasem, *, Settaporn Sriwiai, hitiporn Chanwimauang and suyoshi Isshiki 3 Abstract A nove supervised cassification agorithm is presented for remotey sensed images using the eve set method under a statistica framework. he eve set method was empoyed to capture the connectivity properties of and cover casses. his work demonstrated that and cover mapping under the maximum a posteriori criteria can be converted into an energy minimization probem of eve set functions. Since the eve set functions are rea-vaued, the optimum soution can be easiy obtained from a gradient search technique. he experimenta resuts showed significant improvements in term of the cassification performance of the approach on both synthetic and sateite images when compared to the maximum ikeihood cassifier. Keywords: image cassification, and cover mapping, image segmentation, eve set method Introduction Remote sensing images are widey used in a wide range of fieds such as natura resource monitoring, urban panning, hazard assessment and especiay and cover mapping. Image cassification or and cover mapping is one of the most important appications of remote sensed images. he task of image cassification is to categorize a pixe or group of pixes in a remote sensing image into one of severa homogeneous and cover casses. Athough this task is usuay simpe for trained personne, it is difficut to program and hence, there is aways a need for more sophisticated image cassification agorithms. Gao and Mas (008) considered two different kinds of cassification methods namey pixe-based and region-based cassifications. In pixe-based methods (Wang et a., 006), a feature vector corresponding to the detaied spectrum of refected ight is assigned to each pixe in an image. hen, by using these feature vectors, each pixe can be abeed into one of the designated and cover casses by comparison with a signature vectors of the casses of interest. Basicay, a pixe wi be abeed as Cass A if its feature vector is cosest to the signature vector of Cass A. In region-based methods (arabaka et a. 009), firsty, the image is divided into many regions using an image segmentation agorithm. hen, each region is cassified into a and cover cass based on its averaged feature vector in the region. he region-based approach is suitabe for and cover mapping on remote sensing images since the and cover casses are ikey to appear in connected regions rather than as isoated pixes. However, since region-based approaches Department of Eectrica Engineering, Facuty of Engineering, Kasetsart University Bangkok 0900, haiand. Image echnoogy Laboratory, Nationa Eectronics and Computer echnoogy Center, Pathum hani 0, haiand. 3 Department of Communications and Integrated Systems, okyo Institute of echnoogy, Ookayama, Meguro-ku, okyo , Japan. * Corresponding author, emai: fengtsk@ku.ac.th Received date : 30/05/3 Accepted date : 5/08/3

2 954 Kasetsart J. (Nat. Sci.) 47(6) assign an entire region to one and cover cass, the performance of this approach can be severey degraded in a scenario where the signa to noise ratio is ow (arabaka et a., 009). he approach that incorporates the spatia dependency of the and cover cass among neighboring pixes into the pixe-based image cassification shoud be more robust when deaing with severe noise than the region-based approaches since the effect of noise can be minimized when information from the neighboring pixes is incorporated (Kasetkasem and Varshney, 003). Consequenty, the objective of this paper was to combine the pixe-based and region-based agorithms for and cover mapping of remotey sensed images. Instead of assigning a pixe to one of the isted and cover casses, the approach used determined the edge of each and cover cass such that the entire region inside the edge beongs to ony one and cover cass. o find the edge between and cover casses, the and cover mapping probem was modified into an image segmentation probem where active contour modes can be appied. he active contour mode was first introduced by Kass et. a. (987) as an image segmentation agorithm to segment objects in an image using dynamic curves. he current approach aimed to mode the dynamic curves as a snake that attempts to rest on the edges among homogenous regions. he resutant position of the snake corresponds to the minimization of an energy function. In fact, energy minimization approaches have been appied successfuy in various image processing probems such as Kasetkasem and Varshney (00, 003), Kasetkasem et a. (005), Kasetkasem and Varshney (0) and Hachama et a. (0). In recent years, the active contour mode has been popuary impemented using the eve set method (Osher and Sethian, 988) and is caed the geometric active contour mode. In this mode, contours are represented as the zero eve set of a higher dimensiona function that may break or merge naturay during the evoution, and the topoogica changes are thus automaticay handed. herefore, the geometric mode is suitabe for the proposed approach agorithm. Materia And Methods Probem statement Let X(S) denote the and cover map (LCM) where S is a set of pixes. We assume that there are L and cover casses in the area of interest and we et Λ {0,,, L } be the cass abes. herefore, we can express the LCM as X(S) Λ S. he abe of LCM at pixe s = (u, v) is denoted by x s which can aso be caed the configuration of X(S) at the site s. he goa of the LCM is to abe each pixe in the image into one of the known and cover casses. Figure shows an exampe of the abeing of a two-cass LCM. Here, the pixes outside and inside the rectanguar box are abeed as one and two to indicate that they beong to Casses and, respectivey. As an aternative to abeing each pixe, one can aso consider the and cover mapping process as a border extraction probem; that is, we want to find the borders between casses. For instance, if we extract the border (Figure ) between Cass and Cass in Figure, we can identify that a pixes outside and inside the border beong to Casses Figure Exampe of a two-cass and cover map.

3 Kasetsart J. (Nat. Sci.) 47(6) 955 and, respectivey. here are many approaches to represent borders. For instance, a border may be modeed as piece-wise continuous ines (Kass et a., 987) or graphs of vertices and borders (Osher and Sethian, 988). A more interesting idea is to represent contours as the zero eve set of a higher dimensiona function (such as two dimensiona to three dimensiona) caed the signed distance function. he signed distance function determines the distance of a given point s from the boundary Ω in a space. Here, the sign is used to indicate whether s is inside or outside Ω. In this paper, we denote φ (S R ) for Λ as a signed distance function for Cass defined in a domain S R R where R denotes the set of rea numbers. he domain S R is caed the extended pixe domain, and can be viewed as an extension of S that incudes non-integer coordinates.since φ (S R ) is the signed distance function, the vaue of φ (s) represents how far a pixe s is from the edge, as given by Equation : d(s, Ω φ (s) = )if x(s) = () d(s, Ω )if x(s) where Ω is the border of the and cover cass and d(s, Ω ) is the shortest distance from s to the border Ω. For exampe, there are two signed distance functions, φ (s) and φ (s), indicating whether a pixe s is inside the border of Casses or, respectivey. Figures 3a and 3b dispay the signed distance functions with respect to Cass and Cass, respectivey, of the LCM given in Figure. We observe that, for pixes inside the border given in Figure, φ (s) is negative whereas φ (s) is positive. he signs of φ (s) and φ (s) are reversed when a pixe is outside the border given in Figure. In fact, we have φ (s) = φ (s). Note here that both signed distance functions are zero at the border pixes in Figure. From the definition of the signed distance function, we can represent the LCM as Equation : L X( S)= H φ ( S) () = 0 ( ) Figure Border of the and cover map given in Figure. Figure 3 Signed distance functions of (a) Cass and (b) Cass for the and cover map in Figure.

4 956 Kasetsart J. (Nat. Sci.) 47(6) where H(z) is the Heaviside function defined as shown in Equation 3: { 0, x < 0 H( z)= (3), x 0 Since the LCM is a function of the eve set function, the probabiity density function of the LCM is the function of a signed distance functions (Equation 4): Pr(X) = Pr(φ 0,, φ L ) (4) Here and throughout the rest of the paper, we omit (S) for the sake of abbreviation. Hence, the margina probabiity density function of the LCM can be written as Equation 5: exp E Pr X Pr X φ ( )= ( φ )= (5) Z where ф = {φ 0,, φ L } is the coection of a signed distance functions, Z is the normaizing constant and E x (ф) is the LCM energy function depending on the vaue of φ 0,, φ L. his energy function shoud be defined such that and cover casses are more ikey to appear as a connected region rather than as isoated pixes and a pixes in the LCM must beong to one and ony one and cover cass. Here, we appy the idea of the eve set method proposed in Chan and Vese (00) to mode E x (ф), and we have Equation 6: E x (ф) = E p (ф) + E (ф) + E a (ф). (6) he first energy term, E p, ensures that φ is a vaid signed distance function and we define the energy term as Equation 7: L ( ) Ep ( φ)= σ ( φ ( s) ) (7) = 0s S where is the gradient operation and α is a nonnegative constant. his term imposes the condition that a signed distance functions in the Eucidean space must have the magnitude of the gradient equa to one, that is, φ (s) = (Li et a., 005). he second and third energy terms, E and E a, represent the ength (Li et a., 005) and the area (Li et a., 005) of the zero eve curve φ (s), and are defined by Equation 8: E φ λ c φ s φ s L ( )= ( ( )) ( ) = 0s S, (8) and Equation 9: E φ ν H φ s a L ( )= ( ( )) = 0 s S, (9) respectivey. Here, c(.) is one if φ (s) changes sign within a pixe s, λ is a non-negative constant and ν can be positive or negative. We observe that the terms c(φ (s)) φ (s) in Equation 8, and H(φ (s)) in Equation 9 have non-zero vaues ony on and inside the border of Cass, respectivey. As a resut, a and cover cass associated with a arge vaue of v is penaized more, and is ess ikey to occur in the LCM. Next, we denote Y(S) as the observed mutispectra image whose observation at a pixe s can be represented in the vector form as y s R B where B is the number of spectra bands. Here, we assume further that observed data at different pixes are statisticay independent for a given LCM, as shown by Equation 0: Pr Y X Pr y x. (0) ( )= ( s s) s S By using the representation given in Equation, the conditiona probabiity can be written as a function of φ 0,, φ L as L ( )= ( )= ( s s = ) ( φ ) Pr Y X Pr Y φ Pr y x H s S = 0 () In this paper, the observed vector for a given and cover cass is assumed to be mutivariate Gaussian distributed (Equation ): exp ( ys x x y s ) s ( s xs ) Pr ( y x µ Σ µ )= s s ( π) B Σ xs () where μ xs and E xs are the mean vector and covariance matrix of the and cover cass x s. By substituting Equation into Equation, the conditiona probabiity becomes Equation 3: exp E Y φ Pr ( Y φ )= (3) ( ) Z Y where Equation 4 defines the reevant term: L E( Y φ )= H ( s) φ ys µ Σ y µ = 0 s S ( ) ( ) ( ) s

5 Kasetsart J. (Nat. Sci.) 47(6) Σ n, (4) and Z Y is a normaizing constant. Note again that the term H(φ (s)) is one if φ (s) > 0 and zero otherwise. By using the chain rue, the a posteriori probabiity of the LCM given the observed mutispectra images can be written as Equation 5: Pr ( Y φ) Pr ( φ) Pr ( X Y )= Pr ( φ Y )=. (5) Pr( Y) Since Pr(Y) is independent of the choice of ф, it can be treated as a constant. Hence, we have Equation 6: Pr φ Y C Pr Y φ Pr φ. (6) ( )= ( ) ( ) s S By substituting Equation 3 into Equation 6, we obtain Equation 7: Pr ( φ Y)= exp E ( φ Y ), Z' (7) where Z is a normaizing constant and independent of the choice of X, and Equation 8: E ( φ Y)= EX ( φ)+ E( Y φ). (8) By substituting Equation 6 Equation 9 and Equation 4 into Equation 8, we obtain Equation 9: L α E φ Y φ s ( )= ( ) = 0s S L = 0s S L = 0s S L = 0 s S Σ ( ) + λc ( φ ( s) ) φ ( s) + ( ( s) ) ν H φ + H ( φ ) ( y µ ) s ( y µ )+ n Σ (9) s Next, we approximate the summation over a pixes in S by the integration over S R and the above equation can be written as Equation 0: L α E ( φ Y) ( φ ) + λδ( φ) φ + νh( φ) s S R = 0 + H( φ ) ( y s µ ) Σ ( s )+ Σ y µ n ds (0) Note here that we repace the function c(.) by the impuse function δ(.) since s S δφ ( ) ds is the R ength of the border of Cass. We aso omit the term (s) for the sake of abbreviation. Optimum and cover mapping probem he cassifier based on the maximum a posteriori (MAP) criterion seects the most ikey LCM among a possibe LCMs given the observed image. he resuting probabiity of error is the minimum among a other cassifiers. he MAP criterion is expressed as Equation (Van rees, 968 and Varshney 997): opt X = argmax Pr ( X Y) () X In genera, Pr(X Y) is a non-convex function and, therefore, a conventiona optimization agorithm may not be appicabe to sove Equation. Furthermore, the number of possibe LCMs is extremey arge. For instance, there are more than possibe LCM images assuming that an LCM is a binary image (having ony two casses) of size 0 0 pixes. For muticass probems such as and cover cassification, this number increases greaty. As a resut, in this paper, we propose to find the optimum soution with respect to φ instead. By using Equations 5 and 7, the optimization probem becomes Equation : opt φ = argmin E ( φ Y ) ( φ) () Optimization agorithm Here, we assume that an anayst seects a sufficient number of training pixes from the observed image. hese training pixes are used to estimate the unknown parameters (for exampe, mean vectors and covariance matrices) used in the characterization of each and cover casses. From our image mode, and since φ 0,, φ L are reavaue functions, the optimum soution of Equation can be obtained by etting the derivative of E(ф Y) with respect to φ for be equa to zero (Equation 3): E ( φ Y )= 0; = 0,,, L. (3) φ

6 958 Kasetsart J. (Nat. Sci.) 47(6) By the cacuus of variations (Li et a., 005), the first variation of the above energy function can be written as Equation 4: E( φo,, φl Y) φ α φ φ φ div λδ( φ ) div φ φ + νδ( φ ) + ( ) δ φ ( ) ( )+ ys µ Σ ys µ n Σ (4) where is the Lapacian operator (Evans, 998) and div is the Divergence operator (Evans, 998). herefore, the function φ that minimizes this function satisfies the Euer Lagrange equations E( φo,, φl Y) = 0. he steepest descent process for φ minimization of the function E ( φo,, φl Y) can be empoyed and we have Equation 5: k k ( ) E φ φ k k o L Y + φ = φ τ,, φ (5) where the superscript k = 0,,, denotes the iteration number, τ > 0 is the step size and φ 0 is the initia signed distance function of Cass. In this work, the initia signed distance functions are derived from the initia LCM denoted by X init. Here, the signed distance function at a pixe s of Cass is set to a positive vaue ρ if a pixe s in the initia LCM beongs to Cass, and is set to ρ, otherwise (Equation 6): ρ φ 0, xinit ( s)= ( s)= (6) ρ, xinit ( s) where X init (s) is the abe of a pixe s in the initia LCM. Note here that, in this paper, ρ is equa to. Since the derivative given in Equation 4 invoves the impuse function, the derivative cannot be computed numericay. As a resut, we foow the work of Samson et a. (000) by approximating the Heaviside and impuse functions as Equation 7: φ πφ + + φ ε ε π ε Hε ( φi )= sin, (7), φ > ε 0, φ < ε, and Equation 8: πφ dh ( φi ) + cos φ δ ( φi )= =, φ dφ (8) i 0, φ >, respectivey. Here is a sma positive vaue and, in this paper, we use the vaue of equa to.0. By appying the approximation given in Equation 8 into Equation 4, the first variation can be approximated as Equation 9: ( ) E φo,, φl Y φ where (Equation 30): E (9) φ φ E = α φ div div λδ ( φ ) φ φ + ( )+ ( ) ν δ φ δ φ ( µ ) ( µ )+ ys Σ ys n Σ (30) Hence, from Equation 30, a new set of signed distance functions can be obtained from Equation 3: k Φ + k k = Φ τ Φ (3) where Φ k = k φ 0 φl is a vector of the signed distance functions at a pixe and k Φ = [ E0 EL ] is the updating vector for the k th iteration. Here, (.) denotes the matrix transpose operation. For a given pixe, the new set of signed distance functions given in Equation 3 can ead to three scenarios: ) ony one signed distance function is greater than zero; ) two or more signed distance functions are greater than zero; and 3) no signed distance function is greater than zero. In the first scenario, one and ony one and cover cass wi be presented on a given pixe whereas the second and third scenarios correspond to cases where more than one and cover cass are present and a and cover casses are absent on a pixe, respectivey. Ceary, the second and third scenarios produce an invaid LCM. As a resut, we propose to imit the update direction of Equation L 3 to be in the region such that = 0 H( φ )= to ensure that one and ony one and cover cass is present on a given pixe. o do that, the update direction must be perpendicuar to the gradient of k

7 Kasetsart J. (Nat. Sci.) 47(6) 959 L = 0 H ( φ )=. Hence, the vaid update direction is given by Equation 3: *k k Φ = Φ Φ k, nn (3) where.,. is the inner product operation, and from Equation 33: L n = δ ( φ0) δ ( φ ) (33) δ ( φ0) δ ( φl ) is the normaized gradient vector of L = 0 H ( φ )=. Again, we repace H(φ ) with H (φ ) due to the same impementation reason given eary in this section. Figure 4 summarizes the proposed agorithm given in this section. Resuts AND DISCUSSION he performance of the proposed agorithm was examined with simuated and actua sateite data sets. hese experiments compared the performance of the agorithm with the maximum ikeihood cassifier (MLC) since the MLC is weknown and widey used in remote sensing image cassification (Richards and Xiuping, 999). Simuated dataset he simuated experiment used the pixe gray scae image with two casses with mean vaues of 0 and 00 for Casses 0 and, respectivey. Figure 5 dispays the ground truth image used in this exampe. Note here that Cass appears as a ring in Figure 5. Next, the independent additive Gaussian noises with zero mean and standard deviation of σ were added to a pixes in the noiseess image to produce the observed noisy image. he vaues of σ were varied from 0 to,000 to simuate different eve of randomness. For σ = 0, the signa to noise ratio (SNR) of the observed noisy image was equa to 0 db whie, for σ =,000, the SNR was equa to db. Figures 6a 6c show the noisy images for the SNRs equa to 0, -., -0dB, respectivey. Sateite image Input data Mean and covariance matrix cacuation raining process Maximum ikeihood cassifier Initiaizing process Energy cacuation Updating surface Evoution process erminate? Land cover mapping image Output data Figure 4 Fow chart for proposed agorithm.

8 960 Kasetsart J. (Nat. Sci.) 47(6) Next, the noisy images were initiay cassified using the maximum ikeihood cassifier (Wang et a., 006) based on the given mean vaues and noise standard deviation. he initia cassified images are given in Figures 7a 7c for various noise Figure 5 Synthetic image with two casses. eves. As the noise standard deviation increased, the number of isoated pixes increased. In particuar, for the noise standard deviation equa to,000, the initia LCM became very noisy and the structure of the ring disappeared. he percentages of correcty cassified pixes of the initia LCMs for σ equa to 0, 9.5 and,000 were 00, 65. and 5.3%, respectivey. hese initia LCMs were submitted to the proposed agorithm and the resuting LCMs obtained from the agorithms after,000 iterations for the parameter setup of α = 0.05, λ = 30.0, ν 0 = ν = -5.0, and τ = are shown in Figures 8a 8c, which show that the agorithm can successfuy extract the ring structure back for σ = 0 and 9.5. However, the agorithm coud ony partiay extract the ring structure back from Figure 6 Noisy images with signa to noise ratio of: (a) 0dB, (b) -.db and (c) -0dB. Figure 7 Cassified images using the maximum ikeihood functions with signa to noise ratio of: (a) 0dB, (b) -.db and (c) -0dB.

9 Kasetsart J. (Nat. Sci.) 47(6) 96 the noisy observed image for the case where σ =,000. he percentages of correcty cassified pixes obtained from the proposed agorithm for σ equa to 0, 9.5 and,000 were 00, and 65.49%, respectivey. Next, the above experiment was repeated 50 times and the averaged percentages of correcty cassified pixes obtained from the proposed agorithm and the maximum ikeihood cassified are summarized in abe. From the t-statistics and the critica vaue for 5% type I error given in abe, the resuting LCMs obtained from the proposed agorithm were significanty better than those obtained from the MLC for σ = In fact, ony at very high SNR (σ = 0) did both the proposed agorithm and the MLC perform simiary because both agorithms made very few cassification errors. Sateite data set A mutispectra image of a part of the Kasetsart University campus, Bangkok, haiand from the QuickBird sateite (Figure 9) and ground data obtained by visua reference (Figure 0) were used for this experiment. Eight and cover casses were identified grass, water, road, Figure 8 Cassified images using the proposed method with signa to noise ratio of: (a) 0dB, (b) -.db, (c) -0dB. abe Percentages of correcty cassified pixes for various noise eves. Noise MLC Proposed Agorithm standard deviation SNR Mean SD Mean SD t-statistic Critica Vaue for 5% ype I Error * * * * * * * * *.003 SNR = Signa to noise ratio; MLC = Maximum ikeihood cassifier. * = Significant difference at P < 0.05 eve of testing.

10 96 Kasetsart J. (Nat. Sci.) 47(6) shadow, buiding, buiding, buiding3 and tree. Buiding, buiding and buiding3 corresponded to different roof coors in the sateite image. In the first stage, mean vectors and covariance matrices were estimated for a casses by manuay seecting,4,,48,,44,,50, 4,0,,667, 3,03 and,870 pixes for buiding, buiding, buiding3, grass, water, road, shadow and tree, respectivey. he mean vectors for the eight casses are given in abe (the covariance matrices are not shown for brevity). hese mean vectors and the covariance matrices were used to obtain the initia LCM (Figure ). A visua comparison between the initia LCM and the ground data (Figure 0) iustrates the poor performance of the MLC since there are many isoated pixes in the initia LCM. Next, the initia LCM, mean vectors and covariance matrices were input to the proposed agorithm and the resuting LCM after,00 iterations is dispayed in Figure. In this experiment, the eve set parameters were: α =.0, λ = 5.0, ν grass = ν water = ν road = ν shadow = ν buiding = ν buiding = ν buiding3 = ν tree = 35.0, and τ = By visua inspection of Figures and, the resuting LCM obtained from the proposed agorithm is more connected with a substantia performance improvement over the initia LCM. Furthermore, the LCM in Figure matched we with the reference data in terms of the smoothness of the casses. here were many misabeed Figure 9 Mutispectra (Quickbird) image of a part of Kasetsart University, Bangkok, haiand. Figure 0 Ground data for sampe area at Kasetsart University campus, Bangkok, haiand.

11 Kasetsart J. (Nat. Sci.) 47(6) 963 pixes between the casses of tree and grass in the initia LCM. However, these misabeed pixes disappeared in the resuting LCM. For the quantitative performance evauation, the confusion matrices for the initia LCMs and the resuting LCMs are shown in abes 3 and 4. he majority of pixes beonged to the tree cass. From abes 3 and 4, the percentages of correcty cassified pixes for the initia and resuting LCMs were 54.5 and 7.03%, respectivey. he performance difference of more than 5% demonstrates the superior performance of the proposed agorithm. abe Mean vectors for a casses for sampe area at Kasetsart University campus, Bangkok, haiand. Red Bue Green Near Infrared Buiding Buiding Buiding Grass Water Road Shadow ree Figure Initia and cover map for sampe area at Kasetsart University campus, Bangkok, haiand. Figure Resuting and cover map for sampe area at Kasetsart University campus, Bangkok, haiand from proposed method after 00 iterations.

12 964 Kasetsart J. (Nat. Sci.) 47(6) Next, the producer (abe 5) and user (abe 6) accuracies were compared for each and cover cass between the initia (MLC) and resuting LCMs. he producer accuracies for the casses of tree and grass increased whie the accuracies of the other and cover casses decreased. In particuar, the producer accuracy for tree increased more than 75% mainy because in the initia LCM (Figure), a arge number of pixes beonging to the tree cass were misabeed as grass. After appying the initia LCM to the proposed agorithm, these sma misabeed patches were removed and repaced by the surrounding tree cass. Since the MAP criteria were empoyed in this paper, the goa of the proposed agorithm was to minimize the overa probabiity of miscassification for a and cover casses rather than the probabiity of miscassification for an individua and cover cass. As a resut, the overa miscassification probaby depended substantiay on the misabeed pixes in the cass of tree because the majority of the area of interest was covered by trees. For abe 3 Confusion matrix for the initia and cover map for sampe area at Kasetsart University campus, Bangkok, haiand. Ground Data Cassified image Buiding Buiding Buiding3 Grass Water Road Shadow ree Number of ground data pixes Buiding Buiding Buiding Grass Water Road Shadow ree Number cassified abe 4 Confusion matrix for the resuting and cover map for sampe area at Kasetsart University campus, Bangkok, haiand. Ground Data Cassified image Buiding Buiding Buiding3 Grass Water Road Shadow ree Number of ground data pixes Buiding Buiding Buiding Grass Water Road Shadow ree Number cassified

13 Kasetsart J. (Nat. Sci.) 47(6) 965 the user accuracy, most and cover casses had higher accuracies when the resuting LCM was compared with the initia one. However, the casses of buiding and tree had ow accuracies due to the increase in the misabeed pixes in the resuting LCM. he main reason for the decrease in the user accuracy for the tree cass was due to the sma areas of roads, water and shadows that surrounded the trees and were cassified in the tree cass. Since the proposed agorithm promotes a more connected and cover map, the sma patches of water, shadow and road were overwhemed by the arge patch of the tree cass. Concusion A nove supervised cassification agorithm for remotey sensed images was presented using the eve set method under a statistica framework. he and cover mapping probem was abe to be converted to the energy minimization of the signed distance functions where the gradient search technique coud be appied. As a resut, the proposed method coud be easiy impemented. he performance of the proposed agorithm using synthetic and sateite images was demonstrated. he experimenta resuts showed that the proposed agorithm coud substantiay outperform the maximum ikeihood cassifier for a simuated and rea dataset. ACKNOWLEDGMEN his research was supported in part by the Kasetsart Research and Deveopment Institute (KURDI) under Grant Number his research work was aso supported in part by the haiand Advanced Institute of Science and abe 5 Comparison of percentage producer accuracy from the initia (MLC) and the resuting and cover map (LCM) for sampe area at Kasetsart University campus, Bangkok, haiand. Land cover cass MLC (%) Resuting LCM (%) Buiding Buiding Buiding Grass Water Road Shadow ree abe 6 Comparison of percentage user accuracy from the initia (MLC) and the resuting and cover map (LCM) for sampe area at Kasetsart University campus, Bangkok, haiand. Land cover cass MLC (%) Resuting LCM (%) Buiding Buiding Buiding Grass Water Road Shadow ree

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