Use of spectral and temporal unmixing for crop identification using multi-spectral data

Transcription

1 Use of spectral and temporal unmixing for crop identification using multi-spectral data Samia Ali March, 2002

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3 Use of spectral and temporal unmixing for crop identification using multi-spectral data by Samia Ali Thesis submitted to the International Institute for Geo-information Science and Earth Observation in partial fulfilment of the requirements for the degree in Master of Science in Geoinformatics. Degree Assessment Board Chairman First supervisor Second supervisor External examiner Dr. Ing. Yola Georgiadou Mr. Tal Feingersh, M.Sc. Prof. Dr. F.D. van der Meer Dr. Ir. B.G.H. Gorte INTERNATIONAL INSTITUTE FOR GEO-INFORMATION SCIENCE AND EARTH OBSERVATION ENSCHEDE, THE NETHERLANDS

4 Disclaimer This document describes work undertaken as part of a programme of study at the International Institute for Geo-information Science and Earth Observation (ITC). All views and opinions expressed therein remain the sole responsibility of the author, and do not necessarily represent those of the institute.

5 Acknowledgements I would like to thank Synoptics bv, The Netherlands, for providing Earth Observation and reference data used for this study. Thanks are due to Mr. Leon Schouten at Synoptics for sharing his knowledge. I appreciate his patience, he showed during this period, to answer my questions and queries, whenever I needed. I am thankful to International Water Management Institute (IWMI) and Dr. S. A. Prathapar (the then Director IWMI, Pakistan National program) for the study leave, during which I could complete my M.Sc. at ITC. I sincerely thank to my supervisors; Mr. Tal Feingersh and Prof. Dr. F.D. van der Meer for their constant and valuable guidance during thesis period. The provocative discussions and their constructive comments helped me to complete this study. I am grateful to all the staff of the Geoinformatics division for the useful knowledge, I gained at ITC. Thanks are extended to Dr. Rolf de By for introducing L A TEX to us and saving the time, otherwise needed for layout and formatting a thesis. His constant help to solve related problems is highly appreciated. I thank to Drs. Wan Bakx and Ard Blenke for their help, whenever needed. I extend my thanks to Mr. Gerrit Huurneman, who is ever ready to solve any problem that is bothering us. Thanks are extended to all my GFM-2000 classmates for their unforgettable and friendly company. I enjoyed sharing with them a mix of fun and frustration of the study at ITC. Beside tough and long study hours at ITC, there have been some stress-free and memorable moments during my stay at Netherlands. I appreciate a great deal the company of my friends, Rubina, Mobin, Sadia, little Manal, Paul, Saim, Somia, Mounira, Zhao, Aftab, Mubashar, Falak, Adel, Abdel-Rehman. I appreciate the love and effort of my brother, Tariq and my friend Zeenath, they made to visit me at The Nethrlands. My deepest gratitude and thanks are extended to my family; my parents, sisters and brothers, for the strength imparted to me by their regular messages, prayers and love. I dedicate this work to my beloved parents. i

6 Acknowledgements ii

7 Abstract The reflectance values of pixels, recorded by remote sensors, often result from spectral mixture of a number of ground spectral classes, constituting the area of a pixel. This, the so-called mixed pixel problem, has always been an obstacle in image classification in deriving accurate land cover classes. This study suggests the use of a sub-pixel classification technique: spectral linear unmixing, for an improved crop classification. If mixing is considered linear, then the resulting pixel reflectance is a linear summation of the individual material reflectance multiplied by the surface fraction they constitute. In addition to the problem of mixed pixels, limited spectral separability among different agricultural crop types is another problem that causes inaccuracy in classification. For this reason, linear unmixing is applied to multitemporal Landsat images to take an advantage of the spectral discrepancies shown by crops over the course of their growing cycle. It is expected that the multitemporal profile for each crop s fraction values will be distinct from each other due to their respective growth cycle and hence an additional aid to improve for the unmixing classification results. These experiments are applied to the municipality of Maasbree in the south of The Netherlands. Three Landsat images, dating May 14, August 01 and August 26, are used for this study. Experiments have shown unique information over time in the spectral-reflectance profiles and vegetation indices of the agricultural crops. Root Mean Square (RMS) images of May14 and Aug01 has shown better accuracy in the unmixing results than for Aug26. Keywords Sub-pixel, Linear spectral unmixing, multitemporal profile, endmember iii

8 Abstract iv

9 Contents Acknowledgements i Abstract iii List of Tables ix List of Figures xi 1 Introduction Problem definition Motivation Research question Objectives Outline of the thesis Subpixel Classification Methods The Pixel Sub-pixel classification Spectral mixture analysis Fuzzy classification A selection from different models One approach to perform Linear unmixing Endmember selection Output of linear unmixing v

10 Contents 2.5 Summary Study Area and Data Study area Data Earth Observation data Field reference data Data from the Central Bureau for Statistics (CBS) Crop calendar Selection criteria Data preparation Geometric corrections Radiometric corrections Reference data is refined Temporal Analysis Available Methods Vegetation Indices Temporal-spectral unmixing profile Temporal-spectral profiles Temporal-NDVI profiles Summary Results and Discussion Endmember Selection Pixel Purity Index (PPI) Principal Component Analysis (PCA) Crop statistics from CBS Spectral Angle Mapping (SAM) Linear spectral unmixing vi

11 Contents Spectra collection Unmixing results Discussion Conclusion and Recommendations Conclusions Recommendations Bibliography 53 A Endmember selection through PCA 55 B Statistics from linear spectral unmixing 57 vii

12 Contents viii

13 List of Tables 2.1 Applicability of mixture models to different application [11] Satellite remote sensing data Landsat ETM+ spectral channels Confusion matrix for SAM classification Unmixing results showing main statistics for 3 Landsat images B.1 Pixel fractions constituted by Maize ix

14 List of Tables x

15 List of Figures 2.1 Four cases of mixed pixels [7] Geometric representation of mixing model [1] The linear model of spectral mixing [1] Two dimensional example of the Spectral Angle Mapper [1] Study Area [9] Mean field spectra for eight endmembers for three dates (a) May14 (b) Aug01 (c) Aug Mean NDVI on three dates at field level for (a) maize(b) wheat Temporal-NDVI profiles for (a) potato (b) wheat (c) maize (d) sugarbeet PPI image showing the purest pixels (in white) with an overlay of crop reference polygons SAM rule images for (a) Asperges (b) Maize (c) Potato (d) Leek A classification result of the SAM (Aug01) Endmember spectra for Maize, Grass, Sugarbeet and Soil Fraction images for May14 [(a),(b),(c)] and Aug01 [(d),(e),(f)] Statistics of 3 fraction maps and RMS image for Aug01 calculated with (a) 6VIR bands (b) bands RMS images for (a) May14 (b) Aug01 (c) Aug Composite of 3 endmember fraction images for (a)may14 (b)aug01 (c)aug xi

16 List of Figures A.1 Eigne Value Plot xii

17 Chapter 1 Introduction Earth observation from space as we call it Remote Sensing offers unrivalled capabilities for understanding, monitoring, forecasting, managing and decision making about our planet s resources. It provides a rich harvest of information on our planet and environment. United Nations statistics show that conventional maps cover only 44 % of the world s landmasses. Many are also obsolete, unreliable or inaccurate, and are often difficult to obtain. In contrast, satellite imagery is comprehensive, reliable, regularly updated, and has been acquired practically worldwide. Nevertheless, trustworthiness and reliability of this information depend on the way we interpret this information. Interpretation of remote sensing data is a challenging task. A popular and practised interpretation of digital remote sensing data is by image classification. The purpose of image classification is to assign each pixel in a digital image to one of the predefined and limited number of classes (a theme). Hence we obtain a thematic map from a digital image where each theme is a particular land cover class in the scene. Each pixel is allotted this particular theme depending on its digital number, so the pixel is used as a classification unit. 1.1 Problem definition Using traditional classification methods, information can be extracted to the pixel level as described in the previous section. If an Instantaneous Field of View (IFOV) of a sensor is larger than the feature of interest on the ground, pixels cover more 1

18 1.2. Motivation than one feature or cover type. Scientists deal with the problem by labelling the pixel as Mixed pixel. As a result, these pixels are ineffective to give us information about the association to any specific feature and we lose data without obtaining information. This is because reflection of a mixed pixel is not representative of a particular feature but rather a composite of other features along with it (within that pixel). The interpretation of this mixed pixel can be made by an understanding of the spectral components within each pixel. The procedure carried out to separate and identify these spectral components is called subpixel classification. Subpixel processing/analysis is defined as the capability to detect or classify objects that are smaller than the size of an image pixel [10]. The following section describes briefly the significance of subpixel classification for agricultural monitoring and management, and hence the motivation for this research. 1.2 Motivation The importance of monitoring agricultural production and acquiring relevant statistics is increasing with today s rapid development and consequent considerable changes on the Earth s surface. The significance of this monitoring for a better management of land resources and food production is even more acute for those countries, where agriculture is one of the main resources of their economy. One important parameter to assess and evaluate an agricultural systems is identification of various crop types. In many countries, taxation and subsidy systems depend on the crop type that a farmer grows. Estimating exact crop acreage can be used to calculate crop yield, which itself is an important parameter to monitor the efficiency of an agricultural system. Classification of satellite remote sensing data has been widely used for the crop identification and classifying an agricultural land into different crop types. Each pixel in the image is assigned to the most similar crop type and a thematic map is obtained. However, pixels on the edges of fields and sometimes in a small cropping system, where the crop fields are fragmented into each other, result into mixed pixels. In addition to the problem of mixed pixels, limited spectral separability among different crop types is another problem, which causes difficulty and errors in clas- 2

19 Chapter 1. Introduction sification. These problems are being addressed in this thesis and are investigated by applying subpixel classification on remote sensing data. This study is carried out in cooperation with Synoptics bv, the Netherlands (Integrated Remote Sensing and GIS Applications), by provision of the remote sensing data, field data and experience in crop mapping. PiriReis is one of their products; a digital crop map of The Netherlands, which is produced on a yearly basis. Piri- Reis provides detailed information on which crop has been grown on a particular parcel during the past growing season. This experience from Synoptics bv is expected to be useful for this study as well. 1.3 Research question Subpixel classification is performed by comparing the observed spectra of pixels in an image with the pure spectra of the endmembers (an endmember is a pixel component which is a pure cover type). Basically, it is performed by segregating a pixel into its components on the basis of their different spectral characteristics. The purpose of this study is to discriminate different crop types at the sub-pixel level. It is anticipated that spectral characteristics of many crops are not very distinctive from each other. It is planned, therefore, to exploit temporal characteristics of crops in addition to their spectral characteristics, to make the classification of the crops more significant and accurate. It is expected that the spectral profile (reflectance curve) of each of the crops does not follow the same pattern, when studied at different instants in time. Based on this assumption, it will be tried to answer the following question through this research: How is it possible to take an extra benefit from multitemporal data for crop (sub-pixel) classification? Will it improve subpixel classification results and make the identification of crops more significant? 1.4 Objectives The main objective of this study is to explore temporal and spectral characteristics of different crop types for an improved crop classification methodology. 3

20 1.5. Outline of the thesis This objective is planned to be achieved in the following sequence of steps: Exploration of different theoretical and technical issues in subpixel classification procedures (to chose an appropriate one), Exploring the temporal significance in an agricultural environment, Selection of correct number of cover types (endmembers), Obtaining pure spectra from the images for the selected endmembers, Subpixel classification will be applied on a series of remote sensing images, in order to obtain abundance(fraction) maps for each crop, Temporal analysis of the spectral unmixing results. 1.5 Outline of the thesis The organization of this work is described below: General factors to cause mixed pixels in an image are described in Chapter 2. The existing methods for soft classification (subpixel classification) are reviewed. Chapter 3 is giving a brief description of the study area, data and materials used for the study. Chapter 4 is elaborating the importance of temporal factor in crop monitoring and classification. An implementation of linear unmixing on Landsat images is done in Chapter 5 and results are discussed. Chapter 6 is summarizing and concluding the study and recommendations for a future research are suggested. 4

21 Chapter 2 Subpixel Classification Methods 2.1 The Pixel A digital image consists of a two dimensional array of individual picture elements called pixels. Each pixel represents an area on the Earth s surface and has an intensity value, represented by a digital number. This intensity value is a measure of the energy reflected (or emitted) from the ground. This value is normally an average of the whole ground area covered by the pixel. Resolution of an image is constrained by the pixel size and this pixel size is determined by the Instantaneous Field of View (IFOV) of the sensor s optical system. IFOV is a measure of the ground area viewed by a single detector element in a given instance in time. Therefore, more than one land cover type or feature may be included in an IFOV, resulting in mixed pixels. The number of mixed pixels in an image is a function of the IFOV of the instrument and the spatial complexity of the phenomenon being imaged [13]. A mixed pixel in an image can be the consequence of any of the following situations on the ground [7]: Boundaries between two or more mapping units (e.g. field-woodland boundary), The intergrade between central concepts of the mappable phenomena (ecotone), Linear sub-pixel objects (e.g. a narrow road), or 5

22 2.2. Sub-pixel classification small sub-pixel objects (e.g. a house or a tree). These situations are shown in Figure 2.1. Figure 2.1: Four cases of mixed pixels [7] The presence of these mixed pixels is a nuisance when performing classification, because in the conventional classification procedures, a pixel is considered as an elementary unit for the analysis. Each pixel is, therefore, assigned to a single feature or cover type, even though it is not true for a mixed pixel. It introduces inaccuracy and imprecision in the classification results. The problem of mixed pixels is dealt by subpixel classification. In Section 2.2 and the following sub-sections, subpixel classification and general approaches to perform it, are described. In Section 2.3, the applicability of these models in different fields of application is presented. In Section 2.4, the method that will be implemented in this study for crop classification is explained. 2.2 Sub-pixel classification A considerable amount of work is now available in literature which is based on rejection of the idea that a pixel can be assigned to a single cover type only [7]. 6

23 Chapter 2. Subpixel Classification Methods These sub-pixel procedures attempt to extract components of the pixel, recognizing that more than one land cover type may exist within a pixel. These components of a pixel are referred to as endmembers as they represent the cases where 100 percent of the sensor s IFOV is occupied by a single homogeneous cover type [13]. Subpixel classification is mainly performed by two methods; Spectral Mixture Analysis and Fuzzy Classification Spectral mixture analysis The usual approach to carry out spectral mixture analysis is by modelling of spectral mixtures. Mixture modelling is the process of deriving mixed signals from pure endmember spectra while spectral unmixing aims at doing the reverse, deriving the fractions of the pure endmembers from the mixed pixel [20]. Several models have been proposed in the last couple of years to unmix pixels and determine proportions of their components. The more particular ones are linear, probabilistic, geometric or geometric-optical and stochastic geometric models [11]. These models are comprised of known and unknown parameters. The known parameters are always the observed reflectance from the pixel and the pure spectra of the pixel components (or endmembers). In most of the cases the unknown parameters (which have to be determined by properly using known parameters) are the areal proportions of the endmembers. In the following sections, these mixture models are described briefly. The Linear model In linear mixing, it is assumed that the observed pixel reflectance is a linear mixture of pure spectra of all of its component endmembers (in that pixel) multiplied by their respective areal proportions in each spectral band [18, 16, 11]. Hence, mathematically, the observed reflectance r i for a pixel in band i will be; r i = f 1 a i,1 + f 2 a i,2 + + f c a i,c + e i, (2.1) where e is an error term, f is fraction of an endmember in a pixel, c is possible number of endmembers in the scene, a is the pure (or characteristic) spectra from the respective endmember. If we replace j = 1,, c, then Equation 2.1 can be simplified as: 7

24 2.2. Sub-pixel classification c r i = f j a ij + e i (2.2) j=1 Hence for a multispectral image of n bands; i = 1,, n, there will be n linear equations. In addition to these n equations, there will be another equation, which is called sum-to-unity constraint equation: f 1 + f f c = 1 (2.3) It states that the sum of component proportions for each pixel should sum to 1 (provided that none of the fraction is negative). Hence we have a system of linear equations, which can be solved in a number of ways. Input for the model is the observed reflectance and the pure spectra of components in the pixel. Substituting, these known parameters in these equations, the areal proportion for c endmembers is determined. The number of unknowns should be less or equal to the number of equations for a unique solution. Hence an image of n bands will give n versions of Equation 2.2 and in all n + 1 equations (including Equation 2.3). Hence, this system is capable of yielding a distinct solution for c endmembers where c = n + 1. However, if c < n + 1, it is possible to calculate magnitude of the error term e, using the principle of least-squares. It is pointed out in the literature, however, that it is not so straight forward and n is not always the number of bands, but the intrinsic dimensionality of spectral data which can be revealed by Principal Component Analysis (PCA). PCA is a statistical procedure for transforming a set of correlated variables into a new set of uncorrelated variables by rotating the original axes to new orientations that are orthogonal to each other and therefore there is no correlation. Hence when PCA is applied to a multi-band image, it decorrelates the data by transforming DN distributions around sets of new multi-spaced axes [15]. Hence, in case of, for example, Landsat TM data, if the fifth and sixth PCs of the data contain nothing but noise then the true dimensionality of the data is 4 and not 6 [16]. An intuitive way to understand spectral mixing is geometry of feature space. Mixed pixels are visualized as points in n-dimensional spectral space, where n is the number of bands. In two dimensions, if only two endmembers mix, then the mixed pixels will fall in a line. The pure endmembers will fall at the two ends of the mixing line. If three endmembers mix, then the mixed pixels will fall inside of a 8

25 Chapter 2. Subpixel Classification Methods triangle (Figure 2.2). Mixtures of endmembers fill in between the endmembers in the absence of noise and with non-negative proportions [1, 16]. All mixed spectra are interior to the pure endmembers, inside the simplex formed by the endmember vertices. This convex set of mixed pixels can be used to determine how many endmembers are present and to determine their spectra [1]. Figure 2.2: Geometric representation of mixing model [1] The Probabilistic model Probabilistic models are based on one of several probability techniques such as maximum likelihood [11]. A series of probabilistic models was developed to achieve subpixel resolution for analysis of crop acreage by the Environmental Research Institute of Michigan [14]. A complex Maximum Likelihood algorithm was developed, based upon the weighted combinations of component class mean vectors and covariance matrices. This method was proved promising to calculate the proportions where the spectral separation was high. An approximate maximum likelihood technique was developed by [14]; an example of the probabilistic model. This technique was applied on 4 bands of Landsat MSS data. Pure pixels from two different homogeneous geological components were selected and their reflectance values in the 4 bands were transformed into a single variable for the analysis using a linear discriminant analysis. This single transformed value represents an oblique projection of the sample onto the linear discriminant line. This line in the original four dimensional feature space joins the multivariate means for the two classes of homogeneous pixels. Squared distances measured along the discriminant function line are called Mahalanobis or M-distances. This M-distance is calculated between the the means of two homogeneous components X and Y and between each mixed pixel m and the means of two pure components X and Y respectively. These M-distances are incorporated 9

26 2.2. Sub-pixel classification in the following formula to calculate proportion of each of the component in the mixed pixels. The formula is: Where: P y = P y =proportion of component Y in the mixed pixel; d(m, x) d(m, y), (2.4) d(x, y) d(x, y) =M-distance between means of homogeneous components X and Y ; d(m, x) =M-distance between mixed pixel m and mean X; d(m, y) =M-distance between mixed pixel m and mean Y ; P y = 0, if result is negative; and P y = 1, if the result is greater than 1.0. A major drawback of this method is that the probabilistic model is limited to determine proportions of up to two endmembers only in a mixed pixel. The Geometric and Stochastic-Geometric models These are two examples of mixture models which are more complex and need more input than the linear and probabilistic models [11]. In the geometric or geometric optical models, (when applied for the forest classification), the geometry of tree crowns, their distribution and the direction of solar illumination are taken into account in order to evaluate the relative proportions of the crown, shadow and background in pixels. The stochastic geometric model is a special case of geometric model in which the scene geometric parameters are treated as random varieties in order to absorb the random variabilities in their spatial structure Fuzzy classification Another approach for subpixel classification is Fuzzy classification. It helps in dealing with uncertainty, vagueness and complexity using the concept of fuzzy sets. Membership conception in fuzzy sets allow us to allocate one entity to more than one class. Hence, in case of image classification, we can assign a pixel to more than 10

27 Chapter 2. Subpixel Classification Methods one attributes or classes and this assignment is described in terms of membership grade. In conventional classification procedures, a pixel is assigned to one class only with a membership grade 1 always. This is why, it is called hard classification. In fuzzy classification, membership grades range from 0 to 1; the more similar a pixel is to an attribute class, the closer will be the membership grade to 1 for this class and vice versa. The membership grades for an entity (or pixel) assigned to different classes should always sum to 1. The similarity is often defined in terms of distance of the unknown pixel to a class cluster. It can be Euclidian distance (a diagonal where attributes are scaled to have equal variance or Mahalanobis distance when both variance and covariance are considered for distance scaling [5]. In fuzzy classification, class boundaries in feature space overlap each other and do not have hard boundaries. This overlap of classes is defined by a parameter q, called fuzzy exponent. The fuzzy exponent, q, for the class overlap can be limited by the user. Fuzzy classification can also be performed in two ways as standard image classification, that is, supervised and unsupervised classification. In unsupervised classification, features are classified merely on basis of their spectral characteristics which is generally achieved by some clustering techniques. In supervised classification some prior knowledge is used to create a training set for different classes and this training set is used to define and identify the spectral characteristics of different classes in the scene. Fuzzy classification can be classified similarly as: Fuzzy Clustering (K-means) It is conceptually similar to K-means unsupervised classification. Fuzzy Supervised This approach is similar to Maximum Likelihood classification with a few amendments. 2.3 A selection from different models A comparative study among different types of mixture models (including Fuzzy classification) is done by [11]. All these models are alike in the sense that the observed pixel reflectance is taken as a function of both the spectral signature and the 11

28 2.3. A selection from different models areal proportion of its component endmembers. The difference is, however, in the way they include the scene and imaging characteristics into this function. In linear models, the scene variability is accounted for by means of random residual while in geometric-optical and stochastic-geometric models, it is based on the analysis of the scene geometry. In the probabilistic and fuzzy models, it is done through some statistical method like for instance, maximum likelihood technique. Table 2.1: Applicability of mixture models to different application [11] Application Model Applicability Estimation of... Linear Probabilistic Geometric Stochastic Fuzzy Optical Geometric Vegetation versus bare ground proportions in a dense forest yes yes no no yes Vegetation versus bare ground proportions in a sparse forest yes yes yes yes yes Proportions of different plant communities yes yes no no yes Average tree height, size, and density no no yes no no Proportions of area coverage of different crops yes yes no no yes Proportions of different soil or rock types yes yes no no yes Proportions of different minerals yes yes no no yes Proportions of miscellaneous land covers yes yes no no yes Table 2.1 is giving an overview of different spectral mixture models in terms of their applicability in different fields of applications [11]. It is obvious from this table that for our application, which is to identify different crop types and to calculate area coverage by each crop, linear mixture model (highlighted) can be used. Four types of mixtures of the materials which are generally found in the real world are described by [6]: Linear Mixture The materials in the field of view are optically separated so there is no multiple scattering between components. The combined signal is simply 12

29 Chapter 2. Subpixel Classification Methods the sum of the fractional area times the spectrum of each component. This is also called areal mixture. Intimate Mixture An intimate mixture occurs when different materials are in intimate contact in a scattering surface, such as the mineral grains in a soil or rock. Depending on the optical properties of each component, the resulting signal is a highly non-linear combination of the end-member spectra. Coatings Coatings occur when one material coats another. Each coating is a scattering/transmitting layer whose optical thickness varies with material properties and wavelength. Molecular Mixtures Molecular mixtures occur on a molecular level, such as two liquids, or a liquid and a solid mixed together. For examples, water adsorbed onto a mineral. The close contact of the mixture components can cause band shifts in the adsorbate, such as water in plants. Looking through these definitions provided for different type of mixtures, it seems quite safer to say that a signal from different crop types can be a linear mixture. Hence this section can be concluded by describing the following points in support of linear unmixing for this application: 1. If there is no multiple scattering and photons interact with a single material only, which is possible in large scale areal mixing, then it can be considered as linear mixing [17]. 2. The linear model is easier to implement and does not need many complicated input parameters like geometric models. 3. Also, this model does not have a restriction like probabilistic models to unmix a pixel up to two components only. 4. Most classifiers rely on a gaussian probability distribution of the spectral signature of the training data which often exhibits a non-gaussian distribution [19]. The methods that will be followed to implement the model, is described in the following section. 13

30 2.4. One approach to perform Linear unmixing 2.4 One approach to perform Linear unmixing A general description of linear mixture model is given in Section It was described, the system of linear equations can be solved in different ways. The method implemented in this research is matrix-inversion. Equation 2.2 can be expressed in vector-matrix notation as: r = Af + e (2.5) Where the observed spectrum r (a vector) is a product of mixture of pure endmember spectra A (a matrix) and endmember fraction f (a vector) plus an error (vector) e. If n is number of bands and c is number of cover type components (endmembers), then A is an nxc matrix, f is cx1 vector as f = (f 1, f 2,, f c ) T and r is nx1 vector as r = (r 1, r 2,, r n ) T. This can be seen in Figure 2.3: Figure 2.3: The linear model of spectral mixing [1] Rewriting Equation 2.5 as: ra 1 = f + e (2.6) Hence a simple vector-matrix multiplication between the inverse pure spectra matrix and an observed mixed spectrum gives an estimate of the fraction (proportion) of the endmembers [1]. e i is the residual error in band i. This residual error is the difference between the measured and the modelled spectrum in each band. In Equation 2.5, r is measured 14

31 Chapter 2. Subpixel Classification Methods spectrum and (Af) (or simply ŕ) is the modelled spectrum. In an image of m pixels and n bands, residuals over all bands for each pixel in the image can be averaged to give an RMS error, portrayed as an image, which is calculated from the difference of measured r jk and modelled r jk pixel spectrum. RMS = 1 m n (r jk ŕ jk ) 2 m n k=1 j=1 (2.7) Implementation of linear unmixing can be performed in two ways; unconstrained unmixing and constrained unmixing. In unconstrained unmixing, the fraction values of the endmembers can have any value required to minimize the residual error. However, in constrained unmixing the fraction values for each pixel are forced to sum to one and no negative fractions are allowed. In addition to these two conditions, there is another type of condition which is called partially constrained condition. This condition takes unity constraint but allows negative values for the endmember fractions. Constraining the data is artificial as it will just apply a linear correction after having unmixed the data (a scaling of the data) Endmember selection Pure features in a mixed pixel are referred to as endmembers of that pixel. The selection of appropriate endmembers to input into a linear model is very important. It can be achieved in two ways [20]. 1. From a spectral (field or laboratory) library 2. From the purest pixels in the image Endmembers obtained through the first option are generally referred as known, while the one from the second option are called as derived. Derived endmembers have preference over the known because they are collected under the same atmospheric conditions. It saves from the necessity to atmospherically correct the image and calibrate the data to reflectance space. Also it sets aside the possibility of ignoring a pure endmember in the scene. 15

32 2.4. One approach to perform Linear unmixing Principal Component Analysis (PCA) There is a tendency for multiband images to be somewhat redundant wherever bands are adjacent to each other in the multispectral range. Thus, such bands are said to be correlated (relatively small variations in DNs for some features). A statistically-based program, called Principal Components Analysis, decorrelates the data by transforming DN distributions around sets of new multi-spaced axes. In case of Landsat TM data, over 90% of the spectral variability is mapped into first two PCs [20]. Thus a scatterplot of PC1 and PC2 can be used to select spectrally pure endmembers. Pixel Purity Index (PPI) PPI is an algorithm to find spectrally pure pixels from an image [4]. It utilizes the concept of convex geometry as described in Section These correspond to the materials with spectra that combine linearly to produce all of the spectra in the image. The PPI is computed by using projections of n-dimensional (n is number of bands in the image) scatterplots to 2-D space and marking the extreme pixels in each projection. The output is an image (the PPI Image) in which the digital number (DN) of each pixel in the image corresponds to the number of times that pixel was recorded as extreme. Thus bright pixels in the image show the spatial location of spectral endmembers [1]. From RMS image Spatial pattern of a root mean squared (RMS) image is an indicator to tell that some pure endmembers in the scene are still missing as the model input. Hence, additional endmembers are selected on the basis of clearly visible spatial pattern in the RMS image until it does not show any obvious systematic spatial pattern of error distribution [20]. Spectral Angle Mapper (SAM) Another approach implemented by [18] to select the most important endmembers from a bulk of endmembers present in a scene is Spectral Angel Mapping tech- 16

33 Chapter 2. Subpixel Classification Methods nique (SAM). This technique was used to extract the most important components constituting the bulk of the spectral variability throughout the data set. The Spectral Angle Mapper (SAM) compares a reference spectrum (of a pixel, e.g.) to individual spectra or a spectral library [1]. The algorithm determines the similarity between two spectra by calculating the spectral angle between them, treating them as vectors in a space with dimensionality equal to the number of bands. A simplified explanation of this can be given by considering a reference spectrum and an unknown spectrum from two-band data. The two different materials will be represented in the 2-D scatter plot by a point for each given illumination, or as a line (vector) for all possible illuminations (Figure 2.4). Figure 2.4: Two dimensional example of the Spectral Angle Mapper [1] If r is the reference spectrum and t is an unknown spectrum (or an endmember spectrum), then SAM algorithm generalizes this geometric interpretation for an n- dimensional space (where n is number of bands) by the given equation [1]: ni=1 α = cos 1 t i r i [ n i=1 t 2 i ] 1 2 [ (2.8) n i=1 r 2 i ] 1 2 Hence the output of SAM for each pixel is an angular distance between the two spectra in radians (ranging from 0 to π 2 ). Output of SAM will be a new set of data 17

34 2.5. Summary with as many bands as the number of unknown (endmember) spectra given as input in the algorithm. In addition to this multi-layer image (which is called a rule image), there will be a classified SAM image showing the best SAM match at each pixel. Darker pixels in the rule images represent smaller spectral angles, and thus spectra that are more similar to the endmember spectrum and vice versa. Hence this is a qualitative estimate of the presence or absence of an endmember in a pixel Output of linear unmixing Subpixel classification does not yield an output in the form of a single thematic map, as in pixel-based classification methods. In subpixel classification, we get a series of abundance maps, each map is of the same extent as the original image. These abundance maps represent areal proportions of each of the endmembers (cover types) present in each pixel of the input image. The result is therefore a mass of quantitative and not just thematic data [16]. Linear unmixing provides a root-mean square (RMS) image in the output, along with the abundance maps. The RMS image results from the difference between the the observed pixel spectrum and the spectrum reconstructed from the calculated abundances. The advantage for RMS image is that it accounts for the poorly classified pixels [18], and is a straightforward tool for the evaluation. 2.5 Summary This chapter has described shortly the factors that cause mixed pixels in an image, and then reviewed different methods/models for classification considering the presence of mixed pixels in an image. From the available methods, spectral linear unmixing is found to be adequate for this study. Mixing can be considered a linear process if: (1) no interaction between materials occurs, each photon sees only one material, (2) the scale of mixing is very large as opposed to the size of the materials, and (3) multiple scattering does not occur [20]. Furthermore, it is also described how to incorporate parameters into this model and to evaluate the results. 18

35 Chapter 3 Study Area and Data 3.1 Study area The study area Maasbree is situated in the south of Netherlands, in the province of Limburg, at a latitude of 51 o 23N and 5 o 57E in longitude. Figure 3.1: Study Area [9] The municipality is touching the city of Venlo on its west through which the river Maas is passing. According to the Central Bureau for Statistics (CBS) of The Net- 19

36 3.2. Data herlands, the area of this municipality is km 2, water surface covers 3 km 2 and it is inhabited by a population of 12,850 people [12]. The main cover types in Maasbree are forest, urban and agriculture. The main crop growing season is from April to October. This is a highly heterogeneous area because of high variety of crops and more particularly vegetables. According to the information collected by the ground truth survey (Synoptics bv), crops include potato, sugar beet, maize, strawberry, grass-seed, leek, barley, wheat,different types of cabbage, asperges et cetra. 3.2 Data Data used for this study can be categorized in the following three types: Earth Observation data Field reference data CBS reference data Crop calendar These will be described in detail below Earth Observation data One Landsat-5 and two Landsat-7 satellite images are used for this study. These three Landsat images are acquired during the growing season April October Acquisition dates for these three images are given in Table 3.1. Table 3.1: Satellite remote sensing data Satellite Sensor Date Landsat-5 TM 14/05/00 Landsat-7 ETM+ 01/08/00 Landsat-7 ETM+ 26/08/00 The sensor onboard Landsat-5 is thematic Mapper (TM) while Enhanced Thematic Mapper plus (ETM+) on Landsat-7. Both sensors have identical sensor characteristics and spectral band width. the design of ETM+ stresses the provision of the 20

37 Chapter 3. Study Area and Data data continuity with Landsat-4 and -5. Similar orbits and repeat patterns are used as well as the the 185 km swath width for imaging [13]. ETM+ is a passive sensor that measures solar radiation reflected or emitted by the Earth s surface. The instrument has eight bands sensitive to different wavelengths of visible, infrared, and thermal radiation (Table 3.2). Table 3.2: Landsat ETM+ spectral channels Band Spectral Range Nominal Spectral Spatial µm Location resolution Blue Green Red Near Infrared Mid Infrared Thermal Infrared Mid Infrared Panchromatic 15 Hence the difference of ETM+ from the TM sensor, is the improved spatial resolution (from 120m to 60m) of the thermal IR band (Band 6) and the addition of a panchromatic band (Band 8) which are not being used in this study. Therefore, it was possible to use data from both the sensors together in this study Field reference data The date of ground truth survey for collection of reference data, used for this study is August 10, It is provided by Synoptics bv, The Netherlands, in the format of a polygon shape file. These polygons are representing different crop types, fallow land and bare soil Data from the Central Bureau for Statistics (CBS) The spectral resolution of Landsat images (6 bands used in this study) is not enough to classify an area with an existence of more than 15 crop types (endmembers), through spectral unmixing. The crop statistics from CBS, was available with Synoptics. This data was, therefore, requested in order to be able to know the main crops of the area and hence to short-list the endmembers. The database is providing 21

38 3.3. Data preparation acreage per crop, per municipality, per are. One are is equivalent to 0.01 hectare. A shape file to locate these municipalities on the images was also available. This data could also be used later for assessment of area calculation results Crop calendar Crop calendar provides knowledge of the crop development stages for a particular area [13]. This information is useful to determine if a particular crop is likely to be visible on a particular date. This information is available for the following crops: Maize Soil preparation in April, sowing from April 25th till May 10th, full cover from beginning of July, harvest from September 20th till November 1st. Sugar beet Soil preparation and sowing in first week of April, full cover from end of June/beginning of July, harvest in October/November. Potato Soil preparation and planting in first half of April, full cover from end of June/beginning of July, harvest in the end of August Selection criteria Considering availability of the field reference data, crop acreage data from CBS and clear areas in all the three Landsat images, the municipality of Maasbree is selected. However a further subset of the area is prepared by masking out urban and forest cover types to have an image of solely agricultural fields. 3.3 Data preparation Earth observation data needs to undergo some correction procedures before it can be used for processing and analysis. This is due to the distortions and degradations induced to the data during image acquisition. These correction procedures are generally termed preprocessing and can be divided into two categories; geometric corrections and radiometric corrections. 22

39 Chapter 3. Study Area and Data Geometric corrections Geometric corrections are needed for geometric deformation due to the variation in altitude, velocity of the sensor platform, for variations in scan speed and in the sweep of the sensors field of view, earth curvature, relief displacement etc [13]. The systematic errors are normally corrected for at the receiving station. Random distortion needs to be corrected for by the analyst through selection of sufficient number of ground control points (GCPs) with correct coordinates, usually from a map or GPS (Global Positioning System) points, which can be localized in the satellite image. A transformation function is calculated to determine the distorted image positions corresponding to the correct map positions: an undisturbed output grid is defined. After this, each cell in this new grid is assigned a gray level according to the corresponding pixel in the original image, this process is called resampling. The cell size in the original image and the new grid are not the same, therefore the DN values can not be assigned by simply overlying the two but it is done through some interpolation methods. Commonly used resampling algorithms are: Nearest neighbour The pixel value is assigned the DN value of the closest pixel in the original image. Bilinear interpolation Distance-weighted average is calculated over the four nearest pixels in the original image and this value is assigned to the new pixel. Cubic convolution In this scheme, a polynomial approach based on the values of 16 surrounding pixels is applied. The images used in this study are corrected geometrically and resampled by Synoptics bv, however the choice for resampling was told as nearest neighbour. This resampling most closely preserves the spectral integrity of the image pixels. Bilinear interpolation and cubic convolution resampling perform spectral averaging of neighbouring pixels, yielding pixels with spectral properties that are less likely to provide optimal results Radiometric corrections Radiometric corrections are required because of the factors such as changes in scene illumination, atmospheric conditions, viewing geometry and instrument response 23

40 3.3. Data preparation characteristics which influence the radiance measured by any given system over a given object [13]. Haze and sun elevation correction are applied on the data used for this study. Haze correction Satellite images of the earth recorded by optical instruments may contain haze and cloud areas but haze upto a certain optical thickness can be removed in multispectral images. This allows for improved evaluation of satellite imagery, especially for the applications where multitemporal dataset is used. Haze in an image is due to the scattered path radiance, and it reduces the image contrast. The routine generally applied is called dark pixel subtraction which is applied to the dataset used in this study. The pixel in a given image with the lowest brightness value is assumed to have a zero ground reflectance such that its satellite measured radiometric value represents the path radiance contribution of the atmosphere that needs to be factored out of the dataset. This method requires suitable dark pixels to exist somewhere on the image. In the images of May14 and Aug26, water bodies and in Aug01 cloud shadows were used to represent dark pixels in the image and for the haze correction. Sun elevation correction This correction is necessary in applications in which images taken at different times are used [13]. The sun elevation correction accounts for the seasonal position of the sun relative to the earth. Through this process, image data acquired under different solar illumination angles are normalized by calculating pixel brightness values assuming the sun was at the zenith on each date of sensing. This correction was applied by dividing each pixel value in a scene by the sine of the solar elevation angle for the particular time and location of imaging. ` DN = DN Sineδ (3.1) Where ` DN is the DN value in the corrected image and δ is the sun elevation angle (this information is obtained along the images). This correction was applied on the haze corrected images. 24

41 Chapter 3. Study Area and Data Reference data is refined Pure spectra representing an endmember (crop type in this study) is an important input for the mixture model. In this study, these endmember spectra are collected from the scene overlaying the field reference data on the images. Hence the endmember spectrum for a crop is a mean spectrum of all the pixel spectra covered by the representative reference polygons of that particular crop. The procedure of pure spectra collection is considered to be an iterative process unless a proper output is obtain from the mixture model. (Proper output means that fraction values for all the endmembers are non-negative and their sum for a single pixel does not exceed unity and RMS image is not showing a high spatial variation). Once the mixture model was run, results obtained were not satisfactory. The reason for this could be the pixels which are at the field boundaries. They are generally mixed pixels due to a mixed reflection from different crop types in adjacent fields. It was decided then to refine these reference polygons to achieve purer endmember spectra. For this the boundary pixels from all the polygons were excluded and in addition to that if a pixel among many is giving an odd visualization, it was also excluded. 25

42 3.3. Data preparation 26

43 Chapter 4 Temporal Analysis 4.1 Available Methods Crop type classification in agricultural areas using remote sensing data has been employed since more than two decades like many other earth resource applications. However, in an environment like agriculture which is highly variable in time and space, feature identification becomes complicated by analysing their spectral properties. Use of multitemporal data may be a solution and a way to take the advantage of the spectral discrepancies over time. Multitemporal data can be exploited through different ways to improve crop classification. A simple way is to merge two (or more) images from different dates during the growing season to prepare a product for visual interpretation. An image which is acquired at the beginning of the season can show fields with bare soil which means a season crop is being sown and presence of a mature crop would mean that a previous crop is not being harvested yet. A crop calendar which provides the knowledge of crop development stages for an area can be helpful to determine the presence of a particular crop at certain date. For an automated classification, the multidate images can be combined to prepare a single product and classification can be performed. Alternatively, principal component analysis can be used to reduce the dimensionality of the combined dataset prior to the classification [13]. For example, to merge two Landsat TM or ETM+ images, it is possible to take first three principal components computed from each individual image and then merge to create a 6-band dataset for classification. 27

44 4.1. Available Methods Another way of dealing with multitemporal data for crop classification is the multitemporal profile approach. In this approach, classification is based on physical modelling of the time behaviour of each crop s spectral response pattern. Temporal pattern of spectral data represents the phenological development of a crop, that is, the progress from seedling emergence to maturity of the crop [8]. Hence by relating the observed temporal-spectral pattern to the expected phenological development pattern associated with different crops, a crop identity or label can be assigned to the field. It has been found that the time behaviour of the greenness of annual crops is sigmoidal. (It is described more in detail in [13].) This profile is relatable with vegetation indices and biophysical crop parameters. This is briefly reviewed in the following section Vegetation Indices A vegetation index (VI) is an indicator sensitive to chlorophyll activity and to the density of vegetation cover [2]. Any VI is formulated to subtract the effect of reflectance in visible band from near infrared (NIR) reflectance. Hence, a vegetated surface will yield high values because of their high NIR reflectance and low visible reflectance, rock and bare soil will result in 0 values due to similar reflectance in the two bands and clouds, water and snow have larger visible reflectance than NIR, thus these feature yield negative index values. The simplest VI is Simple Ratio (SR = N IR/R) and the most common is Normalized Difference Vegetation Index (NDV I = NIR R/NIR + R). A list of the intrinsic, soil-adjusted and atmospherically corrected indices can be seen in [3]. Temporal significance of the VIs is that it varies in parallel to the biomass of vegetation coverage. It grows and recedes in phase with the growth cycle of the plant. For annual crops, the evolution of the vegetation index over the course of a season can be divided into three key periods: the installation of vegetation (ascending phase), flowering and formation of fruit (plateau), and maturation of the fruit, senescence, and harvest (descending phase) [2]. This temporal VI curve will be different for different crops depending on crop s phenological cycle and hence being a tool for crop classification. Then there are biophysical crop parameters, which play a major role in the description of vegetation development, like fractional vegetation cover (ν c ), Leaf Area Index (LAI), etc [3]. Few studies have been cited by [3], where attempts are made to relate ν c and LAI with VIs. A high correlation (r 2 ) of ν c with SR (r 2 = 0.90) 28

45 Chapter 4. Temporal Analysis and with NDVI (r 2 = 0.79) and a linear relationship between LAI and SAVI (Soil Adjusted Vegetation Index) has been reported. 4.2 Temporal-spectral unmixing profile In this study, the intension is to observe the multitemporal behaviour of the fraction values derived through spectral unmixing. As vegetation indices and crop parameters (some of them being mentioned in Section 4.1.1), when plotted against time, have a well recognized relationship with the crop phenological cycle. Similarly, in this study, general behaviour of temporal profile of an endmember s fraction values obtained by applying spectral unmixing to multitemporal Landsat images will be studied. The multitemporal profiles acquired for different crops will be compared, expecting a relationship with the respective crop s phenological cycle. This will be achieved by applying spectral unmixing to the three Landsat images acquired during the growing season These experiments are described in Chapter 5. In this Chapter, small experimentation is done to observe the variance shown by data over time and hence the significance of temporal analysis Temporal-spectral profiles Spectra for eight different crop types existing in the study area are plotted for three available images. These are the mean spectra of various fields of each crop obtained from the field reference data (Figure 4.1). The endmember spectra for almost all the crops are showing a similar pattern to each other on May14 (except for wheat, barley and grass). In the other two dates, they are manifesting some uniqueness. It can also be seen that leek and barley curves are not as similar to each other in other two dates as in Aug01. On the other hand, wheat and barley curves are very close to each other on Aug26, especially in infrared bands, while revealing quite different behaviour in other two dates Temporal-NDVI profiles NDVI images are prepared for 3 Landsat scenes. Then mean NDVI is extracted for 10 fields of each of maize, sugarbeet, potato and wheat. This mean NDVI for these fields are plotted for the three dates and are shown in Figure

46 4.2. Temporal-spectral unmixing profile Figure 4.1: Mean field spectra for eight endmembers for three dates (a) May14 (b) Aug01 (c) Aug26 30

47 Chapter 4. Temporal Analysis (a) (b) Figure 4.2: Mean NDVI on three dates at field level for (a) maize(b) wheat (a) (b) (c) (d) Figure 4.3: Temporal-NDVI profiles for (a) potato (b) wheat (c) maize (d) sugarbeet for maize and wheat. NDVI for maize is quite stable from field to field while wheat is showing a high spatial variation especially on Aug01 and Aug26. It may be due to multi-sowing dates, muti-variety of crop or varying distribution of plants in different fields. The same information is plotted differently in Figure 4.3. The multitemporal-ndvi profiles for the four crops are exhibiting different pattern from each other. A very obvious development (descending and ascending) in the vegetation index can be seen from the symmetrical and uniform curves obtained from wheat fields. Profiles 31

48 4.3. Summary for maise and sugarbeet are also quite stable in pattern. But for potato field, a very high variance is obvious as if they are not from the same crop. It s possible to say that classification of potato fields is not as reliable as for wheat, maise and sugarbeet. 4.3 Summary In this chapter, significance of multitemporal data for crop classification is described and the practised approaches are mentioned. Generally, while reviewing literature, it has been found that an accurate crop classification is almost impossible through data acquisition on a single date. Later, some experimentation is performed on multitemporal data to demonstrate the variance shown by data over time and hence the significance of temporal analysis. 32

49 Chapter 5 Results and Discussion Linear spectral unmixing is applied on multitemporal Landsat images. Different steps and approaches for endmember selection, collection of endmember spectra from the scene and application of linear unmixing are described in this chapter. Results from processing are described and discussed. 5.1 Endmember Selection The maximum number of materials that can be unmixed through linear unmixing is n 1, where n is number of bands in the input image. This brings a unique solution that minimizes the error of the model. Selection of pure pixels representing these materials is the first step for unmixing. Following the different approaches, as suggested in Section 2.4.1, Pixel Purity Index (PPI) and Principal Component Analysis (PCA) are attempted. These are now described Pixel Purity Index (PPI) The Pixel Purity Index (PPI) function is applied to locate the most spectrally pure or extreme pixels in the scene. It was applied to Landsat image of Aug01. As this image is closest to the field survey date (August 10). A threshold 2 was entered. It means it marks all pixels greater than two digital numbers (DN) from the extreme pixels as being extreme. The PPI procedure was tried with different number of iterations. A series of 5,000 iterations could mark 550 pure pixels in the scene while an iteration of 10,000 could not go beyond 575 pixels. Plot of iterations versus 33

50 5.1. Endmember Selection number of pure pixels have shown quite stability in the curve after reaching 500 extreme pixels. The second step was to relate these pure pixels to an endmember (a crop or bare soil) in order to give an identity to these pixels. For this, field reference polygons were overlaid on the PPI image. This is shown in Figure 5.1. These pure pixels selected by PPI did not correspond with the field data except a few in the cabbage polygon. It was not possible, therefore, to use the output from PPI. Figure 5.1: PPI image showing the purest pixels (in white) with an overlay of crop reference polygons Principal Component Analysis (PCA) In a second attempt to locate endmembers, a PCA was calculated for Aug01 image. It was avoided to apply PCA to the stack of multidate layers as probability increases to mix spectral and temporal information. Eigenvalue plot has shown much more noise and less information in last four PCs as compared to PC1 and PC2(Appendix A). Pure pixels were, therefore, marked from a scatterplot of PC1 and PC2. The same problem was faced as in case of PPI. These pixels do not relate to the endmembers in reference data. The above two approaches have not been proved successful in this research. Field reference data was used to select pure pixels from the scene and then crop statistics from CBS and Spectral Angle Mapping (SAM) technique are used to reduce the endmembers to input in linear spectral unmixing. 34

51 Chapter 5. Results and Discussion Crop statistics from CBS A combined use of the CBS data and SAM to short-list the endmembers from 15 to 3 or 4, which are possible to unmix using a 6-band image. Soil was introduced as one endmember, as the presence of soil in the background of vegetation is a main reason of mixed reflection from vegetation. According to the statistics from CBS, The following crops have comparatively more acreage in the municipality of Maasbree than the rest of the crops. 1. Potato 2. Maize 3. Sugar beet 4. Leek/Asperges 5. Strawberry In outcome of SAM, these crops were given more weight Spectral Angle Mapping (SAM) SAM is applied to Landsat ETM+ of Aug01. Spectra of 14 endmembers are obtained from the field survey data. This reference data is providing several polygons for each endmember. These polygons are converted to Regions of Interest (ROIs). Hence a mean spectrum from the respective ROI is obtained for each endmember and entered into the SAM classifier. Eight of these endmember spectra can be seen in Figure 4.1. This is the input for the SAM classifier. The output obtained from SAM is a classified SAM image. This classification image is one band with coded (nominal) values for all classes. A code shows the best match for a pixel (for example, potato is coded 10). A second output to the SAM is a rule image. This is an image with 14 layers, each for one endmember showing the angular distance of this endmember from the reference spectrum in radians. Hence smaller values mean more similarity and these are darker pixels in the image and vice versa. In Figure 5.2, four layers from the rule image are shown. These are selected arbitrarily to show visually a difference in the endmember images that are possessing different spectral similarities from the input image (Aug01). 35

52 5.1. Endmember Selection (a) (b) (c) (d) Figure 5.2: SAM rule images for (a) Asperges (b) Maize (c) Potato (d) Leek. Looking on these four images, it is quite obvious that potato and maize are contributing more to the scene as compared to asperges and leek. Similarly, the strawberry image has shown less spectral similarity, with brighter pixels throughout the scene. Hence through a visual analysis of these SAM images, potato, maize and sugar beet can be stronger candidates than asperges, strawberry and prei in the list of endmembers based on CBS statistics. The classified SAM image is also evaluated. This image is created by labelling each pixel with the endmember for which SAM classifier has found the best match. This image is shown in Figure 5.3. Looking at the SAM classified image, it is obvious that maize, potato, sugar beet, and grass are mostly contributing to the scene. Some leek can be seen but only in a 36

53 Chapter 5. Results and Discussion Figure 5.3: A classification result of the SAM (Aug01) particular part (east) of the scene. However, selection of these endmembers is not finalized by this visual analysis. SAM classification results are quantified, and it is confirmed that maize, potato, grass and sugarbeet are four main crops in the scene. Crop Pixel (%) Maize Potato Grass Sugar beet Leek 5.34 Hence grass has also emerged as an important endmember in addition to Potato, 37

54 5.1. Endmember Selection 38

55 Chapter 5. Results and Discussion Maize and Sugarbeet. Accuracy of SAM classification results are assessed by a conventional confusion matrix. Field reference data is used for this assessment. A summary of the matrix is given in Table 5.1. Though, the overall accuracy of SAM classification is only 44 73%, but looking individually to endmembers, independent of the overall accuracy, some endmembers have shown a reasonable accuracy. For example, maize, sugarbeet and grass. Especially, Producer s accuracy for grass and sugarbeet is 84 62% and 75 80% respectively. However, potato has shown very little reliability (Producer s accuracy = % and User s accuracy = 34 62). It is due to multivarieties of the crop. The reference data is not enough to represent these different varieties of potato. This is why, potato is dropped from the list of the endmembers. Table 5.1: Confusion matrix for SAM classification Reference Classified Correctly Producer s User s Class name total pixelx total pixels classified Accuracy Accuracy % % Asperges Soil Barley Cabagerd Cabagest Cabagewt Fallow Grass Maize Potato Leek Sugar beet Tree crops Wheat Unclassified Total Overall Classification Accuracy = % 39

56 5.2. Linear spectral unmixing Hence a final selection of the endmembers made for linear unmixing is maize, grass, sugar beet and bare soil. Soil is selected even though it has shown very low accuracy as to see a mixed effect of soil with vegetation. 5.2 Linear spectral unmixing Linear spectral unmixing is applied on the above endmembers to complete dataset of multitemporal Landsat images. Unconstrained unmixing is chosen. It is preferred over constrained unmixing as there is no use of artificially constraining the mixing. It will just apply a linear correction after having unmixed the data. Hence the advantage of unconstrained unmixing is that we can assess the results. If there are negative abundances for any of the endmembers, or the abundances for all of the endmembers for the same pixel sum to a quantity greater than 1, then the unmixing doesn t make any physical sense. One reason for this may be the incorrect selection of endmembers. Hence, it is better to run unmixing iteratively to examine the abundance images and RMS error image. Ideally, the RMS image should not have high errors, and all of the abundance images are non-negative and sum to less than one. This iterative method is much more accurate than trying to artificially constrain the mixing, as in this way, it is possible to detect the errors of the model Spectra collection The spectra for the four endmembers were collected from the scene by overlaying field reference data, as described in Section The four endmember spectra for Landsat ETM+, dated Aug26, are shown in Figure 5.4. These are the representative spectra of the endmembers, used in the unmixing process, to classify them. These endmembers were obtained after refining the reference data by excluding boundary pixels from the polygons Unmixing results Linear spectral unmixing to the four endmembers, maize, grass, sugar beet and bare soil is applied to multitemporal Landsat images several times. Different combinations of three and four endmembers altogether were tried. Fraction values for the 40

57 Chapter 5. Results and Discussion Figure 5.4: Endmember spectra for Maize, Grass, Sugarbeet and Soil endmembers are overflown and RMS image is showing a high spatial range. Finally, it is applied to maize, sugar beet and bare soil. Fraction images for these three endmembers for May14 and Aug01 are shown in Figure 5.5. Brighter pixels are showing higher abundance of an endmember and vice versa. Theoretically, the fraction values should be in range from 0 to 1, as, for example, a fraction value of 0.2 means 20 % of that endmember in that particular pixel. Hence the sum of all the endmember fractions for a pixel should not exceed 1. It could not be achieved. Similarly an RMS image which is showing at each pixel a difference of modelled and measured pixel spectrum, are compared for the three dates. RMS image for Aug26 is showing a high spatial pattern, which means some endmembers are missing in the model. RMS image for May14 and Aug01 have shown comparatively better results. Statistics for the three fraction images of maize, sugarbeet and soil and the RMS image for the three dates are shown in Table 5.2. An unmixing applied on a spectral subset (bands 5432) instead of using all the 6 VIR Landsat bands, has shown a dramatic fall in the RMS values. There is some improvement in the endmember fractions as well. This is shown in Figure 5.6. It means that the extra two bands are just a source of redundant information in the data and inclusion of them does not provide an extra benefit in the analysis. Three endmember fraction maps are combined and a composite map is prepared 41

58 5.3. Discussion Table 5.2: Unmixing results showing main statistics for 3 Landsat images May14 Minimum Maximum Mean Standard deviation Maize Sugarbeet Soil RMS Aug01 Maize Sugarbeet Soil RMS Aug26 Maize Sugarbeet Soil RMS for each date. These classification maps are shown in Figure 5.8. Three fraction images obtained for maize, sugarbeet and soil has shown a positive relationship with the crop calendar information. Unmixing results of May14 has shown more proportion of soil and very little proportion of the two crops. This is because, sugarbeet is sown just in first week of April and maize in last week of April (Section 3.2.4). These crops have shown progress in their proportions towards August as per expectation. Hence implementation of linear unmixing to multitemporal images has shown an additional aid to identify a particular crop. The three RMS images obtained for the three dates are shown in Figure Discussion Due to negative fractions values in the unmixing results, we could not use these values for our further analysis and the results are limited to visual interpretation. Three composite maps shown in Figure 5.8, are confirming the fact that sugar beet and maize which are sown in beginning April and beginning May have shown little 42

59 Chapter 5. Results and Discussion (a) maize (d) maize (b) sugarbeet (e) sugarbeet (c) soil (f) soil Figure 5.5: Fraction images for May14 [(a),(b),(c)] and Aug01 [(d),(e),(f)] 43

60 5.3. Discussion (a) (b) Figure 5.6: Statistics of 3 fraction maps and RMS image for Aug01 calculated with (a) 6VIR bands (b) bands 5432 presence in the May 14th image and are appearing as fields in August images. It is also obvious from the fraction images in Figure 5.5, that the fraction image for soil has turned very dark from may to august, confirming that mostly, the soil has been covered by the crops in August images. These negative and non-unity values may be explained by a high spatial and temporal variability of the nature of the phenomenon being mapped. Difference in the sowing dates for a crop in scene can cause a spectral variability for the same crop, similarly distribution of crop plants may not be uniformly spread in the scene, it may be dense in a field and sparse in another which will also be received by the sensor as highly variable signals. Also, the selected endmembers (crops) that are tried to be unmixed on a sub-pixel level, can hardly be regarded as statistically independent of each other and are linearly scaled versions of each other. In a complex system of linear equations such as presented by the spectral unmixing technique, such linear scaling will result in un-precise estimates of fractions and in extreme case in singular matrices and hence leading to errors in estimates of their fractions. 44

61 Chapter 5. Results and Discussion Figure 5.7: RMS images for (a) May14 (b) Aug01 (c) Aug26 45

62 5.3. Discussion 46

63 Chapter 5. Results and Discussion Figure 5.8: Composite of 3 endmember fraction images for (a)may14 (b)aug01 (c)aug26 47