Supervised Classification High-Resolution Remote-Sensing Image Based on Interval Type-2 Fuzzy Membership Function

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1 remote sensing Article Supervised Classification High-Resolution Remote-Sensing Image Based on Interval Type-2 Fuzzy Membership Function Chunyan Wang 1, Aigong Xu 2, * Xiaoli Li 2 ID 1 School Mining Industry Technology, Liaoning Technical University, Huludao , China; wangchunyan@lntu.edu.cn 2 School Geomatics, Liaoning Technical University, Fuxin , China; lixiaolilntu@163.com * Correspondence: xu_ag@126.com; Tel.: Received: 14 March 2018; Accepted: 2 May 2018; Published: 4 May 2018 Abstract: Because degradation classification accuracy that is caused by uncertainty pixel class classification decisions high-resolution remote-sensing images, we proposed a supervised classification method that is based on an interval type-2 for high-resolution remote-sensing images. We analyze data features a high-resolution remote-sensing image construct a type-1 model in a homogenous region by supervised sampling in order to characterize uncertainty pixel class. On basis model in homogeneous region in accordance with 3σ criterion normal distribution, we proposed a method for modeling three types interval type-2 s analyze different types s to improve uncertainty pixel class expressed by type-1 to enhance accuracy classification decision. According to principle that importance will increase with a decrease in distance between original, upper, lower training data corresponding frequency value in histogram, we use weighted average sum three types as new pixel to be classified n integrated into neighborhood pixel relations, constructing a classification decision model. We use proposed method to classify real high-resolution remote-sensing images syntic images. Additionally, we qualitatively quantitatively evaluate test results. The results show that a higher classification accuracy can be achieved with proposed algorithm. Keywords: interval type-2 ; weighted average; high resolution; remote sensing image classification; type-1 1. Introduction Image classification is basic task for processing remote-sensing images. Its results will greatly affect accuracy subsequent tasks, such as feature extraction, target recognition, ground object classification. Benefiting from rich detailed information ground objects, high-resolution remote-sensing images have good application prospects advantages in large-scale accurate object classification. A high-resolution remote-sensing image, however, has two uncertainties, uncertainty pixel class uncertainty classification decision, both m introduce new problems to design classification algorithm. Remote Sens. 2018, 10, 710; doi: /rs

2 Remote Sens. 2018, 10, The uncertainty pixel class is derived mainly from mixed pixels for medium low-resolution remote-sensing images. For high-resolution remote-sensing images, it is mainly caused by clearly visible surface information. For example, stones on grass, cracks on asphalt pavement, manhole covers on road are clearly visible in high-resolution remote-sensing images. Such detailed information can bring changes to characteristic distribution curve in homogeneous region, reby aggravating uncertainty pixel class causing great difficulties for classification. In addition, for high-resolution remote-sensing images, uncertainty classification decision is furr increased by complexity diversity ground objects lack real surface information. Type-1 ory has a wide range applications in image processing, because it can effectively characterize uncertainty image data itself [1,2], such as uncertainty pixel, inaccuracy boundary contour, so on. Among existing classification algorithms, clustering is one most common effective methods to solve clustering problem uncertain data. For example, Fuzzy C-means (FCM) method is proposed, bringing in local (neighborhood) spatial information. In proposed method, neighborhood relation is modeled by defining deterministic neighborhood pixel spectral measure [3 8], correlation model neighborhood pixels is integrated into FCM based image classification algorithm after establishment by use Markov Rom Field (MRF) model [9,10]. Although uncertainty pixel class caused by pixel spatial correlation is effectively solved, noise is smood, classification accuracy algorithm is improved to a certain extent by se methods, adverse effects on high-resolution images caused by uncertainty classification decision still cannot be hled by se clustering methods. A type-2 [11] is characterized by primary secondary. The each element in type-2 is a set (called primary ) between [0, 1], rar than a single definite value, each element in primary has its corresponding (called secondary ). The three-dimensional, which can describe a large amount uncertain information, is used by type-2. So, when compared with type-1, type-2 can provide richer information present a stronger ability to hle uncertainties. Its popularization application in more extensive fields is limited, however, because complexity its expression reduced type calculation. For type-2 [12], computational cost can be overcome because secondary s all elements in primary are defined as 1. Therefore, data modeling that is based on interval type-2 ory is most commonly used format in practical work. At present, interval type-2 ory has been applied successfully in fields control [13,14], time series decisions [15], speech recognition [16], clustering [17,18], medical image segmentation [19]. The main construction forms, principles, applications interval type-2 model are shown in Table 1.

3 Remote Sens. 2018, 10, Table 1. Type, principle, application interval type-2 model. Model Principle Application Interval type-2 model based on information entropy [20,21] Interval type-2 model based on FCM [22 24] Interval type-2 neural network model [25,26] Interval type-2 Gaussian mixture model [27 29] Based on information entropy in information ory, construct interval type-2 information entropy model by defining conditions information entropy Under framework FCM, construct interval type-2 FCM model by exponential factorization, or clustering center Neural network model operated in accordance with Zadeh Extension Theorem, with interval type-2 signal, interval type-2 or interval type-2 logic activation Mean or stard deviation in Gaussian mixture model Image segmentation/ classification edge detection Fuzzy clustering Fuzzy control Time sequence decision Segmentation/Classification Object identification Type-reducing is a key difficult aspect type-2 ory application. Regarding feature recognition, type-reducing is intended to defuzzify type-2 model to construct a decision model whose quality will directly affect recognition accuracy. For interval type-2 neural network model [30 32], common construction method for decision model is designed as a sum weights used to link upper lower boundary information. The symbol weight is used to judge role on objective. If symbol weight is positive, information is activated. Orwise, information is inhibited. For interval type-2 FCM [33 36] method, factor in its objective is fuzzily, interval matrix interval clustering center are computed by factor. Then, centroid interval clustering center regarding as cluster center is calculated to improve classification accuracy. The decision model, which is modeled by a linear combination upper lower s in Gaussian mixture models (GMM) training samples, is used for speech recognition by Zeng Liu [27]. When compared with traditional construction method for decision model, although uncertainty a decision is considered recognition accuracy is improved to some extent in previous modeling method that is based on interval type-2 model, two problems persist. First, important influence type-1 on a decision is not considered;, second, influence data s spatial correlation on a decision is not considered. The modeling method that is based on interval type-2 ory can be applied to hle a large amount uncertain information from multiple fields. Therefore, to address uncertainty pixel class classification decision high-resolution remote-sensing data, this paper proposes a weighted average supervised classification method based on interval type-2 ory. The classification method is based on a type-1 an interval type-2, it takes pixel spatial correlation into consideration, which can realize accurate classification high-resolution remote-sensing images. This paper is organized as follows. Section 2 contains algorithm description. The construction principle method type-1 model, interval type-2 model, classification decision model are introduced. Additionally, we analyzed application three interval type-2 models. Section 3 contains experiments results. We conducted classification experiments regarding high-resolution remote-sensing images with different resolutions different scales by use both proposed method a traditional method. Additionally, we quantitatively qualitatively analyzed classification results. Section 4 contains conclusions, summarizes proposed method, suggests furr research in future.

4 Remote Sens. 2018, 10, Algorithm Descriptions 2.1. Type-1 Fuzzy Membership Function Model for Homogeneous Region To characterize uncertainty pixel class, for a given image X = {x i, i = 1,..., n}, where n is total number pixels, i is pixel index, x i is spectral measure ith pixel (i.e., grayscale value). The following matrix is established for high-resolution remote-sensing images. U = [ U ]n k, (1) where k is number classeses; j = 1,..., k is category index;, 0 U 1 is ith pixel belonging to jth category, satisfying constraint condition k U = 1. j=1 The Gaussian model is a universal distribution model with good computational performance. In this paper, it is used as type-1 model U for homogeneous region image. { ( ) 2 } 1 xi u j U (x; u, σ) = α j exp 2πσj where α j, u j, σ j are coefficients (0 < α j < 1), mean stard deviation jth homogeneous region model, respectively. In this paper, we supervised each homogenous region selected about its 30% as training samples, n we obtained parameters Gaussian model by use least square histogram fitting method. 1a1 c1 are high-resolution panchromatic remote-sensing images with a resolution 0.5 m, covering typical agricultural areas. 1a2 c2 correspond to type-1 ( Gaussian ) models that were constructed in accordance with proposed method, where * is training data histogram curve is corresponding type-1 model. In 1a1, spectral measure within farml is evenly distributed, so its training data histogram is Gaussian. Therefore, histogram is well fitted by type-1 model that is proposed in this paper. In 1b1, training data histogram exhibits an asymmetrical distribution, because part farml is covered by snow, its spectral measure is overall shifted to right when compared with spectral measure in 1a1. Therefore, proposed type-1 model can reflect only basic distribution histogram. In 1c1, within farml, re are two homogenous regions with distinct differences in spectral measure, spectral measure in two regions is distributed evenly, so corresponding histogram shows a bimodal distribution. In this case, spectral features cannot be characterized accurately by type-1 with a unimodal feature. It is evident that spectral features histogram features same ground object will change uncertainly because clearly visible details ground object in a high-resolution remote-sensing image. Therefore, se uncertain features cannot be characterized by type-1 model. At same time, model established based on pixels with uncertain feature should also be uncertain, this uncertainty will furr cause difficulty classification decision. Therefore, an interval type-2 model for a homogenous region is constructed to characterize model uncertainty to enhance accuracy classification decision. 2σ j 2 (2)

5 model. At same time, model established based on pixels with uncertain feature should also be uncertain, this uncertainty will furr cause difficulty classification decision. Therefore, an interval type-2 model for a homogenous region is Remote constructed Sens. 2018, to 10, characterize 710 model uncertainty to enhance accuracy classification 5 22 decision. Remote Sens. 2018, 10, x FOR PEER REVIEW 5 21 (a1) (b1) (c1) (a2) (b2) (c2) Farml Farml corresponding corresponding model. model. (a1) (a1) Farml Farml 1; (b1) 1; (b1) Farml Farml 2; (c1) 2; (c1) Farml Farml 3; (a2) 3; (a2) Fuzzy Fuzzy model model farml farml1; 1; (b2) Fuzzy Fuzzy model model farml farml 2; 2;,, (c2) (c2) Fuzzy Fuzzy model model farml farml Interval Type-2 Fuzzy Membership Function Model for a Homogenous Region 2.2. Interval Type-2 Fuzzy Membership Function Model for a Homogenous Region On basis Gaussian in homogeneous regions according to On basis Gaussian in homogeneous regions according to 3σ criterion Gaussian distribution, parameters for a homogeneous 3σ criterion Gaussian distribution, parameters for a region are fuzzed to build following three interval type-2 models. homogeneous region are fuzzed to build following three interval type-2 They are models with uncertain mean, with uncertain stard deviation, with uncertain models. They are models with uncertain mean, with uncertain stard deviation, mean uncertain stard deviation, respectively. For previous interval type-2 models, with uncertain mean uncertain stard deviation, respectively. For previous interval type each pixel is an interval, all elements in interval appear with 2 models, each pixel is an interval, all elements in interval same probability. appear with same probability. The Gaussian distributions with uncertain mean or uncertain stard deviation, with The Gaussian distributions with uncertain mean or uncertain stard deviation, with uncertain mean uncertain stard deviation are defined, as follows: uncertain mean uncertain stard deviation are defined, as follows: ( ;, = exp U [, x; u, σ ) { ( ) 2 } 1 xi u j = α j exp u j [u j,] u or + j ] or (3) (3) 2πσj ;, = exp ( U [, ] or (4) x; u, σ ) { ( ) 2 } 1 xi u j = α j exp σ j [σ j, σ + j ] or (4) 2πσj 1 ;, = U ( { ( ) 2 } x; u, σ ) 1 xi u j = α 2 2,, [, j exp u ] 2πσj 2σ 2 j [u j, u + j ], σ j [σ j, σ + j ] (5) j where u u σ σ denote uncertain mean stard deviation. uj u j μj µ + + j σj σ j σj +, σare + j, are left left right right boundary jth interval jth interval mean mean stard deviation. The upper lower s interval type-2 model with uncertain mean, as shown in 2, are given by: ;, < U (x; u, σ) x i < u = j < (6) U + (x) = α j u ; j < x i < u + j, (6), > U (x; u +, σ) x i > u + j ;, = ;, + 2 > + 2, (7) The upper lower s interval type-2 model with uncertain 2σ j 2 2σ j 2

6 Remote Sens. 2018, 10, U + (x) = U (x; u +, σ) U (x; u, σ) x i u j +u + j 2 x i > u j +u + j 2, (7) The upper lower s interval type-2 model with uncertain stard deviation, as shown in 3, are written as: F + (x) = U ( x; u, σ ), (8) F (x) = U ( x; u, σ + ), (9) The upper lower s interval type-2 model with uncertain mean uncertain stard deviation, as shown in 4, are formulated as: Z + = { U + U + F + F + U + < F +, (10) Z = { U F U F U < F The factors a j b j control intervals in which parameters vary, (11) u j = u j a j σ j u + j = u j + a j σ j a j [0, 3], (12) σ j = σ j b j σ + j = σ j b j b j = [0.3, 1], (13) According to 3σ criterion, probability that true value falls in [µ 3σ, µ + 3σ] is 99.7%. Additionally, mean stard deviation for a high-resolution remote-sensing image are positive, so a j [0, 3] b j [0.3, 1] are set to control change range Footprint Uncertainty (FOU) an interval type-2 model. The bigger a j or smaller b j is, wider FOU range larger uncertainty constructed interval type-2 model. Because obvious features ground objects in a high-resolution remote-sensing image, difference in grayscale measures ground objects in homogeneous regions is significant, uncertainty training samples is also relatively large. Therefore, training samples that were extracted by different users or even by same one at different times may not be same, corresponding model for homogenous regions also will change greatly. The Gaussian model that was constructed for a homogeneous region can be any curve shown in 2a or 3a, uncertainty also meets 3σ criterion normal distribution. That is to say, if a series models are constructed within (µ 3σ, µ + 3σ) or (σ j /0.3, σ j ), a qualified curve can be found within this region, no matter what kind uncertainty exists (e.g., different grayscale measure, different people, different prior knowledge, different data source). Training samples local sampling are uncertain, type-1 model based on uncertain local training samples is also uncertain. In this case, interval type-2 model (given an uncertain region for type-1 model) can effectively characterize modeling uncertainty. The interval type-2 model essentially realizes a global constraint on parameter changes type-1 image model, it describes global in same region by modeling uncertainty classification decision. As shown in s 2b, 3b, 4, for a given variable x, re is a clear U in original type-1, is within [U, U + ] for interval type-2. If a is set to be 3 (0.3), in accordance with Equation (5), n re is a 99.7% probability that re is a real (true value corresponding to

7 Remote Sens. 2018, 10, observed value) x within [U, U + ], boundary information reflects uncertainty degree model. As shown in 2, interval type-2 model with an uncertain mean is region that is surrounded by red solid lines in 2b. With change adjustment factor a, region that is covered by interval type-2 model with an uncertain mean will change in horizontal direction, but it will not change in vertical direction. Therefore, this model is suitable for characterizing uncertainty spectral measure in a homogenous region. Remote Sens. 2018, 10, x FOR PEER REVIEW 7 21 Remote Sens. 2018, 10, x FOR PEER REVIEW Interval type-2 model with uncertain mean. Type-1 2. Interval type-2 model with uncertain mean. Type-1 with uncertainty 2. Interval type-2 horizontal direction; model with, uncertain Interval mean. Type-2 Type-1. with uncertainty horizontal direction;, Interval Type-2. with uncertainty horizontal direction;, Interval Type-2. 3a is expression type-1 model with same mean different 3astard is is expression deviations, type-1 3b is expression model with with interval same type-2 samean mean different different stard stard deviations, deviations, with uncertain stard 3b is 3b deviation, expression is expression where interval solid type-2 red interval line represents type-2 upper with uncertain lower boundaries with stard uncertain deviation, stard interval where type-2 deviation, solid where red linesolid represents, red line represents upper solid blue lower upper line boundaries represents lower original boundaries interval type-1 type-2 interval type-2., As shown, in solid 3, blue for line solid interval represents blue line original type-2 represents type-1 original type-1 model. with As uncertain. shownstard As shown in deviation, in 3, for 3, for interval changes interval type-2 type-2 adjustment factor b, region that model is covered with by uncertain interval stard type-2 deviation, changes model with uncertain stard deviation, changes adjustment factor adjustment model will factor change b, in region vertical that direction. is covered Therefore, by interval this model type-2 is suitable for homogeneous b, region that is covered by interval type-2 model will change in model region will where change change in vertical spectral direction. measure Therefore, is not obvious, this model while is suitable difference for homogeneous frequency is vertical region direction. Therefore, this model is suitable for homogeneous region where change relatively where large. change spectral measure is not obvious, while difference frequency is spectral relatively measure large. is not obvious, while difference frequency is relatively large. 3. Interval type-2 model with uncertain stard deviation. Type-1 3. Interval type-2 with uncertainty model with vertical uncertain direction; stard, deviation. Interval Type-1 type-2 3. Interval type-2 model with uncertain stard deviation. Type-1. with uncertainty vertical direction;, Interval type-2 with uncertainty vertical direction;, Interval type shows interval type-2 model with uncertain mean stard deviation. 4 shows The interval uncertainty type-2 is modeled in accordance with 3σ model criterion with in uncertain both mean horizontal stard vertical deviation. directions, The uncertainty spectral is modeled measure in accordance uncertainty with 3σ criterion frequency in both uncertainty horizontal homogeneous vertical region directions, can be simultaneously spectral measure characterized. uncertainty frequency uncertainty homogeneous region can be simultaneously characterized.

8 Remote Sens. 2018, 10, shows interval type-2 model with uncertain mean stard deviation. The uncertainty is modeled in accordance with 3σ criterion in both horizontal vertical directions, spectral measure uncertainty frequency uncertainty homogeneous Remote Sens. 2018, region 10, x can FOR bepeer simultaneously REVIEW characterized Type-2 4. Type-2 model model with with uncertain uncertain mean mean stard stard deviation. deviation. The The parameters parameters α, µ, α, σ, μ, a, σ, a, b need b need to be to estimated be estimated for for construction construction an interval an interval type-2 type-2 model model in any in any homogeneous homogeneous region. region. The The adjustment adjustment factors factors a a b in b this in this paper paper can can be determined, be determined, according according to prior to prior knowledge. knowledge. The The estimation estimation steps steps for for parameters parameters interval interval type-2 type-2 model model are as are follows. as follows. (1) Supervise sample each region to be classified, n solve parameters α, μ, σ by fitting (1) Supervise sample each region to be classified, n solve parameters α, µ, σ by fitting least square histogram. least square histogram. (2) Add adjustment factors a b, in accordance with prior knowledge, n according to (2) Add Equations adjustment (12) factors (13), a construct b, in accordance interval with type-2 prior knowledge, n according model to with Equations uncertain (12) mean, (13), interval construct type-2 interval type-2 model with uncertain model stard with uncertain deviation, mean, or interval interval type-2 type-2 model model with with uncertain uncertain stard mean deviation, uncertain or stard interval deviation. type-2 model with uncertain mean uncertain stard deviation Classification Decision Model 2.3. Classification Decision Model For category any point on image, its classification is only based on single For category any point on image, its classification is only based on single when traditional classification method is used. In this paper, we proposes a when traditional classification method is used. In this paper, we proposes classification decision model that is based on weighted average method considering a classification decision model that is based on weighted average method considering neighborhood pixel correlation. The modeling principle is as follows: in grayscale space, neighborhood pixel correlation. The modeling principle is as follows: in grayscale space, ith pixel belonging to jth category is related not only to three kinds ith pixel belonging to jth category is related not only to three kinds, but also to neighborhood pixel belonging to jth category., but also to neighborhood pixel belonging to jth category. The greater neighborhood pixel belonging to jth category, higher The greater neighborhood pixel belonging to jth category, higher ith pixel belonging to jth category; that is, category a certain pixel is ith pixel belonging to jth category; that is, category a certain pixel actually determined by s pixel itself its neighborhood pixels toger. We is actually determined by s pixel itself its neighborhood pixels toger. constructed classification decision model integrated with spatial relations according to this We constructed a classification decision model integrated with spatial relations according to principle: this principle: F " 1 * = F 1 #N= U, i, (14) (14) i # NN i i ' i N where F is ith pixel belonging to jth classification decision N i where F is ith pixel belonging to jth classification decision Ni is is set 3 3 windows that are centered on ith pixel in jth category. set 3 3 windows that are centered on ith pixel in jth category. Defining Ni = 9, where i = 1,, 9 is pixel index for window, U* can be calculated according to following formula: i U * = P + U + + P + P U + P + + P P U (15)

9 Remote Sens. 2018, 10, Defining N i = 9, where i = 1,..., 9 is pixel index for window, U * can be calculated according to following formula: U = P+ U+ + P U + P U P + + P + P (15) where P, P +, P are weights ith pixel belonging to jth type-1, upper, lower, respectively. U, U, U + are weights ith pixel belonging to jth type-1, lower, upper, respectively. The weight parameters are determined according to similarity between training data belonging to main, upper, lower s, training data histogram. We defined similarity measure by Euclidean distance, that is, weight decreases with increasing in Euclidean distance between value training data corresponding frequency value. Calculation can be carried out, as follows: P = 1 (y U ) 2, P+ = 1 (y U + )2, P = 1 (y U )2 (16) where y is frequency value z i in jth training sample, constraint that weight this point is 1, weight or points is 0 when any denominator in Equation (16) is 0 is satisfied. The classification decision is determined by only when any in a certain category a pixel coincides with histogram this pixel. The interval type-2 model is type-reduced to a type-1 model by previous classification decision model. According to Equations (14) (16), we analyse image to obtain following matrix: F = [F ] (17) n k To obtain a clear classification result, matrix F* classification decision model needs to be defuzzified. In this paper, we carried out defuzzification, according to maximum criterion to realize region classification. D i = arg j {max{f }} i = 1,..., n; j = 1,..., k (18) where D i is category to which ith pixel belongs, classification result is represented by D ={D 1, D 2,..., D n }. 5 shows determination weight parameters when weighted average method is used to construct classification decision model. The red green solid lines, respectively, represent lower upper s interval type-2 model; blue solid line represents type-1 ;, black dot represents frequency ith pixel in sample data jth category. In least square histogram fitting process, frequency value y grayscale x in histogram jth category is considered to be expected value, corresponding is considered to be measured value. The closer measured value is to expected value, higher accuracy measured value will be, greater effect corresponding in classification decision is, vice versa. This principle can be characterized by Euclidean distance among three kinds s corresponding histogram frequency. The effect corresponding in classification decision will increase with a decrease in distance among three kinds training samples in a certain category corresponding frequency. In 5, 1/P, 1/P +, 1/P represent weight type-1, upper, lower ith pixel over y, respectively.

10 Remote Sens. 2018, 10, The specific flowchart for proposed method is shown in 6, where solid line frame Remote for each Sens. task 2018, needs 10, x FOR to be PEER completed, REVIEW dashed line frame is technique for realizing 10 task. 21 Remote Sens. 2018, 10, x FOR PEER REVIEW Schematic diagram weighted average method for classification decision model. 5. Schematic diagram weighted average method for classification decision model. High resolution remote sensing image High resolution remote sensing image Gaussian Type-1 Gaussian Type-1 Homogeneous area sampling supervision sampling Homogeneous area sampling supervision sampling Least Squares Parameter Estimation Least Squares Uncertain mean;uncertain stard deviation;uncertain mean Uncertain uncertain mean;uncertain stard deviation stard deviation;uncertain mean uncertain stard deviation Neighborhood weighted average Neighborhood weighted average Parameter Estimation Interval type-2 Interval type-2 Classification decision model Classification decision model Classification result Classification result 6. The flowchart proposed method. Confusion matrix measure Confusion matrix measure Algorithm verification precision analysis Algorithm verification precision analysis 6. The flowchart proposed method. 3. Experiments Results 6. The flowchart proposed method. 3. Experiments To verify feasibility Results effectiveness proposed method, we carry out classification 3. Experiments Results experiments To verify on high-resolution feasibility remote-sensing effectiveness images with proposed different method, resolutions we carry out different classification scales using To verify proposed feasibility method effectiveness a traditional method. proposed Additionally, method, we we carry quantitatively out classification experiments on high-resolution remote-sensing images with different resolutions different scales qualitatively experiments on evaluate high-resolution classification remote-sensing results. images with different resolutions different scales using proposed method a traditional method. Additionally, we quantitatively using proposed method a traditional method. Additionally, we quantitatively qualitatively qualitatively evaluate classification results evaluate Experimental classification Results results. Analysis Syntic High-Resolution Remote-Sensing Images Experimental Experimental 7 is a syntic Results Results image Analysis Analysis that is Syntic composed Syntic High-Resolution High-Resolution by four types Remote-Sensing Remote-Sensing ground objects Images Images that were acquired from a 0.6 m-resolution QuickBird panchromatic image. The size image is pixels contains four 7 7 ground is is a a syntic syntic object image image types: that that forest is is composed composed I), mine by by four four types types II), farml ground ground objects objects III), that that were were acquired from a 0.6 m-resolution QuickBird panchromatic image. The size image is residential acquired pixels area from contains a 0.6 m-resolution four IV), ground where object pits QuickBird types: rocks panchromatic forest exist in image. I), mine mining The area size II), image farml II), two is 256 kinds 256 III), crops pixels residential with different area grayscales IV), where exist pits in farml rocks exist area in mining III), area houses, roads, II), two kinds vegetation crops exist with in different residential grayscales area exist IV). in These farml detailed area features results III), in significant houses, roads, differences vegetation in internal exist in spectral residential measure area each homogeneous IV). These detailed region, features whereas results spectral in significant measures differences heterogeneous in internal regions have strong similarities, thus increasing classification difficulty. spectral measure each homogeneous region, whereas spectral measures heterogeneous regions have strong similarities, thus increasing classification difficulty.

11 Remote Sens. 2018, 10, contains four ground object types: forest Remote I), mine Sens. 2018, 10, II), x FOR farml PEER REVIEW III), residential area IV), where pits rocks exist in mining area II), two kinds crops with different grayscales exist in farml area III), houses, roads, vegetation exist in residential area IV). These detailed features results in significant differences in internal spectral measure each homogeneous region, whereas spectral measures heterogeneous Remote Sens. 2018, regions 10, x have FOR strong PEER similarities, REVIEW thus increasing classification difficulty Remote Sens. 2018, 10, x FOR PEER R 7. Quick Bird syntic image. 7 is a model in a homogeneous region training data romly sampled from 7 by category by a horizontal axis is intensity vertical axis is. The so represent training models Region I to IV, respectively;, *, corresponding training data histogram four categories, respectively model ( Gaussian ; a classification model based on uncertain mean uncertain stard der Quick fitting Birdeffect syntic image. classification image. accuracy when we adopt 7 is weighted a membershi aver = 0.3, a1 = a2 = a3 = a4 = 3). training data romly sam 7 is a 7 is a model in ain homogeneous In a 8, region training constructed region data histogram based constructed horizontal training forest based axis is on intensity I, represen a data romly sampled from 7 by category area byii, a percentage represented by 30%. blue The + ) horizontal presents represent axis an is asymmetric training model distri training data sampled from 7 by category by a percentage 30%. The intensity vertical axis is. detailed The solid features lines in four homogenous colors represent region, corresponding training histogram training farml data h horizontal axis models is intensity Region I to IV, respectively; vertical, *, axis green +, is )., presents are a bimodal The corresponding solid distribution, lines training datahistogram four colors model represent histogram training models four categories, Region respectively. I to complex IV, respectively; 8airregular is a type-1 distribution, *, +, IV,, represented classification model by model pink are based Δ ). onb ( Gaussian ;, difference 8b is among best classification internal model spectral based measures on fitting uncertain for effect homogenous classification re corresponding training data histogram four categories, respectively. 8a is a type-1 mean uncertain stard derivation, whichground has best objects fitting in effect Quick classification Bird syntic accuracy = 0.3, image, a1 when = a2 ir = a3 = histograms a4 = 3). we adopt weighted model average ( method Gaussian (b 1 = boverlapping 2 = b 3 = b 4 = areas, 0.3, a 1 which = a; 2 = will a 3 = cause a 4 = 3)., classification In 8b difficulty. is 8, These training best histo d classification model In based 8, on training uncertain data histogram mean can not forest uncertain be accurately I, stard represented fitted by derivation, by red * ) Gaussian area which mining has II, represented best b fitting effect area classification II, representedaccuracy by blue + ) when presents shown we anadopt asymmetric in 8a. distribution If it used weighted resulting as classification average from detailed method detailed stard, features in result homw (b1 = b2 = b3 = b4 features in homogenous region, histogram fitting quality. farml As shown III, in represented 8b, by green proposed ) presents method, a bimo fo = 0.3, a1 = a2 = a3 = a4 = 3). presents a bimodal distribution, histogram present an asymmetric residential unimodal area presents distribution, a complex complex irregular farml irregular area distributi also pres In distribution 8, training IV, data represented histogram by pink ). all forest Because can be accurately significant I, represented fitted. In difference addition, by irregular difference among red * ) curve among fitting mining can interna be a area internal II, represented spectral measures by for blue homogenous + ) presents area regions with an irregular asymmetric fourdistribution. kinds ground distribution objects in ground resulting Quick objects from in Quic Bird syntic image, ir histograms have different degrees overlapping areas, whichoverlapping will cause areas, which will detailed features in homogenous region, histogram farml III, represented by classification difficulty. These histogram distribution features can not be accurately fitted can not by be accurately fitted b green ) presents Gaussian a bimodal distribution, (type-1 model), histogram as shown in 8a. residential If it isshown used as area in presents 8a. If it is a us complex irregular classification distribution stard, result will IV, be affected represented by poor by fitting pink quality. Δ ). AsBecause shown infitting quality. 8b, significant As shown in by proposed method, forest mining areas present an asymmetric unimodal distribution, present an asymmetric unimo difference among internal spectral measures for homogenous regions four kinds farml area also presents a bimodal distribution all can be accurately fitted. In addition, all can be accurately fitte ground objects irregular in curve fitting Quick canbird be achieved syntic for residential image, ir area with histograms irregular distribution. have different area with irregular degrees distributio overlapping areas, which will cause classification difficulty. These histogram distribution features can not be accurately fitted by Gaussian (type-1 model), as shown in 8a. If it is used as classification stard, result will be affected by poor fitting quality. As shown in 8b, by proposed method, forest mining areas present an asymmetric unimodal distribution, farml area also presents a bimodal distribution all can be accurately fitted. In addition, irregular curve fitting can be achieved for residential area with irregular distribution.

12 can not be accurately fitted by Gaussian (type-1 model), as shown in 8a. If it is used as classification stard, result will be affected by poor fitting quality. As shown in 8b, by proposed method, forest mining areas present an asymmetric unimodal distribution, farml area also presents a bimodal distribution all can be accurately fitted. In addition, irregular curve fitting can be achieved for residential Remote Sens. 2018, 10, area with irregular distribution. Remote Sens. 2018, 10, x FOR PEER REVIEW Quick QuickBird syntic image image training training data data histogram histogram best classification best classification model. model. Type-1 Type-1 model; model;,, Best classification Best classification decision decision model deviation. model deviation. 9 shows classification results that were obtained by different classification methods. 9 shows classification results that were obtained by different classification methods. 9a f 9a f are are Gaussian Gaussian classification classification (type-1 (type-1 model), model), maximum maximum likelihood classification, classification, FCM FCM classification, classification, HMRF-FCM HMRF-FCM classification, classification, optimal classification optimal classification weighted average weighted method, average method, optimal classification optimal classification neighborhood neighborhood weighted average weighted average method, method, respectively. respectively. (c)

13 Type-1 model;, Best classification decision model deviation. 9 shows classification results that were obtained by different classification methods. 9a f are Gaussian classification (type-1 model), maximum likelihood classification, FCM classification, HMRF-FCM classification, optimal Remoteclassification Sens. 2018, 10, 710 weighted average method, optimal classification neighborhood weighted average method, respectively. (c) (d) (e) (f) Forest Mining area Farml Residential l 9. Quick Bird syntic image classification results. Gauss method; 9. Quick Bird syntic image classification results. Gauss method; Maximum likelihood method; (c) Fuzzy C-means (FCM); (d) Hidden Markov Rom Field Maximum likelihood method; (c) Fuzzy C-means (FCM); (d) Hidden Markov Rom Field (HMRF-FCM); (e) Weighted average method;, (f) Neighborhood weighted average method. (HMRF-FCM); (e) Weighted average method;, (f) Neighborhood weighted average method. Table 2 lists user accuracy, product accuracy, total accuracy, Kappa coefficient that were obtained from classification QuickBird syntic image in 7 by previous methods. The higher se indicators are, more accurate classification results are. 9a,b are classification results that were obtained by Gaussian (type-1 model) maximum likelihood method, respectively. The distribution curves each ground object are assumed to be subject to Gaussian distribution, modeling principles are same. For each region, although re are differences between user accuracy product accuracy after we adopt two classification methods, total classification accuracy is same (total accuracy is Kappa coefficient is 0.839). 9c is classification result that was obtained by FCM method, it is sensitive to difference in grayscale measure homogeneous region because FCM classification principle. The grayscale in homogeneous regions four ground objects in 7 is obviously changed, among all classification methods, only FCM method HMRF-FCM method are unsupervised. Generally, classification accuracy unsupervised classification method is lower than that supervised method if neighborhood relations are not considered. Therefore, accuracy FCM classification method is lowest (user accuracy is product accuracy is 0.809) compared with or classification methods. 9d shows classification result that was obtained by HMRF-FCM method, salt--pepper noise classified area is largely suppressed as relations among neighborhood pixels are considered in classification process. Therefore, when compared with FCM method, Gaussian, maximum likelihood method, classification accuracy HMRF-FCM method is enhanced to some extent (user accuracy is product accuracy is 0.863). Although salt--pepper noise is effectively suppressed by HMRF-FCM method, regional noise is amplified over classification phenomenon is exacerbated, as shown in light areas in upper left corner lower right corner mining area. 9e shows classification result that was obtained by weighted average method based on interval type-2 model. Thanks to supervised sampling, pixel

14 Remote Sens. 2018, 10, grayscale distribution corresponding category can be reflected accurately by histogram information training samples, training sample histogram can be more accurately fitted by constructed classification decision model, all improving noise immunity. Therefore, classification accuracy is higher than that maximum likelihood method, FCM method, HMRF-FCM method. The classification results have a lot noise because noise sensitivity to spatial relationship pixels is not considered in maximum likelihood method, FCM method, weighted average method. The fitting curves in 8 correspond to Regions I, III, II, IV in 9, from left to right. As shown in 8, four ground objects in fitting models have different degrees overlapping areas, whereas misclassified pixels are concentrated in overlapping areas quality pixel classification within se areas cannot be significantly improved by accurately fitting histogram distribution features. For this reason, we integrated neighborhood relations pixels into space image, as shown in 9f. Then, we effectively solved misclassified pixels in overlapping areas fitted models significantly improved classification quality. The user accuracy product accuracy neighborhood weighted method are both above 0.99, presenting best classification result. As shown in Table 2, classification accuracy FCM method is lowest, with a total accuracy a Kappa value When we integrated spatial relations into FCM method, we significantly improved classification accuracy HMRF-FCM method, with a total accuracy a Kappa coefficient When compared with Gaussian (type-1 model) method, maximum likelihood method HMRF-FCM method, total accuracy weighted average method is improved by 4.1%, 3.7%, 3.2%, respectively, Kappa coefficient is increased by 5.0%, 4.9%, 2.6%, respectively. This result proves again that classification accuracy is affected by quality fitted model. The more accurate fitting model, higher classification accuracy. The HMRF-FCM method is suitable for classification high-resolution remote-sensing images as its classification accuracy is furr improved. Table 2. User accuracy, product precision, user accuracy, Kappa value. Method Type-1 model Maximum likelihood FCM HMRF-FCM Weighted average Neighborhood weighted average Accuracy Indicator Homogenous Region I II III IV User accuracy Product precision Total accuracy = 0.879; Kappa = User accuracy Product precision Total accuracy = 0.879; Kappa = User accuracy Product precision Total accuracy = 0.857; Kappa = User accuracy Product precision Total accuracy = 0.898; Kappa = User accuracy Product precision Total accuracy = 0.920; Kappa = User accuracy Product precision Total accuracy = 0.994; Kappa = 0.992

15 User accuracy Weighted average Product precision Total accuracy = 0.920; Kappa = User accuracy Neighborhood Remote Sens. 2018, 10, 710 Product precision weighted average Total accuracy = 0.994; Kappa = Experimental Results Analysis Real High-Resolution Remote-Sensing Images 10 10shows panchromatic images images that that were were taken taken from different from different high-resolution high-resolution remote- remote-sensing images. images. 10a is an IKONOS 10a is animage IKONOS with image a resolution with a resolution 1 m an image 1 m size an image sizepixels pixels. 10b,c are WorldView-2 10b,c are WorldView-2 images with images a resolution with a resolution 0.5 m an 0.5image m size image 256 size 256 pixels pixels pixels, 1024 respectively, pixels, respectively, grayscale is grayscale from light isto from dark. light to dark. 10a contains 10athree contains kinds three ground kinds objects, groundincluding objects, including l, grass, l, grass, forest; forest; 10b contains 10b contains five kinds five kinds ground ground objects, objects, including including snow, snow, building, building, vegetation, ice, ice, water;, 10c contains three kinds ground objects, including buildings, vegetation, water. (c) High-resolution High-resolution remote-sensing remote-sensing images. images. IKONOS IKONOS image; image; World World View-2 View-2 image; image;,, (c) (c) World World View-2 View-2 image. image. s show classification results three images in a e show s show classification results three images in a e show results that we obtained using classification methods in following order: maximum results that we obtained using classification methods in following order: maximum likelihood likelihood method, FCM method, HMRF-FCM method, weighted average method (optimal method, FCM method, HMRF-FCM method, weighted average method (optimal classification), classification), neighborhood weighted average method (optimal classification). For type-1 neighborhood weighted average method (optimal classification). For type-1 model model method maximum likelihood method, only classification result latter method maximum likelihood method, only classification result latter is given in experiment, because ir classification principles are same ir classification accuracy is similar. To quantitatively evaluate classification results, total accuracy, Kappa value, time cost classification results obtained by different classification methods, training data (about 30% total data) different regions each image in 10 are given in Table 3. For three areas to be classified in 10a, due to significant differences in grayscale measurements, all methods, except for FCM method, can achieve higher classification quality. If spatial relationship neighborhood pixels is not considered, misclassified pixels are concentrated primarily in forest area where grayscale changes greatly at boundary between l grass where transitional grayscale exists. For FCM method, by segmenting nonsimilar measure between pixel points cluster centers, a large number pixels in forest area are classified as l, which has a similar grayscale, resulting in a decrease in total classification quality. The total classification accuracy training data is Kappa coefficient is 0.956, presenting lowest classification accuracy. As shown in 11, when compared with maximum likelihood method (see 11a), classification quality is improved by accurate fitting method (see 11d), when weighted average method is used, total classification accuracy training data is Kappa coefficient is Although classification accuracy is improved by weighted average method to some extent, salt--pepper noise cannot be suppressed. Therefore, a certain degree noise still exists in 11d. Because re exist obvious difference in grayscale measure among three kinds regions to be classified salt--pepper noise can be hled effectively by HMRF-FCM method, classification accuracy HMRF-FCM method is higher than that

16 weighted average method is used, total classification accuracy training data is Kappa coefficient is Although classification accuracy is improved by weighted average method to some extent, salt--pepper noise cannot be suppressed. Therefore, a certain degree noise still exists in 11d. Because re exist obvious difference in grayscale Remote measure Sens. 2018, among 10, 710 three kinds regions to be classified salt--pepper noise 16 can 22 be hled effectively by HMRF-FCM method, classification accuracy HMRF-FCM method is higher than that or classification methods without consideration for spatial relationship. or classification Only sporadic methods salt--pepper without consideration noise exists in for forest spatial area, relationship. total Only accuracy sporadic salt--pepper training data noise is close exists to in 1. As forest shown area, in 11e, total by accuracy using mean training all data pixels is close in to 1. As shown in space window 11e, by using as its center mean, all pixels noise in in homogeneous space region window is nearly as its center eliminated,, only a small noise amount in homogeneous noise exists region at is boundary nearly eliminated, heterogeneous only a small region, amount thus achieving noise exists high at classification boundary quality. heterogeneous region, thus achieving high classification quality. (c) (d) (e) Forest L Grass 11. IKONOS image image classification results. results. Maximum Maximum likelihood likelihood method method HMRF-FCM; HMRF-FCM; FCM; (c) FCM; HMRF-FCM; (c) HMRF-FCM; (d) Weighted (d) Weighted average average method; method;, (e), Neighborhood (e) Neighborhood weighted weighted average. average. The five ground objects in 10b have following features: grayscales ice water are similar y can not be visually judged; with ridgeline as division, grayscale difference between both sides gable ro is significant corresponding histogram gable ro presents a bimodal distribution; difference in grayscale vegetation coverage is large as a result bare ground trees;, spectral measure snow is evident throughout almost entire grayscale interval. We classified image in 10b using FCM method. According to similar grayscale measure criterion, regions with a similar spectral measure will be classified as same region. When we adopt FCM method, ice is misclassified as water due to similar grayscale between ice water. For house classification, because dissimilarity measure, as defined by Euclidean distance, which is sensitive to noise outliers, applies FCM method, pixels brighter part ro are misclassified as snow, which has a similar grayscale measure because greatly changed brightness feature on both sides ro. For vegetation classification, we could not classify this area using FCM method because complex grayscale feature in region. Among se classification methods, FCM method shows lowest classification quality, with a total accuracy a Kappa coefficient Among all methods in this paper, FCM HMRF-FCM methods are unsupervised classification methods, rest ones are supervised. Among supervised classification methods, maximum likelihood method can not model bimodal characteristics buildings because its histogram is a unimodal symmetric curve. Therefore, regarding classification a building s

17 Remote Sens. 2018, 10, ro when we adopt maximum likelihood method, ro on light side will be completely misclassified as snow, which has a similar grayscale. When compared with Gaussian maximum likelihood method, fitting weighted average method is more accurate. As training data histogram light backlight side gable ro presents a bimodal distribution, even for maximum uncertainty interval that was obtained by use interval type-2 model in accordance with 3σ criterion, training data histogram light side cannot be included within range interval type-2 model. Therefore, weighted average method, Gaussian method, maximum likelihood method present a similar classification quality for house classification. Similarly, neighborhood weighted average method cannot obviously improve quality house classification. Regarding water ice, when we adopt stard FCM method HMRF-FCM method, we carried out classification based on minimum distance between pixel spectral measure cluster center. According to this principle, similar spectral measures will be classified as same category. Therefore, water ice cannot be distinguished by use stard FCM method HMRF-FCM method because similar grayscale measures. Except for previous two methods, all methods that were used in this paper are supervised sampling methods, classification is carried out according to characteristic distribution curve ice water in line with maximum principle. As corresponding distribution curve spectral measure varies with category ground object, classification water ice can be achieved by all methods that were used in this paper, except for FCM HMRF-FCM methods. The classification accuracy water ice by use all supervised classification methods that are in this paper is higher than that stard FCM method HMRF-FCM method, as shown in Table 3. Regarding classification snow, all methods, except for FCM, misclassify backlight side gable ro as snow. The classification quality snow cannot be improved by HMRF-FCM method, maximum likelihood method, weighted average method, or neighborhood weighted average method. The grayscale feature homogeneous region in vegetation area is complex because existence low plants, trees, bare ground. Regarding classification vegetation when we adopt FCM method, according to similarity spectral measure, pixels that have a similar measure with ice will be misclassified as ice, pixels that have a similar measure with houses will be misclassified as houses, only a small part area can be correctly classified. Therefore, FCM method presents lowest accuracy for vegetation classification. For HMRF-FCM method, salt--pepper noise in vegetation area can be greatly reduced with consideration neighborhood pixels, presenting an obviously higher classification quality than FCM method. Because bare ground that has a similar spectral measure with houses is misclassified as a house, classification quality HMRF-FCM method is obviously lower than or methods. High-resolution remote sensing image classification is suitable for multiple coverage types large scale. Among all supervised classification methods, classification decision maximum likelihood method is based only on Gaussian feature image, whereas classification decision weighted average method is based on primary (Gaussian ), upper, lower s. Therefore, weighted average method is superior to maximum likelihood method for classification vegetation. On or h, proposed method is generally applicable. In follow-up work, proposed method will be applied to classification different types high-resolution remote sensing images (such as multi-spectral images, SAR images, etc.) or tasks, such as feature extraction, target identification, etc., in order to demonstrate its wide applicability.

18 decision weighted average method is based on primary (Gaussian ), upper, lower s. Therefore, weighted average method is superior to maximum likelihood method for classification vegetation. On or h, proposed method is generally applicable. In follow-up work, proposed method will be applied to classification Remote different Sens. 2018, types 10, 710 high-resolution remote sensing images (such as multi-spectral images, 18SAR 22 images, etc.) or tasks, such as feature extraction, target identification, etc., in order to demonstrate its wide applicability. The The fitting fitting models models for for three three ground ground objects objects in in 10c 10c have have following following features: features: grayscale grayscale difference difference building s building s ro ro is is clearly clearly visible visible because because high-resolution high-resolution features; features; spectral spectral measure measure almost almost covers covers entire entire grayscale grayscale measure measure interval; interval; training training data data histogram histogram shows shows an an irregular irregular distribution; distribution; training training data histogram data histogram presents presents an independent an independent double Gaussian double Gaussian distribution distribution as surface as surface water in water lower in right lower corner right corner 10c is frozen; 10c, is frozen; image, size image size 10a c are a c 256 are pixels, pixels, pixels, pixels, 1024 pixels, 1024 respectively, 1024 pixels, so respectively, image size so image 10c is size four times larger 10c than is four that times larger 10a,b. than that 10a,b. (c) (d) (e) Building Vegetation Snow Waters Ice 12. Word View-2 image classification results. Maximum likelihood method; FCM; (c) 12. Word View-2 image classification results. Maximum likelihood method; FCM; HMRF-FCM; (d) Weighted average method;, (e) Neighborhood weighted average. (c) HMRF-FCM; (d) Weighted average method;, (e) Neighborhood weighted average. For classification buildings, we could not visually compare classification quality methods For in this classification paper. However, buildings, by comparing we could not accuracy visually in compare Table 3, it is classification evident that quality proposed method methods can in this obtain paper. higher However, classification by comparing accuracy accuracy than in maximum Table 3, it is likelihood evident that method. proposed For method can obtain higher classification accuracy than maximum likelihood method. For classification vegetation, shadows within building areas are misclassified as water by all methods in this paper. The building areas covered by vegetation, shadows buildings that have similar pixel grayscale with water, shadow features cannot be hled by classification methods that are based on pixels. When we adopt FCM HMRF-FCM methods, we assumed regions to be classified are subject to Gaussian distribution, we could carry out image classification according to minimum similar measure principle. Therefore, buildings corresponding shadows that have large differences in grayscale measure will be misclassified as water when we adopt FCM method, leading to an overclassification water, which reduces total classification accuracy. For HMRF-FCM method, although salt--pepper noise can be effectively hled, regional noise is furr enlarged overclassification phenomenon is furr aggravated, presenting lower total classification accuracy than that FCM method. For classification water, its curve with a double independent Gaussian distribution cannot be accurately fitted by maximum likelihood method, weighted average method, or neighborhood

19 misclassified as water when we adopt FCM method, leading to an overclassification water, which reduces total classification accuracy. For HMRF-FCM method, although salt-pepper noise can be effectively hled, regional noise is furr enlarged overclassification phenomenon is furr aggravated, presenting lower total classification accuracy Remote than that Sens. 2018, 10, FCM 710 method For classification water, its curve with a double independent Gaussian distribution cannot be accurately fitted by maximum likelihood method, weighted average method, or neighborhood weighted average method. Therefore, correct classification frozen water in in lower right corner image cannot be achieved. Note that frozen water is also misclassified as vegetation when we we adopt HMRF-FCM method. For computation time, regardless time-consumption that is caused by manual participation, times that are required for classification 10a c by by maximum likelihood method proposed proposed method method are are about about 1 s, 1 s, 1 s, 1 s, s, respectively. s, respectively. The The times times that that are required are required for for classification classification 10a c 10a c by by FCM method FCM method are about are 150 about s, s, s, s, s, respectively, s, respectively, whereas whereas time that istime required that is byrequired HMRF-FCM by HMRF-FCM method increases method from increases original from 5 s to original about 5133 s to s. about Thus, 133 we s. concluded Thus, we that concluded timethat cost time supervised cost classification supervised classification methods is obviously methods is lower obviously than that lower than unsupervised that unsupervised methods formethods a large map for a sheet. large map sheet. (c) (d) (e) Residential area Vegetation Waters Word Word View-2 View-2 image image classification classification results. results. Maximum Maximum likelihood likelihood method; method; FCM; FCM; (c) (c) HMRF-FCM; HMRF-FCM; (d) (d) Weighted Weighted average average method; method;,, (e) (e) Neighborhood Neighborhood weighted weighted average. average. The following conclusions can be drawn by analyzing classification results syntic The following conclusions can be drawn by analyzing classification results syntic images images real high-resolution images: real high-resolution images: (1) When ground object to be classified complies with stard Gaussian distribution grayscale heterogeneous region overlaps a little, classification accuracy maximum likelihood method, FCM method, weighted average is similar without considering spatial relations. The HMRF-FCM method proposed neighborhood weighted average method can furr improve classification accuracy. (2) When histogram homogenous regions presents a continuous asymmetric unimodal, continuous multimodel, or irregular distribution feature, weighted average method proposed in this paper can accurately fit feature. (3) The classification decision model integrated with spatial relations that is proposed in this paper can effectively deal with salt--pepper noise in image deal with grayscale overlapping in different regions to some extent.

20 Remote Sens. 2018, 10, (4) The time cost proposed method is relatively small for a large map sheet. For example, when map sheet size increases by four times, computation time will increase from original 1 s to 13 s. Therefore, method that is proposed in this paper can be applied to data processing large-scale remote-sensing images. (5) Although accuracy evaluation training data can reflect classification quality different classification methods, it can not precisely reflect classification accuracy whole image. (6) When compared with traditional methods, proposed method can improve classification accuracy is suitable for classification high-resolution remote-sensing images. Table 3. The real high-resolution remote-sensing images evaluation. Images ( 10) (c) Accuracy Indicator Maximum Likelihood Method FCM HMRF-FCM Weighted Average Neighborhood Weighted Total accuracy Kappa Tims (s) Total accuracy Kappa Tims (s) Total accuracy Kappa Tims (s) Conclusions This paper proposes a supervised image segmentation method that is based on interval type-2 model with spatial relationship. The proposed method improves uncertainty expression for pixel, solves problems that is caused by complicated spatial relevance, makes segmentation strategy more accurately. The experiments show that this method is effective feasible. To verify feasibility effectiveness proposed algorithm, we tests classification experiments on syntic images real high-resolution remote-sensing images using proposed method, type-1 model (syntic images), maximum likelihood method, FCM method, HRFCM method. Then, through qualitative quantitative comparisons analyses, we prove that classification accuracy proposed algorithm can be improved. The proposed method is suitable for classification high resolution remote sensing images with multiple coverage types a large scale. The asymmetric unimodal distribution, continuous multimodel distribution, or irregular distribution homogeneous regions can be accurately fitted by proposed method, effect internal noise is suppressed after considering spatial relationship, presenting a relatively good classification high-resolution remote-sensing images. A blurred boundary appeared at same time, however. Therefore, to furr improve proposed algorithm, this will be focus future research. On or h, proposed method is universal in ory. In furr work, proposed method will be applied to classification different types high-resolution remote sensing images (such as multi-spectral images, SAR images, etc.) or tasks, such as feature extraction, target identification, etc. Author Contributions: C.W. A.X. conceived designed experiment; C.W. performed experiment; C.W. X.L. wrote paper. Acknowledgments: This work was supported by National Key Research Development Program China (No. 2016YFC ), Liaoning Provincial Innovation Team Program China (No. LT ), Liaoning Provincial Education Department Program China (LJYL036). We would like to thank LetPub ( for providing linguistic assistance during preparation this manuscript. Conflicts Interest: The authors declare no conflict interest.

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