AUTOMATIC PARAMETER ESTIMATION IN MRF BASED SUPER RESOLUTION MAPPING

Transcription

1 AUTOMATIC PARAMETER ESTIMATION IN MRF BASED SUPER RESOLUTION MAPPING ANTENEH LEMMI ESHETE March, 0 SUPERVISORS: Dr. V. A. Toekin Dr. N. A. S. Hamm

2 AUTOMATIC PARAMETER ESTIMATION IN MRF BASED SUPER RESOLUTION MAPPING ANTENEH LEMMI ESHETE Enschede, The Netherands, March, 0 Thesis submitted to the Facuty of Geo-Information Science and Earth Observation of the University of Twente in artia fufiment of the requirements for the degree of Master of Science in Geo-information Science and Earth Observation. Seciaization: Geo-informatics SUPERVISORS: Dr. V. A. Toekin Dr. N. A. S. Hamm THESIS ASSESSMENT BOARD: Prof. Dr.Ir. A. stein Chair Dr. Ir.B.G.H.Gorte Externa Examiner

3 DISCLAIMER This document describes work undertaken as art of a rogramme of study at the Facuty of Geo-Information Science and Earth Observation of the University of Twente. A views and oinions exressed therein remain the soe resonsibiity of the author, and do not necessariy reresent those of the Facuty.

4 ABSTRACT In Markov Random Fied MRF based suer resoution maing SRM the accuracy of cassification is deend on the otima arameters. The smoothness arameter baances the contribution of the rior and ikeihood energy terms. Whereas, arameter baances the contribution of ikeihood energyfrom the anchromatic and mutisectra band. By roer setting of these arameters good cassification accuracy can be obtained. However, oor arameter setting roduces unsatisfactory resuts. Tria and error estimation of the arameters is time consuming. Therefore, this study concentrate on deveoing new modes to estimate the otima smoothness arameter and arameters based on oca energy baance anaysis. The study shows how the otima vaues of the arameters deend on the scae factor and cass searabiity information. The data sets used during this study were synthetic images, generated systematicay with various casssearabiity vaues. This enabes to evauate the modes at different cass searabiity and scae factor information. The contextua and sectra information were modeed with rior and the ikeihood energy functions resectivey. The goba energy was constructed and different combination of and arameters were tried. To find the minimum of the tota energy in ma estimate simuated anneaing agorithm was used. An otima and vaues were identified based on kaa vaue and in order to test the redicted and vaues a range for the otima and vaue was secified. An otima vaue of and arameters exists for each combination of scae and cass searabiity vaues in the anchromatic and mutisectra image. The resut obtained from the deveoed mode for the otima and arameters agree with the emirica data. The study shows that the incororation of information from the anchromatic image increases the cassification accuracy at the ower scae factors, if it is roery estimated. Key words Cass searabiity, Markov random fied MRF, Suer resoution maing SRM. i

5 ACKNOWLEDGEMENTS I exress my secia gratitude to my suervisor Dr. V. A. Toekin for his advice, he and continuous encouragement have contributed significanty to the cometion of this study. I want to extend my areciation to my second suervisor: Dr. N. A. S. Hamm for his critica comments and advice that enhance this work. A woud ike to thank Juan Pabo Ardia Loez, a PhD student at earth Observation Deartment of ITC facuty, University of Twente for his advices and suorts. I am very gratefu to my GFM 00 coeagues for their friendshi over the ast 8 months study eriod. I am thankfu to my Ethioian coeagues for the comany and mora suort. Enumerabe thanks to my famiy members for their ove and suort during my studies in the Netherands. This work woud not have haened without their advices and suorts. Above a, I exress my greatest thanks to Amighty God, who made me His creature and gave me His divine grace to successfuy accomish this study; a this woud not have been ossibe without His wi. Lord, Thank you ii

6 TABLE OF CONTENTS. Introduction..... Background..... Probem statement Research objective Research questions Research setu Structure of the thesis...3. iterature review Previous works of MRF based suer resoution maing Parameter estimation techniques Methods Suer resoution maingsrm Synthetic data sets and cass searabiity MRF Estimation of and arameter Simuated Anneaing Accuracy assessment and erformance anaysis Resuts Exerimenta resuts from synthetic datasets λ and λ estimation resuts from synthetic image arameter estimation resut from the rea image Summary of observation from the resuts discussions,concusion and recommendation Discussions Concusion Recommendations List of references Aendix A. Summary of resuts for otima λ and λ an vaues B. Summary of the resut for otima λ and λ an estimation with average cass searabiity iii

7 LIST OF FIGURES Figure 3.: Construction of synthetic images. a Fine-resoution mutisectra image x. b Reference image with three casses, green: shadow vegetation, white: grass, brown: tree Figure 3.: Degraded synthetic mutisectra 30x30 ixe and anchromatic 60x60 ixe images.... Figure 4.: suer resoution ma resut.a owest kaa, b highest kaa, c reference image Figure 4.: Otima vaue at different scae and cass searabiity in the mutisectra and anchromatic image. Lines are added to faciitate the interretation of the data Figure 4.3: otimaan vaue at different scae and cass searabiity in the mutisectra and anchromatic image. Lines are added to faciitate the interretation of the data Figure 4.4: The effect of cass searabiity on the otima vaues of and an. a and c show the change of the otima and an vaues resectivey, when cass searabiity in the mutisectra image changes for a fixed JMZ vaue of 0.0. Here, b and c show the change of the otima and an vaues resectivey, when cass searabiity in the anchromatic image changes for a fixed JMY vaue of Figure 4.5: The effect of scae factor and cass searabiity in the cassification accuracy kaa vaue Figure 4.6: Otima vaues for varying arameters S and JMY. : The exerimentay determined otima vaues. range: The range of corresonding to K 0.85 k. : The estimation from the mode max Figure 4.7: Otima an vaues for varying arameters S and JMY. The exerimentay determined otima vaues. an range: The range of an corresonding to K 0.85Kmax.* an: The estimation from the mode. 30 Figure 4.8: Otima vaues for varying arameters S and JMY. an & : The exerimentay determined otima vaues. * an & : The estimation from the mode. an range & range: The range of an and corresonding to k 0.85k max. Here a and b for JMY vaue of 0.5 and c and d for JMY vaue of.0. e and f for JMY vaue of.9 for a fixed JMZ vaue of iv

8 LIST OF TABLES y Tabe 3.: Jeffries-Matusita distance between the casses for JM z Tabe 3.: Jeffries-Matusita distance between the casses for JM Tabe 3.3: Reation between minima and average Jeffries-Matusita distance in image y and z... 3 v

9 LIST OF VARIABLES Sectra cass and Cass mean vector t A Transose of the matrix A C Covariance inverse of sectra cass Tr A denotes sum of the diagona eements of the matrix A. C Covariance matrix of the sectra cass avg B JM x Variance of the sectra cass average Bhattacharyya distance Jeffries-Matusita distance Fine resoution mutisectra image λan Panchromatic Y B Bhattacharyya distance in the mutisectra image z B Bhattacharyya distance in the anchromatic image y JM Jeffries-Matusita distance in the mutisectra image z JM Jeffries-Matusita distance in the anchromatic image y JM avg Average Jeffries-Matusita distance in the mutisectra image z JM avg Average Jeffries-Matusita distance in the anchromatic image vi

10 AUTOMATIC PARAMETER ESTIMATION IN MRF BASED SUPER RESOLUTION MAPPING. INTRODUCTION.. Background Land cover maing is a tyica and imortant aication of remote sensing data. Accurate and cover information is needed at a reasonabe cost to many anning and monitoring rograms. Different organization ike geoogica survey and nationa maing agencies are interested in extracting and cover information from remote sensing images. Different image rocessing and anaysis techniques are used to extract information from the image. The traditiona aroach to and cover maing is through hard cassification from remotey sensed data in which each ixe is assigned to one and cover tye. However this cassification method is not aroriate when and cover information is required at sub-ixe eve articuary in coarse satia resoution image, where the resence of more than one tye of and cover casses in a ixe, which is commony referred to as mixed ixe. In sub ixe cassification the ixe is resoved in to various cass roortions to sove the robem of mixed ixes. However, it does not account the satia distribution of cass roortions within the ixe Kasetkasem et a., 005. To overcome these robems suer resoution maing SRM techniques have been deveoed. SRM is a and cover cassification technique that roduces mas of a finer satia resoution than that of an inut image. It can be considered as a further ste after sub-ixe cassification in a sense that not ony the fractions of casses within coarse resoution ixes are estimated, but aso the satia distribution of cass roortions within and between ixes is consideredtoekin and Stein, 009. The cass roortion in coarse resoution ixes is comuted in the soft cassification ste with the use of techniques such as inear sectra unmixing, neura network and fuzzy cassification. Accuracy of any and cover cassification technique is infuenced by sectra searabiity of cassesswain and Davis, 978, which is the measure of simiarity between sectra signatures. For ow cass searabiity, cassification eads to confusion between casses. In SRM accuracy of cassification is infuenced by scae factor and cass searabiity but it is difficut to searate the infuences of the two, because cass searabiity deends on cass sectra variation, which in turn, deends on scae.toekin and Stein, 009 For many aications the information obtained from the singe image is incomete, imrecise or inconsistent. Additiona source may rovide comementary informationsoberg et a., 996. Fine satia resoution images rovide fewer sectra bands and arger within-cass variation than the coarser resoution images whereas, the satia resoution of the coarser resoution images are ess than the fine resoution images. Due to these reasons, techniques have been deveoed that make an advantage to use both fine satia resoution and sectray rich coarse satia resoution images, such as image fusion.soberg et a., 996 Markov random fied theory rovide a suitabe and consistent way for modeing context deendent entities such as image ixes and correated featuresli, 00. In SRM satia deendency between and within ixes can be enhanced by integrating satia context. Satia context is defined by the correation between satiay adjacent ixes in satiay neighbouring ixes. The satia context is very imortant for

11 AUTOMATIC PARAMETER ESTIMATION IN MRF BASED SUPER RESOLUTION MAPPING the interretation of a scene and it may be derived from satia, sectra and temora attributes. More information can be derived by considering the ixe in context with other measurement and the suitabe use of context aows the eimination of ossibe ambiguities, the recovery of missing information, and the correction of errors Tso and Mather, Probem statement Markov Random Fied mode ays an imortant roe in image anaysis because it integrates the contextua information associated with the image data in the anaysis rocess, through the definition of suitabe energy functions. However, an MRF mode usuay requires an estimation of one or more interna arameters before the aication of the mode. Particuary in the context of suervised cassification, tria-and-error rocedures are tyicay used to choose suitabe vaues for at east some of the mode arametersoberg et a., 996. MRF arameter estimation is difficut, eseciay when the number of information sources increase. U c y, z U c U z c U y c. The mode. was introduced by Toekin, et a. 00. is an interna arameter of the MRF based SRM mode which baances the contributions of the conditiona energy from the mutisectra and anchromatic image. Whereas, the smoothness arameter baances the contribution of the rior energy and conditiona energy to the goba energy. To increase the cassification accuracy these arameters must be roery estimated. Tria and error estimation of these arameters is time consuming and inefficient. There is no existing method that estimates the otima arameter automaticay. To obtain higher cassification accuracy efficienty both the and arameter must be estimated otimay. Therefore, this study focuses on deveoing a mode for the automatic estimation of and arameters..3. Research objective.3.. Genera objective The genera objective of this research roject is to deveo modes for the automatic estimation of the otima arameters and in MRF based suer resoution maing..3.. Secific objective To achieve the genera objective the foowing secific objectives have been identified a. To identify how the scae factor and cass searabiity affects the otima and arameter estimation. b. To deveo modes to be used for the otima and arameter estimation. c. To test the modes..4. Research questions a. How does the scae factor infuence the otima and arameters? b. How does cass searabiity affect the otima and arameters? c. How to deveo modes to be used for the otima and arameters estimation? d. How shoud the modes be assessed?

12 AUTOMATIC PARAMETER ESTIMATION IN MRF BASED SUPER RESOLUTION MAPPING.5. Research setu The adoted setu is carried out in six hases:.5.. Synthetic image generation Severa synthetic images are generated by varying the cass searabiity in the assumed high resoution mutisectra image..5.. Image degradation The mutisectra and anchromatic images are degraded satiay and sectray from the assumed high resoution mutisectra image by a degradation mode Modeing the rior and conditiona energies The rior information is modeed from the assumed fine resoution mutisectra image using the Markov Random Fied mode. The conditiona energy of the anchromatic and mutisectra image is modeed from the two satiay and sectray degraded images Parameter estimation The modes are deveoed for the automatic estimation of the otima and arameter in MRF based suer resoution maing based on oca energy baance anaysis Simuated Anneaing otimization The tota conditiona energy and the rior energy are integrated with the MRF mode under the Bayesian framework to obtain the maximum robabiity that is used to get otima soution for the outut image. The MAP estimate for the suer resoution ma is found by minimization of the tota energy by using simuating anneaing agorithm Accuracy assessment and erformance anaysis The accuracy is measured in kaa coefficient and the erformance of the modes is assessed with the numerica otima vaue obtained by the exeriment..6. Structure of the thesis This thesis contains five chaters. Chater describes the background, the robem statement, the objectives, the research questions and the aroach of the research. Chater resents a iterature review on revious work on MRF based suer resoution maing and arameter estimation techniques. Chater 3 describes about synthetic image generation and and arameter estimation techniques deveoed in this study. Chater 4 resents the resut of the research. Finay Chater 5 resents discussion, concusion and recommendation for further research. 3

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14 AUTOMATIC PARAMETER ESTIMATION IN MRF BASED SUPER RESOLUTION MAPPING. LITERATURE REVIEW This chater exains revious works of MRF based suer resoution maing and reviews existing arameter estimation techniques.. Previous works of MRF based suer resoution maing Kasetkasem, et a.005 introduced MRF mode based aroach for the generation of suer resoution and cover ma from remote sensing data. The method works based on the assumtions that there is no mixed ixe in the fine satia resoution images and the sectra vaues of casses in a fine satia resoution image foow a mutivariate norma distribution. It was aied into two hases: in the first hase initia SRM is generated from fraction images and in the second hase otimized SRM is roduced by udating the ixes iterativey. Before imementing the second hase, it is imortant to determine neighbourhood window size that infuences the abeing of the centra ixe in the otimization rocess. Some of the imitation of the method was the weights given to the neighbouring ixes were estimated from the ground truth data which is not aways easy to obtain. Moreover the neighbourhood size was fixed to second order for any scae factor vaue which imits the effectiveness of the method to work correcty at any scae factor. Haiu 006 assessed the suitabiity of MRF based SRM techniques for suer resoution and cover maing with synthetic images and remotey sensing data. First the satia and the sectra information were modeed with the rior and ikeihood energy function then the smoothness arameter was introduced to contro the two energy function. SA was used to erform goba energy minimization and the resut of the MRF based SRM was evauated by comaring to the fine resoution reference ma. Haiu identified severa factors that can affect the accuracy of SRM ike the smoothness arameter, neighborhood size, initia temerature, temerature udating, and cass searabiity, object size and scae factor. Finay, Haiu 006 found that MRF based SRM method roduces a high quaity SRM when the neighborhood size grows in reation to the scae factor and the otima vaue of the smoothness arameter was affected with the tye of scene and cass searabiity. The study aso shows that, it is ossibe to get a reasonabe accuracy even for oory searabe casses by setting the smoothness arameter to the otima vaue. Toekin, et a 00 extended the contextua MRF based SRM method deveoed earier for mutisectra image to incude the anchromatic band for individua tree crown objects extraction urose in urban area. Because of the imited sectra information offered by the sensors, It is difficut to discriminate tree crown objects from other and cover casses such as grass and shrubs by using sectra ixe-based cassification techniques. However, the robem was soved in this method using contextua cassification aroach and the SRM technique was used to sove robems reated to satia resoution of the sensors. 5

15 AUTOMATIC PARAMETER ESTIMATION IN MRF BASED SUPER RESOLUTION MAPPING.. Parameter estimation techniques A number of arameter estimation techniques for MRF have been deveoed by many authors. Serico & Moser 006 emoyed a Ho-Kashya otimization for determining the arameters. Whereas, Jia & Richards 008 resented a method for determining the aroriate weighting of the sectra and satia contributions in the MRF based aroach of contextua cassification. Toekin and Stein 009 used oca energy baance anaysis as a means for estimating the smoothness arameter in MRF mode. The determination of the MRF mode arameter that weight the energy functions is a difficut issue and it is known that the erformance of the mode is deendent both on its functiona form and on the accuracy of the mode arameters estimation. Serico and Moser 006 resented an automatic suervised rocedure for the otimization of the weight arameters of the combinations of distinct energy contributions in MRF modes with the Ho-Kashya agorithm. The Ho-Kashya Agorithm is used for the otimization of the weight arameter setting invoved with MRF modes for suervised image cassification. The method uses training data in order to seect a set of arameters that maximizes the cassification accuracy by deveoing the inear reation between the energy function and the arameter vector. The method does not estimate the true vaues of the arameter of the MRF mode Instead, the arameter vaues giving the highest cassification accuracy are searched. The basic idea of the method is to use the training set in order to state a condition of correct cassification of the training same and find a arameter vector that fufis the condition. To sove the arameter estimation robem, first the energy functions must be exressed as a inear combination of distinct energy contributions then the arameter estimation robem is exressed as the soution of a system of inear equaities. In this method ICM is used for the energy minimization rocess and it is initiaized with a given abe vector generated by a non-contextua suervised cassifier and iterativey modifies the cass abes in order to decrease the energy function. The HK-based arameter setting methods is coued with the ICM cassification aroach for automatic contextua suervised cassification. The major stes of HK-ICM method are. Generate an initia non-contextua cassification ma by using suervised cassification.. Comute the energy difference matrix according to the MRF mode and to the abe vector. 3. Comute an otima arameter vector by running the HK rocedure u to convergence. 4. Generate a contextua cassification ma by running ICM u to convergence. The method has been resented in conjunction with the ICM agorithm for energy minimization and it can be used in conjunction with other energy minimization techniques such as simuated anneaing. The method overcomes tria and error arameter otimization robems in MRF based suervised image cassification. Jia & Richards 008 deveoed a method that determines the aroriate weighting of the satia and sectra contribution in the Markov random fied based aroach of contextua cassification. In this method, first the satia and sectra comonents are normaized to be in the range 0, then the aroriate vaue for the weighting coefficient can be determined. The satia information is incororated in to the cassification by changing the discriminant function through the addition of a term that distinguishes satia correations. 6

16 AUTOMATIC PARAMETER ESTIMATION IN MRF BASED SUPER RESOLUTION MAPPING Toekin and Stein 009 deveoed MRF arameter estimation method based on oca energy baance anaysis. In this method the otima smoothness arameter is estimated by considering cass searabiity and scae factor information. When the abe of the fine resoution ixe a j i is changed from the true cass vauec a j i, to another wrong cass vauec a j i, the resuting change of the oca rior energy wi be = q U N a j i a [ I, c a I, c a ] = q. According to Toekin and Stein 009, The vaue of γ deends on the neighbourhood system size, the configuration of cass abes c a in the neighbourhood N and the choice of ower-aw index n. a j i The smoothness arameter is defined as q q Where 0 q is used to contro the overa magnitude of the weights. The change of the fine resoution ixe abe c from α to β aso causes the change of the a j i comosition of the coarse-resoution ixe b i ; hence a change in the mean vector and the covariance matrix of that ixe vaue. For equa covariance matrices for the cass and, The change in oca ikeihood energy is exressed as:. U = S t C S S.3 For equa covariance matrices for the casses and the B distance is equa to y B = t C 8.4 From the above equations, the change in oca ikeihood energy is exressed with divergence and scae factor as: y 4B U S.5 7

17 AUTOMATIC PARAMETER ESTIMATION IN MRF BASED SUPER RESOLUTION MAPPING The oca contribution to the osterior energy from the considered ixe is ower for c a j i than for c a j i and the contribution of the ikeihood energy shoud comensate the gain in the rior energy. Thus the vaue can be determined from the baance between the changes in the rior and the ikeihood energy vaues. Soving for =.6 U U S.7 y 4B If the smoothness arameter is greater than the otima vaue, the mode wi ead to over smoothing on the contrary vaue that is too sma does not exoit the rior information in the mode. Having reviewed the we known arameter estimation techniques, the focus of this research is to deveo modes that estimate the smoothness arameter and in MRF based suer resoution maing. The modes deveoed in this research is simiar to the method of Toekin and Stein, 009 and in both cases arameter estimation is done by considering cass searabiity information between sectra casses. The detai discussion about the method wi be given in chater 3. 8

18 3. METHODS The owerfu roerty of the MRF modes is that the rior information and the observed data from different sources can be easiy integrated through the use of suitabe energy functions. However, an MRF mode usuay requires an estimation of one or more interna arameters before the aication of the mode Serico and Moser, 006. An aroriate choice of arameters can give successfu resut. Conversey, imroer seection of arameter vaues wi roduce unsatisfactory resut Li, 00. MRF Parameter estimation is difficut, eseciay when the number of information sources increases that make the number of arameter to be estimated increases. The main focus of this chater is to describe the MRF arameter estimation technique which is emoyed in this research. Section 3. describes about suer resoution maing. Section 3. exains how the synthetic images are constructed. Section 3.3 iustrates how the rior and the conditiona energies are modeed. Section 3.4 briefy describes about the roosed method. Section 3.5 exains about simuated anneaing otimization agorithm. Section 3.6 exains how the mode is assessed. 3.. Suer resoution maingsrm SRM theory incuding its formuation described beow is adated from Toekin et a., 00 with some minor changes. Consider the cassification of a coarse resoution mutisectra remote sensing image y that consists of K sectra bands with satia resoution R and ixe ocations d i D, where D is M M ixe matrix and a anchromatic image z with finer satia resoution r R. The resuting suer resoution ma SR ma c is a cassified ma which is defined on the set of ixe ocations A and covers the same extent on the ground as y and z with satia resoution r. The scae factor is denoted as S R / r, which is the ratio between the coarse and fine resoution ixe sizes. Hence each ixe d i wi contain S fine resoution ixes of a. j i Further assume a mutisectra image x having the same sectra bands as y as we as the satia resoution of r is defined on the set of ixes A. Image x is not observed directy whie image y and z are obtained by satiay and sectray degrading the image x. Furthermore it is assumed that every ixe in image x can be assigned to a unique cass: c a j i =, where,, L. The reationshi between y and x, and z and x are estabished by a degradation mode as: y d k i S S x k a j i, j k,..., K 3. For d i D and A a j i K K z a j i xk a j i 3. k 9

19 3.. Synthetic data sets and cass searabiity Synthetic image rovides a usefu source of data for imroving our understanding of information extraction from remotey sensed datatatem et a., 00. Toekin and Stein 009 showed that the otima smoothness arameter is deendent on the scae factor and cass searabiity. Based on their findings, in this study it is assumed that the otima and arameters deends on scae factor and cass searabiity. The main advantage of using a synthetic image in this research is to exore the effects of scae factor and cass searabiity on the otima and arameters. The synthetic image aows to concentrate on secific eement of the robem by ignoring the comexity of rea images and used to erform systematic controed arameter variation.toekin and Stein, 009 The synthetic image generation starts with the reference ma with three casses as shown in Figure 3.b. Pixe vaues are generated through mutivariate seudo random number generator using cass arameter mean and covariance. During image generation the cass searabiity is controed by fixing cass mean and covariance matrices. The fine-resoution mutisectra image x Figure 3.a is roduced by saming from mutivariate norma distribution using mean and covariance obtained from the rea image. This image is consequenty degraded to coarse resoution mutisectra and fine resoution anchromatic image with different scae factor vaues S=, 4, 5, 6,8,0. See equation 3. and 3.. An exame of degraded synthetic image with S= is shown in figure 3.. Severa fine resoution mutisectra images x are constructed from the reference image with various cass-searabiity vaues. Figure 3.: Construction of synthetic images. a Fine-resoution mutisectra image x. b Reference image with three casses, green: shadow vegetation, white: grass, brown: tree. 0

20 Figure 3.: Degraded synthetic mutisectra 30x30 ixe and anchromatic 60x60 ixe images. Cass searabiity is a statistica measure that shows how we the user defined casses can be searated by cassifier. The simest cass searabiity measure is the Eucidean distance evauation where the sectra distance between the mean vectors of each air of cass signature is comuted, and if this distance is not significant for any air of bands avaiabe they may not be distinct enough to roduce successfu cassification. The basic rincie is that ixe vaues within a given and cover tye shoud be cose together in the measurement sace; whereas ixes data in different casses shoud be we searated. To quantify the searation between sectra casses ony distance between means is insufficient since overa wi aso be infuenced by the standard deviations of the distributions. Therefore, a combination of both the distance between means and a measure of standard deviation is requiredrichards, 993. The mean contros the ocation of the distribution and the variance contros the sread of the data. When more than one feature is invoved, then the mutivariate norma distribution has to be used. In mutivariate norma distribution instead of a singe mean controing the ocation of the distribution there is one mean for each feature making u a mean vector. The mutivariate equivaent of the variance is the variance covariance matrix which reresents the variabiity of ixe vaues for each feature within a articuar cass and the correations between the features. These two arameters are used to describe each cass and comuted for each same. There are many cass searabiity measures among them Bhattacharyya distance and Jeffries-Matusita distance is used in this study. Bhattacharyya distance measures the simiarity of two robabiity distributions and it is used to determine the searabiity of casses in cassification. The Bhattacharyya distance of mutisectra band is exressed as: B y 8 t C C n C C C B C 3.3

21 In a simiar way, the Bhattacharyya distance of anchromatic band is exressed with mean and variance as: z B 8 t n z B _ 4 n 3.4 When the number of casses is arger than two, an average Bhattacharyya distance is used y B avg= M M M M y B 3.5 z B avg = M M M M z B 3.6 Jeffries-Matusita distance JM is introduced to transform the Bhattacharyya distance vaues to a secific range and the JM distance tends to overemhasising ow searabiity vaues whie suress high searabiity vaues. JM JM y z e e B Y Z B When the number of casses is arger than two, an average Jeffries-Matusita distance is used y JM avg = M M M M y JM 3.9 z JM avg = M M M M z JM 3.0 Bhattacharyya distance vaues vary from 0 to where as Jeffries-Matusita distance vary from 0 to. If the mean and covariance of the two casses are the same, then B = JM =0, this indicate that, it is

22 imossibe to distinguish between the two casses based on sectra information ony. On the contrary, when B and JM, indicating that the two casses are totay searated in feature sace. Searabiity between the casses increases with increasing JM vaues and because of the saturating behaviour Jeffries-Matusita distances is referred over the Bhattacharyya distance. To see the effect of cass searabiity of the mutisectra image on the otima and arameters y different JM vaues are chosen as 0.5,.0 and.9. An exame of resuting cass searabiity vaues y z between the casses for JM =0.5 and JM =0.0 is resented in tabe 3. and tabe 3. resectivey Simiary, to see the effects of cass searabiity of the anchromatic image on the otima and z arameters the cass searabiity of the anchromatic image is varying with JM vaue of 0.5,.0 and.9. y Tabe 3.: Jeffries-Matusita distance between the casses for JM 0. 5 cass cass cass3 cass 0 cass cass z Tabe 3.: Jeffries-Matusita distance between the casses for JM 0. 0 cass cass cass3 cass cass cass Tabe 3.3: Reation between minima and average Jeffries-Matusita distance in image y and z JM y JM avg z JM avg y z JM It is ossibe to systematicay contro the cass searabiity between sectra casses of the mutisectra and anchromatic image, by exressing their cass searabiity with the cass arameter of the image x. Cass searabiity in the image x can be exressed with Bhattacharyya distance as: x B = 8 x x t C x C x x x + n C x C C x C x x 3. To exress the Bhattacharyya distance of image y in terms of the mean and covariance of image x first the reationshi between the cass arameters of the two images shoud be determined. 3

23 4 Assume image x and image y are sectray simiar. Then, y n =, x n Where, y n reresents mean of image y and, x n reresents mean of image x.,, y m n C = S,, x m n C Where,, y m n C reresent covariance of image y,,, x m n C reresent covariance of image x and S is scae factor. Here n reresents the number of cass, and m reresents the number of bands. Then the Bhattacharyya distance of the Image y is exressed as: y B = 8 t x x S C C x x x x + n x x x x C C C C 3. Where and are the two sectra casses. Simiary, to exress the Bhattacharyya distance of image z interms of mean and covariance of image x first the reationshi between the cass arameters of the two images shoud be determined. It is assumed that, the satia resoution of image x and image z are the same. z k = N b N b x k,, where z k reresents mean of the anchromatic image z and b N Reresents number bands. z k C = b N N b N b m x m c k,,, where z k C reresents covariance of image z. Then the Bhattacharyya distance of the image z is exressed as: z B = 8 N b x x b N N b b N m x x b C C N N b x x b N + b b b b b b N N m N N m x b x b N N m x x b C N C N C C N n 3.3

24 Equation 3. and 3.3 is used to contro the cass searabiity vaues in the mutisectra and anchromatic image ony by changing mean and covariance of the image x in the synthetic image generation MRF The theory of MRF incuding its formuation described beow is adated from Toekin et a., 00 with some minor changes. The advantages of using MRF modes is that, the rior information and the observed data from different sources can be integrated through the use of suitabe energy function. The suer resoution ma SR ma c that corresonds to the maximum a osteriori robabiity c y, z soution for c given observed data y and z can be comuted with Bayes theorem from rior robabiity c and conditiona robabiities y c and z c as: c y, z c y c z c 3.4 Assume y and z are conditionay indeendent given c and due to the equivaence of MRF and Gibbs random fied, the robabiities can be secified by means of energy functions as: U c c = ex A T U y c y c = ex A T U c z c = ex A T U c y, z c y, z = ex A T Where A, A, A3 and A4 are normaizing constants, T is a constant termed the temerature, U c, U y c, U z c and U c y, z are the rior, two conditiona and the osterior energy functions resectivey. The resuting exression, when rewriting the Bayes formua for energy function is U c y, z U c U z c U y c 3.9 5

25 Where 0, is a arameter which baances the contribution of rior and conditiona energy functions. =0 indicates that the contextua information is ignored in the cassification and ony the conditiona energy is used. Whereas, =0.5 indicates that equa weights are assigned to the rior and conditiona energy. = indicates, the conditiona energy is ignored and ony contextua information is used in the cassification which resuts a simiar cass. Likewise, 0, is a arameter which baances the contribution of the anchromatic and mutisectra conditiona energy functions. =0 indicates the conditiona energy from the anchromatic image is ignored and the cassification is done ony by using the ikeihood energy from the mutisectra band. Whereas, = indicates that, the conditiona energy from the mutisectra image is ignored and ony the conditiona energy from the anchromatic image is used. This is simiar to maximum ikeihood cassification of the anchromatic band Prior energy function The rior energy is modeed as the sum of air-site interactions. Li, 00 UC i, j U c a j i i, j N a j i w a I c a j i, c a 3.0 Here, N is the neighbourhood system, U c is the oca contribution to the rior energy from a j i the fine resoution ixe c, w a a j i a j i reresents the weight of the contribution from ixe a N a j i to the rior energy and I c, c takes the vaue 0 if c c and otherwise. This rior mode enaizes the occurrence of ixes with different cass abes in the neighbourhood system N and the weights w a are chosen inversey roortiona to the distance d a between the centra ixe a j i and the ixe a as w a d a, a j i 3. 6

26 3.3.. Conditiona energy functions The ikeihood energies consider the coseness of observed ixe vaues to each and cover cass. The sectra vaues x of a cass is modeed with the norma distribution and it is assumed that the sectra vaues x of the S fine resoution ixe a j i distributed given their cass association. a j i are indeendent: satiay uncorreated and identicay The conditiona energy is defined using the mean vector U y c =U y di c a j i i, j of cass and the covariance matrix as: Where U y d c is the oca contribution to the ikeihood energy from the fine resoution ixe c a j i U y c = i a j i i, j t y di i Ci y di i n Ci 3. The vaues i and C i are modeed as a inear combination of mean vectors and covariance matrices based on roortions of resective and cover casses inside the coarser resoution ixe. Simiary, the anchromatic conditiona energy U z c is defined as: U z c = i, j z a j i n 3.3 Where z a j i is the ixe vaue, is mean of the cass and is the standard deviation of the cass Estimation of and arameter and are interna arameters of the MRF based SRM and it needs to be roery estimated before the method is aied to obtain higher cassification accuracy. Based on the resut obtained in Toekin, et a.00, it is assumed that, the incororation of information from the anchromatic band imroves the cassification resuts when comared to cassification with out information from the anchromatic band, if it is roery estimated. arameter is introduced to baance the contribution of ikeihood energy from the mutisectra and anchromatic image. MRF arameter estimation for SRM is infuenced by cass searabiity and scae factor informationtoekin and Stein, 009. In this study modes are deveoed based on oca energy baance anaysis and by reating the otima and arameter estimation to the cass searabiity and scae factor information. 7

27 First assume correct cassification of casses and consider a case when a fine-resoution ixe true cass abe c a j i a j i with a, to which is assigned a different cass abe and a the other ixes are seected correcty. Then the resuting change in ikeihood energy in mutisectra and anchromatic band is as foows: The change in ikeihood energy of the anchromatic band is: z U = c U z U z c 3.4 Where c is the abe of the fine resoution ixe, and are sectra casses. The anchromatic energy with the true cass abe c a j i is exressed as: U z c = n 3.5 Where reresents standard deviations The anchromatic energy with the wrong cass abe c a j i is exressed as: U z c = n 3.6 The change in energy when the fine resoution ixe abe c changes from to is exressed as: a j i = n n z U = n 3.7 To simify the modeing, it is assumed that, the variances of the two casses are the same. =, then the above exression is simified as: z U = Where is the difference between the mean of the two sectra casses. 3.8 Simiary, equation.8 is simified as: z B Then, the change in energy of the anchromatic band is exressed with the Bhattacharyya distance as: = 4B z 3.30 z U 8

28 The change of the fine resoution ixe abe c from to aso causes the change of the a j i comosition of the coarse-resoution ixe di and thus, to a change in the mean vector and the covariance matrix for this ixe vaue. The change in ikeihood energy of the mutisectra band is cacuated with mean and covariance as: y U = S S t C S 3.3 y t U = C 3.3 S With the same assumtion for the casses and, Equation 3.3 of the Bhattacharyya distance between casses in the mutisectra band is simified as: y B = 8 t C 3.33 Then, the change in energy of the mutisectra band is exressed with the Bhattacharyya distance as: y 4B y U = S 3.34 Subsequenty, the vaue of is determined from the baance between the change in ikeihood energy of the anchromatic and mutisectra band with: = z U y U 3.35 S B B z y 3.36 Likewise, to estimate the smoothness arameter consider aso a case when a fine-resoution ixe a j i with a true cass vaue c a j i,to which is assigned a different cass abe. Then the change of the oca rior energy when the ixe abe c changes from to is a j i 9

29 U = q N a j i a [ I, c a I, c a ] = q 3.37 The vaue of deends on the neighbourhood system size, the configuration of cass abes c a in the neighbourhood N and the choice of ower-aw index n.toekin and Stein, 009. a j i The tota change in ikeihood energy when the ixe abe c changes from to wi be a j i t U = z U + y U t U = 4 B + S 4 z B y 3.38 Then, the smoothness arameter can be determined from the baance between the change in the rior and tota ikeihood energy vaues. = t U 4 B + S 4 z B y = q = t U 4 B + S 4 z B y = 3.39 Finay, soving for S B 4S B y z If the cass searabiity in the mutisectra and anchromatic images is sma, then the smoothness arameter vaue wi aso be sma. On the contrary if the cass searabiity in the mutisectra and anchromatic image is arge, then the smoothness arameter vaue wi be high Simuated Anneaing Once the goba energy constructed and the otima arameters have been determined, the next ste of SRM is to find the minimum of the tota energy in ma estimate. To achieve this simuated anneaing agorithm SA is emoyed to find the ma soution. SA is a stochastic agorithm used to find a good otimization robem based on the use of random numbers and robabiity statistics. Temerature and are the main arameters in the simuated anneaing agorithm that contro the rocess of otimization 0

30 and mosty these arameters are estimated exerimentay. In this study a ower-aw anneaing schedue is used, where the temerature at the iteration n is changed according to T T 3.4 n n The arameter contros the rate of temerature decrease and the arameter T contros the randomness of the otimization agorithm. High temerature means high randomness and ow temerature means ess randomness and the high temerature increases the robabiity of a ixe abe to be reaced with a new abe. Pixe vaues are udated with the Metroois-Hastings samer then the number of successfu udates is counted, being the number of udates that ead to a change of ixe vaue. If the number of successfu udates is beow 0.% of the tota number of ixes during three consecutive iterations the otimization is stoed. The initia suer resoution ma is obtained by first aying inear sectra unmixing, to estimate the roortion of each cass within each coarse resoution ixe d i. Then the coarse resoution ixe is fied with randomy distributed fine resoution ixes of each cass according to their roortions. Finay, by otimizing the satia deendence the SRM is generated. In SRM, the otima vaues of the arameters T O and in the anneaing schedue deends on the scae factor and cass searabiity.toekin and Stein, Accuracy assessment and erformance anaysis. It is necessary to evauate the accuracy of the cassification resut against the reference data to assure its fitness for use of the intended aication. In this context the accuracy is defined as the eve of agreement between abes assigned by the SRM with the reference data. The common way of reresenting the cassification accuracy is with the form of an error matrix which comares the cassification resuts to the corresonding reference data on cass by cass basis.richards, 993. The kaa coefficient is one of the quaity measures that is derived from the whoe error matrix information and estimates the overa agreement between the cassified image and the reference data. The highest vaue of the kaa coefficient is that means there is a erfect agreement between the cassified image and the reference image where as kaa vaue 0 shows the cassified image is cometey different from the reference image. In this thesis the accuracy of the resuts are measured in kaa coefficient and the erformance of the modes are checked with the numerica otima vaues obtained from the exeriment. To do this, exeriments are conducted to identify the otima and arameter for each scae factors and cass searabiity. An otima and vaues are those vaues that resuts the highest kaa vaue. After that, otima and range is secified. Finay the redicted vaues are comared to the exerimentay determined otima vaues.

31

32 4. RESULTS This chater resents the otima and arameter estimation resuts obtained in MRF based suer resoution maing and the anaysis of the resuts. Section 4. resents the exerimenta resuts conducted to check how the scae factor and cass searabiity vaue affects the otima arameters of and. In section 4. the resuts obtained from the modes are resented and anayzed. Section 4.3 summarizes the main findings of the resuts. 4.. Exerimenta resuts from synthetic datasets To understand how the otima and arameters are affected with different scae and cass searabiity vaues, severa synthetic images were generated as mentioned in Section 3.. This rocess of image generation simifies the comexity of rea image. Proer arameter identification and estimation are the most crucia art of this study and for this urose, severa exeriments have been done and the quaity of the resut is measured using kaa coefficient. In each rocess the agorithm is run a minimum of ten times to get a consistent resut and the mean kaa vaue has been determined The effect of scae factor on the otima and arameter. The intension of doing this exeriment is to observe the effects of scae factor on the otima arameter of and. This exeriment is carried out using scae factor vaues of, 4,5,6,8, 0 and combination of vaues which range from and an vaue from are used. The smoothness arameter is used as a baancing factor between the rior and ikeihood energy function whereas is used as a baancing factor between the mutisectra and anchromatic ikeihood energy functions. The first exeriments are conducted to find the otima and combinations, that give maximum cassification accuracy and to quantify there reation with the scae factor. Figure 4. b shows an exame of the suer resoution ma resut obtained with the otima combination of and at scae factor. Figure 4., shows that, as the scae factor increases the otima smoothness arameter vaue decreases. This is mainy due to the no of sub-ixes in the coarser resoution ixes increases with scae factor. This makes the coarser resoution ixes highy mixed and hence, using arger smoothness arameter decreases the cassification accuracy. However, for smaer scae factors, using more contextua information increases the cassification accuracy. As can be seen from figure 4., at the ower scae factor, is very imortant to obtain higher cassification accuracy and amost equa amount of ikeihood energy is contributed from the anchromatic and mutisectra image. However, as the scae factor increases the otima vaue decreases. This means that, the contribution of the ikeihood energy from the anchromatic image decreases. In other words, for arger scae factors the incusion of more ikeihood energy from the anchromatic band decreases the quaity of SRM. 3

33 Figure 4.: suer resoution ma resut. a owest kaa obtained, b highest kaa obtained, c reference image. Figure 4.: Otima vaue at different scae and cass searabiity in the mutisectra and anchromatic image. Lines are added to faciitate the interretation of the data. 4

34 Figure 4.3: otimaan vaue at different scae and cass searabiity in the mutisectra and anchromatic image. Lines are added to faciitate the interretation of the data The effect of cass searabiity on the otima and an arameter. This exeriment is erformed to see the effects of cass searabiity between sectra casses in the mutisectra and anchromatic image on the otima vaues of and arameters in MRF based suer resoution maing. This is carried out first by fixing the cass searabiity vaues in the anchromatic image whie varying cass searabiity vaues in the mutisectra image. To see the effects, y the synthetic images is constructed with cass searabiity vaues in the mutisectra image of JM =0.5, z.0 and.9 with fixed cass searabiity vaue of JM =0.0 in the anchromatic image, for different scae factor vaues. Simiary, to see the effects of the anchromatic image the cass searabiity of the z mutisectra image is fixed whie the cass searabiity of the anchromatic image is varying with JM vaue of 0.5,.0 and.9. As can be seen from Figure 4., when cass searabiity between sectra casses in the mutisectra and anchromatic image is smaer, the otima smoothness arameter vaue becomes ess. This indicates that, the contribution of the ikeihood energy from the mutisectra and anchromatic image to the goba energy shoud be higher to get better cassification accuracy. In another way, when the cass searabiity between sectra casses in the mutisectra image increases the otima smoothness arameter vaue aso increases. This shows that, if the sectra casses are we searated using more contextua information further increases the cassification accuracy. Moreover, when the cass searabiity in the anchromatic image increases the smoothness arameter vaue aso sighty increases. These resuts shows that, cass searabiity and smoothness arameters have direct reationshis. If there is 5

35 maximum cass searabiity between sectra casses in the mutisectra and anchromatic image the smoothness arameter vaue becomes higher. In genera, for most of the scae factors when the cass searabiity in the mutisectra band increases, the otima vaue aso increases. Nevertheess, increase in cass searabiity of the anchromatic image does not significanty affect the otima vaue. As observed from Figure 4., the increase in the cass searabiity between sectra casses resuts in increase the otima arameter. This indicates that, if sectra casses are we searated, using more ikeihood energy from the anchromatic band increases the cassification accuracy. Figure 4.4: The effect of cass searabiity on the otima vaues of and an. a and c show the change of the otima and an vaues resectivey, when cass searabiity in the mutisectra image changes for a fixed JMZ vaue of 0.0. Here, b and c show the change of the otima and an vaues resectivey, when cass searabiity in the anchromatic image changes for a fixed JMY vaue of.0. 6

36 It is ceary seen from Figure 4.3 a, when the cass searabiity between sectra casses in the mutisectra image increases, the otima smoothness arameter vaue as we increases significanty. This indicates good cass searabiity between sectra casses make the rior mode rovide more information for the cassification. The otima smoothness arameter vaue is aso sighty affected with the increase in cass searabiity between sectra casses in the anchromatic image as shown in figure 4.3 b. On the contrary, if cass searabiity in the anchromatic image increases the otima vaue increases more as shown in figure 4.3 d. Where as, Figure 4.3 c show, otima vaue is ess affected with the increase in cass searabiity in the mutisectra image Effect of scae factor and cass searabiity on the cassification accuracy kaa Figure 4.5: The effect of scae factor and cass searabiity in the cassification accuracy kaa vaue. Figure 4.5 indicates that, cassification accuracy kaa vaue show significant increase, when cass searabiity between sectra casses in the mutisectra image increases. On the contrary, very ow cass searabiity eads to confusion between sectra casses, which resut in inferior cassification accuracy. It is aso noticed that, when cass searabiity between sectra casses in the anchromatic image increases the cassification accuracy kaa vaue increases to some extent. Generay it is observed from the figure that, when the scae factor increases the cassification accuracy kaa vaue decreases. nevertheess, at arger cass searabiity in mutisectra and anchromatic image the cassification accuracy kaa vaue does not show big variations, the vaue more or ess remain the same for different scae factors. The effect of scae factor on the cassification accuracy kaa vaue is very sma for widey searabe casses. However, it affects more, if the cass searabiity between sectra casses in the mutisectra and anchromatic image is sma. 7

37 As it is observed from figures A., A. and A.3 in aendix A, the vaue of and has an effect on the y z y vaue of kaa for each combination of S, JM and JM. For every combination of S, JM z and JM, there exist an otima and combination where the cassification accuracy attains the maxima vaue Kmax. There is aso a range of and vaues that resuts cassification accuracy kaa cose to k max. In this study the range for and vaues is defined in such away that the kaa vaue obtained with those and vaues is greater than 0.85 k max. 4.. and estimation resuts from synthetic image In this section the resuts estimated with the modes for otima and arameters are resented. As it is observed from figure 4.5, 4.6 and 4.7, the rediction of and vaue with the mode fits the emirica data obtained from the exeriments. To estimate the arameters with the mode ony scae factor and cass searabiity information is required see equation 3. and 3.6. The cass searabiity between sectra casses in the mutisectra and anchromatic image is cacuated by using equation.7 and.8 resectivey. In figure 4.5, the arameters are estimated by considering the minimum cass searabiity between a casses and if cass searabiity vaues between different airs of casses vary strongy an average cass searabiity vaue can be used. The estimation resuts based on the average cass searabiity vaues of a casses are isted in tabe C. in aendix C. Some adjustment factors are used in the mode deveoed in 3. & 3.6 to best fit the estimation with the exerimenta data. Identification of and is not very recise because the estimation was done by increasing and vaues with ste sites of 0.. 8

38 Figure 4.6: Otima vaues for varying arameters S and JMY. : The exerimentay determined otima vaues. range: The range of corresonding to K 0.85 k. : The estimation from the mode. max 9

39 Figure 4.7: Otima an vaues for varying arameters S and JMY. The exerimentay determined otima vaues. an range: The range of an corresonding to K 0.85Kmax.* an: The estimation from the mode 30

40 Figure 4.8: Otima vaues for varying arameters S and JMY. an & : The exerimentay determined otima vaues. * an & : The estimation from the mode. an range & range: The range of an and corresonding to k 0.85k max. Here a and b for JMY vaue of 0.5 and c and d for JMY vaue of.0. e and f for JMY vaue of.9 for a fixed JMZ vaue of

41 4.3. arameter estimation resut from the rea image The aicabiity of the modes for rea image is tested with the resut obtained from the exeriment, conducted by Wijeratna Nanthamuni 00 MSC student, who works on the tite, Integration of Satia and Sectra data of very high resoution imagery for buiding footrint detection using Suer Resoution Maing. The otima and resuts obtained from the exeriment are 0.8 and 0.3 resectivey and the modes estimates otima vaue equa to 0.98 and for vaue 0.3. This shows that the modes can estimate the otima arameters for rea images with in a toerabe range Summary of observation from the resuts The resut from the exeriments roof that, the otima and arameters have a direct reation shi with cass-searabiity and have an inverse reation shi with the scae factor vaues. There exist an otima combination of and vaues, where the cassification accuracy attains the maximum vaue k max, for each SRM inut arameters scae factor and cass searabiity. The resut obtained from the modes deveoed in this research for the otima and arameter estimation agrees with the emirica data. The ikeihood information obtained from the anchromatic band increases the cassification accuracy at the ower scae factors. 3

42 5. DISCUSSIONS,CONCLUSION AND RECOMMENDATION 5.. Discussions The main objective of this study is to deveo modes based on oca energy baance anaysis for the estimation of otima and P arameters. The smoothness arameter acts as a baancing factor between the rior and conditiona energy in the MRF mode. Whereas P contros the baance between the ikeihood energy from the anchromatic and mutisectra band. In this study the effects of cass searabiity and scae factor on the otima arameters of and P in the MRF based suer resoution maing are studied. The obtained resut from the exeriments show that the otima and P arameters are infuenced with scae factor and cass searabiity vaues. As the scae factor increases the otima smoothness arameter vaue decreases. This is mainy due to the number of sub-ixes in the coarser resoution ixes increases with scae factor and makes the coarser resoution ixes highy mixed. In a simiar way, as the scae factor increases the otima P vaue decreases. This imies that, the contribution of the ikeihood energy from the anchromatic image decreases. Therefore, to obtain better cassification accuracy the ikeihood energy from the mutisectra band shoud be high. As can be seen from Figure 4., when cass searabiity between sectra casses increases the otima vaue aso increases. This resut ointed out that, for higher cass searabiity between sectra casses, the goba energy needs to be modeed with a higher vaue. Whereas, in the case of ower searabiity of casses the goba energy has a tendency to deend on the ikeihood more than the rior energy. In other words, for ower cass searabiity of casses, the cass abeing deends more on the sectra information. This substantiates the need for accurate estimation of mean and covariance matrices for each sectra cass, to obtain better cassification resuts. The cassification accuracy kaa vaue decreases with increasing scae factor as shown in figure 4.5. How ever, an excetion from this observation is an increase in cassification accuracy with increasing scae y z factor vaue for cass searabiity JM 0. 5 and JM 0. 0 at scae factor 5. The reason may be due to the ess number of reaizations of the images. With the same scae factor and cass searabiity information the cassification accuracy kaa vaue is deends on the otima arameters of and as can be seen in figure 4.5. The modes reate and P arameter estimation to scae factor and cass searabiity information of the mutisectra and anchromatic image. To estimate the arameters with the modes ony scae factor and cass searabiity information is needed. The estimation is done by considering minima cass searabiity and an average cass searabiity between sectra casses. The resuts achieved with these modes for the estimation of the otima arameters agree with the exerimenta data as shown in Figure 4.6, 4.7, 4.8. The modes are deveoed based on the assumtion that the covariance matrices of the sectra casses are the same. This assumtion simifies the modeing significanty and considering unequa covariance matrices wi make the mode more owerfu and reaistic. The synthetic image which is used in this study was constructed with the assumtion that the fine resoution ixes are conditionay indeendent. This assumtion simifies the construction of the synthetic images. However in rea images, the sectra vaues 33

43 of ixe are satiay correated. The aicabiity of the modes to rea image is tested and romising resut was found however the modes shoud consider the satia structure of the ixes to be reaistic. To ay the roosed modes for rea images first the scae factor vaue is decided, which is used as an inut for SRM as we as for the mode. Then the and cover casses are defined. Using the training set the cass arameters mean and covariance of each cass from the mutisectra and mean and variance from the anchromatic band is estimated. These vaues are used for cacuating the cass searabiity Bhattacharyya distance between sectra casses in the mutisectra and anchromatic image. Finay the otima and arameter are estimated with the mode based on cass searabiity and scae factor information. 5.. Concusion Automatic MRF arameter estimation is a chaenging task, which is addressed in this research. The modes are deveoed based on oca energy baance anaysis for the automatic estimation of the otima arameters and P in MRF based SRM. The Modes reates the arameter estimation to scae factor and cass searabiity information. The resuts of the exeriments carried out using the synthetic images iustrate that the otima and P arameters deend on the scae factor and cass searabiity. When the scae factor increases the otima and P arameters decreases. On the contrary, when the cass searabiity increases the otima and P arameters aso increase. Furthermore, for each combination of scae factor and cass searabiity vaues in the mutisectra and anchromatic images, an otima and P vaues exist. There exists aso a range of and P vaues for which the cassification accuracy is cose to the otima vaue. The arameter vaues estimated with the mode agreed with the resuts obtained from the exeriment. The deveoed mode aows users to estimate otima and P vaues by using the scae factor and cass searabiity information of the anchromatic and mutisectra images. Because of the incororation of the anchromatic band, the resut obtained for the otima smoothness arameter has a sight difference with the resut obtained in Toekin and Stein Recommendations. It is recommended to imrove the modes for rea images where the sectra vaues of ixes are Satiay correated.. It is aso recommended to imrove the modes by considering unequa cass covariance matrices of the Sectra casses. 34

44 35

45 LIST OF REFERENCES Haiu Kassaye, R Suitabiity of Markov random fied based method for suer resoution and cover maing. ITC, Enschede. Jia, X., and Richards, J. A Managing the Sectra-Satia Mix in Context Cassification Using Markov Random Fieds. Geoscience and Remote Sensing Letters, IEEE, 5, Kasetkasem, T., Arora, M. K., and Varshney, P. K Suer-resoution and cover maing using a Markov random fied based aroach. Remote Sensing of Environment, 963-4, Li, S. Z. 00. Markov random fieds modeing in image anaysis. Tokyo etc.: Sringer. Richards, J. A Remote sensing digita image anaysis : an introduction Second revised and enarged edition ed.. Berin etc.: Sringer-Verag. Serico, S. B., and Moser, G Weight Parameter Otimization by the Ho Kashya Agorithm in MRF Modes for Suervised Image Cassification. Geoscience and Remote Sensing, IEEE Transactions on, 44, Soberg, A. H. S., Taxt, T., and Jain, A. K A Markov random fied mode for cassification of mutisource sateite imagery. Geoscience and Remote Sensing, IEEE Transactions on, 34, Swain, P. H. e., and Davis, S. M. e Remote sensing : the quantitative aroach. New York etc.: McGraw- Hi. Tatem, A. J., Lewis, H. G., Atkinson, P. M., and Nixon, M. S. 00. Suer-resoution and cover attern rediction using a Hofied neura network. Remote Sensing of Environment, 79, -4. Toekin, V. A., Ardia Loez, J. P., and Bijker, W. 00. Suer - resoution maing for extraction of urban tree crown objects from VHR sateite images. In: GEOBIA 00 : geograhic object - based image anaysis, 9 June- Juy 00, Ghent, Begium : roceedings / editor E.A. Addink, F.M.B. Van Coiie. - [s..] : Internationa Society for Photogrammetry and Remote Sensing ISPRS, Toekin, V. A., and Stein, A Quantification of the effects of and - cover - cass sectra searabiity on the accuracy of Markov - random - fied - based suerresoution maing. IEEE Transactions on Geoscience and Remote Sensing, 479. Tso, B., and Mather, P. M. 00. Cassification methods for remotey sensed data. London etc.: Tayor & Francis. 36

46 APPENDIX A. Summary of resuts for otima and an vaues. 37

47 Figure A.: Combination of and an vaues that gives kaa vaue above 0.85Kmax at JMY=0.5 and JMZ=0.0 38

48 Figure A.: Combination of and an vaues that gives kaa vaue above 0.85Kmax at JMY=.0 and JMZ=0.0 39

49 Figure A.3: Combination of and an vaues that gives kaa vaue above 0.85Kmax at JMY=.9 and JMZ=0.0 40