comparing various fractal models for analysing vegetation ...vidya, nidhi, saurav, aditi, smita,...

Comparing Various Fractal Models for Analysing Vegetation Cover Types at Different Resolutions with

the change in Altitude and Season

Chandan Nayak January, 2008

Comparing Various Fractal Models for Analysing Vegetation Cover Types at Different Resolutions with the

change in Altitude and Season

by

Chandan Nayak Thesis submitted to the International Institute for Geo-information Science and Earth Observation in partial fulfilment of the requirements for the degree of Master of Science in Geo-information Science and Earth Observation, Specialisation: (Geoinformatics) Thesis Assessment Board Chairman : Prof. Dr. Ir. A. (Alfred) Stein, ITC External Examiner: Dr. R. D. Garg, IIT, Roorkee IIRS member : Dr. Sameer Saran IIRS member : Dr. C Jeganathan IIRS member : Vandita Srivastava. Thesis supervisors IIRS : Vandita Srivastava ITC : Prof. Dr. Ir. A. (Alfred) Stein

iirs INTERNATIONAL INSTITUTE FOR GEO-INFORMATION SCIENCE AND EARTH OBSERVATION

ENSCHEDE, THE NETHERLANDS &

INDIAN INSTITUTE OF REMOTE SENSING, NATIONAL REMOTE SENSING AGENCY (NRSA), DEPARTMENT OF SPACE, DEHRADUN, INDIA

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

Dedicated to my beloved Ma, For making me the person I am.

COMPARING VARIOUS FRACTAL MODELS FOR ANALYSING VEGETATION COVER TYPES AT DIFFERENT RESOLUTIONS WITH THE CHANGE IN ALTITUDE AND SEASON

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Abstract In the last quarter century, fractal geometry has strived to become a useful tool for modeling natural phenomenon. As remote sensing images tend to be spatially complicated, fractal analysis, the study of complicated phenomenon is used as an alternative to Euclidean concepts for a more accurate representation of the nature of complexity in natural boundaries and surfaces. Fractal dimension (FD) is the central construct of fractal geometry used to describe the geometric complexity of natural phenomenon. The objective of the present study was to compare three fractal models: Isarithm, Variogram and Triangular Prism Surface Area method (TPSAM), for differentiating the vegetation types found in the study area at different resolution with the change in altitude and season. Remote sensing data of different spatial resolution from different sensors like LISS III, LISS IV and ASTER were used to compute FD using the integrated software package ICAMS (Image Characterization and Modeling System). Both local (moving window based) and global (whole image or major subset) approaches were used wherever it could be implemented. Mean FD values from the different methods for every vegetation type were calculated for different subset areas representing Sal, Planted, Mixed broad leaf and Mountain vegetations. This was done for green, red, infra-red band of the sensors and NDVI. It was seen that Variogram method was the better method in differentiating the vegetation type found in the study area with 250 by 250m subset. Other methods, Isarithm and TPSAM, did not give satisfactory results and had comparatively poor performance in terms of standard deviation and R2 values of the FD calculated. It was also found that NDVI and IR bands are the optimal bands which could appreciably distinguish the vegetation types. 23.5m of LISS III was judged to be the best resolution when coupled with Variogram method. Fractal measurements can be used, albeit cautiously, to remote sensing images for discriminating vegetation types, taking other factors into consideration. This could also serve as a metadata for content –based data mining from these imagery. Keywords: Fractal dimension, Isarithm, Variogram, Triangular prism, ICAMS


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Acknowledgements My first and foremost gratitude is expressed to Prof Alfred Stein, the one person who kept my confidence and spirit high throughout the 6 months of thesis work. Every mail from Prof Stein, whether of appreciation or criticism has contributed to do justice to the thesis in one respect or other. His professional yet friendly and humorous ways of communication has helped in the successful completion of thesis with ease and comfort. I extend my thanks to Ms Vandita Srivastava for being my first supervisor. Her suggestions from time to time made me stay focused in the right direction to achieve the objective of the study. I am greatly indebted to IIRS and ITC for allowing me to take up the M.Sc course. The fellowship provided by ITC is appreciated without bounds. Thanks are due in this context to Dr V.K. Dadhwal, Dean, IIRS for providing all the necessary facilities required for the research work. His expert opinion and technical guidance have proved to be precious all through the course. Dr C. Jeganathan, a true teacher, friend and guide….. Jegan sir deserves my sincere respect and gratitude for his support and motivation from the very beginning of the course to the end. A model scientist, few have the mettle like him to inspire his students. I am immensely thankful to Mr Amit Kulkarni, Ph.D student, Louisiana State University for responding to my mails and taking initiative to provide the ICAMS software without which the research would be nowhere. Acknowledgement is due to Dr. Nina Lam, Professor, Louisiana State University, for giving her permission to use the software. I cannot forget to mention Mr P.L.N. Raju, In-charge, Geo-informatics Division, for the help extended in course of the research, especially to acquire satellite data from NRSA. I express my thanks to Ms. Minakshi Kumar, Scientist “SE”, PRSD, Dr S.K Saha, Head of the Department, ASD and Dr Sarnam Singh, Scientist “SE”, FED, IIRS for the time they have spared to provide data and technical help. A word of gratitude is expressed to Dr Valentijn Tolpekin and Dr Nicholas Hamm for their suggestions during the mid–term evaluation. I also thank MSc. W. H. Bakker, Geoinformation Processing Department, ITC for his guidance during the conceptualization of this research. My friend and roomie for the last one and a half years, Mr Gurdeep Singh cannot be missed out in this section. The light moments we have shared during long nights of hard work throughout the research will always stay in memory. I thank each one of my batchmates, Chand sir, Gopal sir, Duminda, Sashi, Sandeep, Jhumur, Rupinder, Gurpreet, Sumona and Pravesh for being there to have fun and frolic at IIRS and ITC. Vidya, Nidhi, Saurav, Aditi, Smita, Tushar, and all in the PGD batch of Geo-informatics and Geo- hazards, 2006-07 are lovingly remembered. My special thanks goes to Ambika for her constant support and help when indeed it mattered the most. I thank my dear baba for encouraging my venture to take up the MSc Geo-informatics course. His love and support are my strengths without which I would not have reached this far.


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Last but not the least; I thank the Royal Govt. of Netherlands for allowing the trip to Netherlands and giving an opportunity to experience the Dutch culture and customs. Chandan Nayak Dehra Dun, India January 2008.


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Table of contents Abstract…………………………………………………………………………………………………i Acknowledgement……………………………………………………………………………………...ii List of figures…………………………………………………………………………………………..vi List of tables…………………………………………………………………………………………...vii 1. Introduction ......................................................................................................................................1

1.1. Use of Fractals in Remote Sensing:..........................................................................................1 1.2. Problem definition:...................................................................................................................2 1.3. Research objective....................................................................................................................3

1.3.1. Main objective..................................................................................................................3 1.3.2. Sub-Objectives .................................................................................................................4

1.4. Research Questions ..................................................................................................................4 1.5. Methodology ............................................................................................................................4 1.6. Chapter schema ........................................................................................................................5

2. Fractal Geometry and Fractal Models ..............................................................................................6 2.1. Background ..............................................................................................................................6 2.2. Natural fractals - statistical self-similarity................................................................................7 2.3. Fractals in remote sensing of land-cover..................................................................................7 2.4. Fractal models ..........................................................................................................................8

2.4.1. Isarithm method..............................................................................................................10 2.4.2. Triangular Prism Surface Area method ..........................................................................11 2.4.3. Variogram method..........................................................................................................13

3. Materials and methods....................................................................................................................16 3.1. Study area and field investigation ..........................................................................................16

3.1.1. Location of study area ....................................................................................................16 3.1.2. Reasons for selecting the study area...............................................................................16 3.1.3. Vegetation in the study area ...........................................................................................17 3.1.4. Field visit........................................................................................................................18

3.2. Image data ..............................................................................................................................20 LISS IV ..........................................................................................................................................20 ASTER ...........................................................................................................................................20 LISS III...........................................................................................................................................20

3.3. Data generation.......................................................................................................................21 Detailed methodology: ...................................................................................................................21

3.4. Software used .........................................................................................................................25 4. Results & Discussions ....................................................................................................................26

4.1. Selection of optimal spectral band(s) for differentiating different vegetation types ..............27 4.2. Change of FD with spatial resolution:....................................................................................31 4.3. Change of FD with seasons....................................................................................................38 4.4. Change of FD with altitude: ...................................................................................................43 4.5. Comparison: ...........................................................................................................................45

4.5.1. Optimal band selection ...................................................................................................45 4.5.2. Fractal dimension and spatial resolution: .......................................................................47 4.5.3. Fractal dimension and change in season: .......................................................................48


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4.5.4. Fractal dimension and altitude........................................................................................49 5. Conclusions and recommendations ................................................................................................50

5.1. Conclusions ............................................................................................................................50 5.2. Limitations of the study..........................................................................................................51 5.3. Future recommendations ........................................................................................................52

6. References ......................................................................................................................................53 Appendix – 1 ..........................................................................................................................................55

ICAMS interface and fractal image....................................................................................................55 Appendix – 2 ..........................................................................................................................................57

Plots of change of FD with Spatial resolution and Spectral bands: ...................................................57 Appendix – 3 ..........................................................................................................................................59

Plots of variation of FD with the change in altitude: .........................................................................59 Appendix – 4 ..........................................................................................................................................62

Plots of change of FD with spectral bands for different vegetation types .........................................62 Appendix – 5 ..........................................................................................................................................65

Plots of Local fractal approach for optimal band selection ................................................................65 Appendix – 6 ..........................................................................................................................................68

FD values calculated with different methods.....................................................................................68 Appendix – 7 ..........................................................................................................................................75

Field photographs...............................................................................................................................75


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List of figures Figure 1-1: Methodology flow chart ........................................................................................................4 Figure 2-1: Estimation of FD using isarithm method ............................................................................10 Figure 2-2: Pictorial representation of the Triangular prism surface area method.................................12 Figure 2-3: The log-log plot of variance and distance as used in variogram method ............................14 Figure 3-1: Location and extent of study areas. .....................................................................................16 Figure 3-2: Altitudinal distribution of forests in western Himalayas.....................................................17 Figure 3-3: Image showing field points and elevation values in Haldwani. ..........................................18 Figure 3-4 DEM showing field points in Haldwani ...............................................................................19 Figure 3-5: Detailed methodology flow chart ........................................................................................22 Figure 3-6: Some selected subsets of vegetations ..................................................................................24 Figure 4-1: Plot of Local Variogram method, ASTER October.............................................................29 Figure 4-2: Plot of Local Variogram method, LISS III November ........................................................29 Figure 4-3: Change of FD with spectral bands ......................................................................................30 Figure 4-4: Variation of range of FD with spatial resolution Sal (NDVI example)...............................33 Figure 4-5: Variation of range of FD with spatial resolution Plantations (NDVI example) ..................34 Figure 4-6: Variation of range of FD with spatial resolution MBL (NDVI example) ...........................36 Figure 4-7: Variation of range of FD with spatial resolution, MV (NDVI example) ............................37 Figure 4-8: Variation of FD with the change in season in Sal ...............................................................39 Figure 4-9: Variation of FD with the change in season in plantation ....................................................40 Figure 4-10: Variation of FD with the change in season in MBL..........................................................41 Figure 4-11: Variation of FD with the change in season in MV............................................................42 Figure 4-12: Effect of change of FD with Altitude, Sal LISS III...........................................................44 Figure 4-13: Effect of Change of FD with Altitude, MBL LISS III ......................................................44 Figure 4-14: Effect of Change of FD with Altitude, MV LISS III ........................................................45 Figure 4-15: Comparison of IR plots for local fractal approach, Haldwani and Dehradun. ..................45 Figure 4-16: Comparison of NDVI plots for local fractal approach, Haldwani and Dehradun. ............46 Figure 4-17 : Plot of variation of FD with spatial resolution, DDN ......................................................47 Figure 4-18: Plot of change of FD with the variation of spectral bands and season, DDN ...................48


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List of tables Table 2-1: Summary of methods for computing fractal dimension........................................................14 Table 3-1: Spectral characteristics of LISS IV.......................................................................................20 Table 3-2: Spectral characteristics of ASTER........................................................................................20 Table 3-3: Spectral characteristics of LISS III .......................................................................................21 Table 4-1: Details of subsets used for local and global fractal approaches............................................27 Table 4-2: Suitable bands and corresponding R2 values of Global approach.........................................29 Table 4-3: Change of FD with spatial resolution; ex: sal (season 1, 250m by 250m subset) ................32 Table 4-4: R-square values for sal forests ..............................................................................................32 Table 4-5: Change of FD with spatial resolution; ex: plantation (season 1, 250m by 250m subset).....33 Table 4-6: R-square values for plantations.............................................................................................34 Table 4-7: Change of FD with spatial resolution; ex: mixed broad leaf (season 1, 250m by 250m subset).....................................................................................................................................................35 Table 4-8: R- square values for mixed broad leaf forests.......................................................................35 Table 4-9: Change of FD with spatial resolution; eg: mountain vegetation (season 1, 250m by 250m subset) ..........................................................................................................36 Table 4-10: R- square values for mountain vegetations.........................................................................37 Table 4-11: Change of FD with Seasons with different methods; Sal (250m by 250m subsets)...........39 Table 4-12: Change of FD with Seasons with different methods; plantations (250m by 250m subsets)................................................................................................................................................................40 Table 4-13: Change of FD with Seasons with different methods; mixed broad leaf (250m by 250m subsets) ...................................................................................................................................................41 Table 4-14: Change of FD with Seasons with different methods; MV (250m by 250m subsets) .........42 Table 4-15: Optimum bands of Dehradun (DDN) and Haldwani (HALD); (Aster) ..............................46 Table 4-16: Global R- square values of Dehradun (DDN) and Haldwani (HALD); (Aster) ................47 Table 4-17: Change of FD with Season; Dehradun Sal ( 250m by 250m subset) .................................48


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1. Introduction

Earth’s vegetation plays a major role in forming the composition and characteristic of the land surface. Information about the vegetation cover is an indirect indicator of land-use, and is highly relevant for environmental studies. Proper environmental planning and management in today’s environmentally insecure world demands accurate classification of various vegetation types along with many other factors, making it immensely valuable to the human society. Mapping of landscape processes like vegetation, land-cover/land-use, soil survey, geological mapping are traditionally done based on hierarchical systems. Depending on the objective, diagnostic features or criteria are chosen. The data required also depends on the objective of the study, though different studies may be using the same data or different ones. Data as of satellite remote sensing provides an important source of land-cover information and it has gained popularity nowadays owing to the wide choice of bands, in and beyond the visible spectrum in which the digital images can be obtained. This opens new avenues for vegetation and soil survey as well as for landscape analysis (Jong, 1994). Several methods are available to describe the variation on the earth surface, all treating the environmental variables as a set of patterns occurring at specific scales. It is known, however, that the processes on the earth surface which are responsible in determining its shape and form occur at different scales; varying from large-scale geological processes, small-scale slope formation, large forests to small agriculture holdings. So it may be of interest to use these different scales when studying the variability of landscapes. Quantifying the complexity between scale and resolution is a challenging task even if several tools and means are available, such as univariate and multivariate statistics, spatial autocorrelation indices like Moran’s I and Geary’s C, and local variance measures within a moving window. These provide some understanding of such interaction but they also have their limitations of assumptions and limits of certainty.(Emerson et al., 1999).

1.1. Use of Fractals in Remote Sensing:

Physicist John A. Wheeler once said that “no one is considered scientifically literate today who does not know what a Gaussian distribution is, or meaning or scope of the concept of entropy. It is possible to believe that no one will be considered scientifically literate tomorrow who is not equally familiar with fractals” (Batty, 1985. cited in (Lam, 1990)). The statement appears to be quite true as fractal analysis is said to be one of the four most significant scientific concepts of the 20th century, with a significant impact similar to that of the general theory of relativity, development of the double-helix model of DNA and quantum mechanics (Clarke and Schweizer, 1991 cited in(Jaggi et al., 1993)). In the context of complexity, i.e. between scale and resolution, the concept of fractal geometry can be a step forward to describe this complex form of natural phenomena. Fractals in the sense of fractal geometry have the property of self similarity, i.e. the behaviour of a system is spatially scale-independent, resulting in comparability between measurements at different scales (Emerson et al., 1999; Read and Lam, 2002). Since its introduction by Mandelbrot in 1975, fractal geometry and its


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scale independent nature have attracted in particular the earth scientists, who observe and study landscape features at various scales. Satellite imagery with improving spectral and spatial resolution reveals more of landscape features at finer resolutions and wider spectral range. Relevance and usefulness of fractal geometry to solving remote sensing problems of exploitation of data, spanning a large order of magnitude of scale ( cartographic, geographic, operational and measurement)(Emerson et al., 1999; Lovejoy et al., 2001) can be attributed to the fact that remotely sensed images are spectrally and spatially complex but also exhibit similarities at different spatial scales. The fractal dimension (FD now onwards) is a central concept of fractal geometry. It can be viewed as a measure of irregularity of spatial arrangements of physical processes. Fractals, self-similarity and FD are the key concepts of fractal geometry on which most of the applications on remote sensing are done. In remote sensing FD is used to measure the roughness or the textural complexity of land surfaces. Major application of fractal geometry and FD in the field of remote sensing include characterization of overall spatial complexity of an image, using textural information for image classification, describing the geometric complexity of the shape of feature classes in a classified image and to examine the behaviour of environmental phenomenon due to scaling (Sun et al., 2006) The FD of remote sensing data yields quantitative insight into spatial complexity and information. Remote sensing images acquired from different sensors at varying spatial and spectral resolutions may thus be comparable using fractal measurements. The FD can then be interpreted and compared with other measures of spatial complexity to understand the significance of spatial relationships within the data.(Jaggi et al., 1993)

1.2. Problem definition:

In Euclidean geometry, dimensions are integers or whole numbers and the topological dimension remain constant no matter how irregular the line or surface may be. Natural surfaces, however, do not usually have a simple Euclidean shape. The idea of using FD is then promising because it captures elements that are lost in traditional geometry. For example, a high spatial complexity of a line or a surface corresponds to a high FD. Hence, FD for lines ranges from 1 to almost 2, and for surfaces from 2 to almost 3. If the FD of fractal surfaces (i.e. complex topologically 2D objects) increases, the surface occupies more of the 3D space.(Parrinello and Vaughan, 2002; Read and Lam, 2002; Sun et al., 2006). Moreover the problem then is not only to quantify the complex inter-relationship but also to efficiently handle and process data. In fact, calculations on such objects place a heavy demand on the data processing and storage capabilities of hardware and software. Solving this problem requires using data efficiently which means using the data at appropriate scale and resolution to characterize phenomenon. This will help accurately provide answer of the questions being asked about characterizing the natural phenomenon studied through remote sensing.(Emerson et al., 1999). This would be particularly helpful in the studies of forests where shape and size play an important role. From the air, natural forests have boundaries similar to islands. Boundaries between forests and meadows are fractal in nature due to their elevation difference. Even inside the forests large patches of vegetation are formed by joining satellite patches. Different species have different characteristics and thus different texture, and thus can have difference in their FD. This study deals with different fractal models and the derivation of FD from them. Observing the change of FD with changes in resolution, we could aim to see the change across different spatial and spectral resolutions and correlate them with environmental variables for achieving a better understanding. For example, at one particular scale FD may change with vegetation type. We could


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then study this relationship, i.e. quantify and interpret it, taking changes in altitude and season into consideration. As the type of vegetation changes with the change in altitude, it would then be of interest to see the changes in the FD and the relation with altitude. Different fractal models exist and three of them, viz., Isarithm, Triangular Prism Surface Area and Variogram method will be used in this study. Isarithm method is based on the idea that the complexity of isarithm or contour lines may be used to approximate the complexity of a surface. Starting with the method, a matrix of z-elevations (or DN values), and an isarithm interval is selected and isarithm lines are constructed on the surface. Lengths are calculated, for each isarithm line, in terms of the number of boundary cells over a number of step sizes, log (number of boundary cells) is regressed against log (step sizes). The slope of the regression line is used to derive the FD of the isarithm line and is repeated for every isarithm line and averaged to find the FD of the surface (Sun et al., 2006). Triangular Prism Surface Area method estimates lumped D values from topographic surfaces or remotely sensed images. This method takes elevation values (DN) at the corners of squares i.e. the centre of a pixel, interpolates the centre value of the square by averaging, divides the square into 4 triangles and then computes the surface areas of the imaginary prism. This is repeated for different square sizes and spacing. The calculation stops when the size of the square is too big to fit an image. The Variogram method is one of the widely used methods to compute FD. In this method, the mean of the squared elevation (or DN) difference or variance is calculated for different distances, and D is calculated from the slope of the regression between the log of variance and distance so that FD = 3 – slope/2. Variogram method is easy to use because it can be used to both regular and irregular data and is more reliable than isarithm method.(Sun et al., 2006). Using different fractal models at different resolution would generate different results and validation of these results requires some time-tested references. This study also aims to compare the results of the present study area with that of another area so as to reveal the relation of different variables used in the study. Therefore the fractal approach may meet the criteria of an easier and quicker method of assessing spatial pattern from remotely sensed images. The most obvious validation method would be ground truth collection, which will involve identification of vegetation species at different locations and altitude. The information acquired during the field will be used in demarcating vegetation patches in the remote sensing images. These patches will then be used to generate subset of suitable dimensions to carry out their fractal analysis and validate the results.

1.3. Research objective

The study compares different fractal models and analyzes their results to come up with an answer which can provide the end–users, using this technique, about the optimal method, spatial resolution and spectral band which can be used to differentiate different vegetation type found in the study area. This will help not only to save time and effort but also help reduce the complications of large data handling and processing.

1.3.1. Main objective

The main objective of the study is to compare various fractal models for analyzing the vegetation cover types at different resolutions.


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1.3.2. Sub-Objectives

• To identify appropriate spectral bands and spatial resolutions of remote sensing images to calculate the fractal dimension of different vegetation types.

• To calculate fractal dimension using various fractal models, for selected spatial resolutions and spectral bands in a given remote sensing image.

• To explore the relation between fractal indices calculated for vegetation cover types and elevation at different spatial resolutions.

• To find out the best parameters for variables in the study which would help in discriminating various vegetation types using calculated fractal dimension.

• To validate the results of differentiation using ground data collection.

1.4. Research Questions

The research questions to be addressed are:

• Which fractal model is best suited to differentiate the vegetation types in the area? • How does the fractal dimension change with spatial resolution and spectral bands for different

vegetations with the change in season and altitude? • Can we differentiate various types of vegetation found in the study area with the help of

fractal dimensions obtained?

1.5. Methodology

Image 1Resolution 1

Image 3Resolution 3

Image 2Resolution 2

Band selection

Compute FD

Compareresults

Effective fractal model

Optimal Spectral bands

DifferentiateVegetation

types

Isarithm,TPSAM,

Variogram

Field dataAnalysis

Figure 1-1: Methodology flow chart


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A broad overview of the methodology is given in the figure above, for more detailed information the reader is directed to chapter 3. The study deals mainly with multi-resolution seasonal data. Raw data acquired from different sources were pre-processed and converted into formats that were recognized by different software packages used in the study. Four different vegetation types: sal, plantations, mixed broad leaf and mountain vegetations were first identified through visual interpretation, local knowledge, expertise and field verification and area subsets of different sizes were generated according to their spatial extent. FD were calculated for all the bands available and NDVI images. Analysis was carried out using relation formed by different variables – spectral bands, spatial resolution, altitude, seasons, methods and vegetations. The results were then tabulated and inference made according to the results they gave.

1.6. Chapter schema

This thesis is divided into 5 chapters. Chapter 1 gives the rationale for the present study with a set of objectives and questions to be attempted. Theory and understanding of different fractal models are summarized in chapter 2. Chapter 3 details about the methodology followed in this study, while the results and discussions are penned down in chapter 4. Finally the thesis is concluded with chapter 5.


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2. Fractal Geometry and Fractal Models

The term fractal (from Latin fractus - irregular, fragmented) applies to objects in space or fluctuations in time that possess a form of self-similarity and cannot be described within a single absolute scale of measurement. Fractals are a family of mathematical functions proposed to describe natural objects with irregular shapes. They are irregular and recurrent in space or time, with themes repeated like the layers of an onion or a cauliflower at different levels or scales. Fragments of a fractal object or sequence are exact or statistical copies of the whole and can be made to match the whole by shifting and stretching (Klonowski, 2000)

2.1. Background

Fractal geometry was coined and popularized by Mandelbrot (Mandelbrot, 1982)to describe and characterize highly complex forms of natural phenomenon such as coastlines and landscapes, and since then it has gained much support in the field of image analysis. Although Mandelbrot’s idea was to describe self-similar geometric figures but the recent researches in earth and environmental sciences have pushed the use of fractals into the territory of metadata representation, environmental monitoring, change detection, and landscape and feature characterization.(Bisoi and Mishra, 2001; Sun et al., 2006; Zhou and Lam, 2005) Fractals have two basic characteristics suitable for modeling the topography of the Earth’s surface: self-similarity and randomness. An important property of fractal geometry is that true fractals display self-similarity, i.e. the shape of a fractal object remains independent of scale at which it is measured, thus measurement made at different scales are comparable (Read and Lam, 2002; Weng, 2003). Dimension can be said to be a function of the observer’s location. If we consider the dimension of a ball of strings, then from very far away it looks like a dot (dimension = 0), closer it is solid (dimension = 3), very close it is a twisted tread (dimension = 1). So here in fractal geometry, dimension brings observer in to the story. An ideal fractal curve or surface has constant dimension, which quantifies subjective notions concerning how densely the fractal occupies the traditional Euclidean space in which it is embedded (Kolibal and Monde, 1998), over all the scales i.e. the form of the curve or surface is invariant with respect to the scale. We can say, however, that it should not be possible to determine the scale of a fractal from its form, i.e. its shape or appearance (Goodchild, 1980). As self-similarity refers to the fact that earth’s morphology appears similar across a range of scales but the concept of self-similarity also contains randomness, because the resemblance of the earth’s morphology at different scales is statistical and not exact (Malinverno,1995, cited in (Weng, 2003). Self-affinity is defined as a union of non-overlapping subset that can linearly map into the whole set. A fractal that includes randomness is said to be self-affine and needs to be scaled as scaling is not uniform in all coordinates but invariant under transformation that scale different coordinates by different amount (Parrinello and Vaughan, 2002). The dimension is called ‘fractal’ as it can have fractional or non-integer value. The concept of fractional dimension was first formulated by Hausdorff and Besicovitch. Mandelbrot called it fractal


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dimension and defined fractal as “a set for which the Hausdorff-Besicovitch dimension strictly exceeds the topological dimension (Klonowski, 2000; Lam, 1990) Mathematically fractal dimension for strictly self-similar surface can be derived by:

)/1(/ rLogLogNFD = Equation 2-1 Where 1/r is a similarity ratio or the degree of self-similarity and N is the number of step sizes or an object of N parts scaled down by a ratio ‘r’. In traditional or Euclidean geometry, the topological dimensions are 1, 2 and 3 for a curve, plane and volume respectively. Conventionally, we consider integer dimensions which are exponents of length, i.e., surface = length2 or volume = length3. The exponent is the dimension. This topological dimension remains constant no matter how irregular the curve or area may be. In this context a straight as well as a crooked line will have the same topological dimension of 1 and hence the line’s regularity or irregularity cannot be discriminated by mere topology. Information about an irregular surface is lost in this type of representation. On the other hand dimension in fractal geometry is treated as a range i.e. a FD of a curve may be any value between 1 and 2 and from 2 to 3 for a surface, depending on the complexity. Fractal geometry allows for there to be measures which change in a non-integer or fractional way when the unit of measurements changes. As fractal dimension is directly related to an object’s complexity, a smooth line having originally FD = 1 will approach FD = 2 when it becomes complex enough to occupy the whole space of a plane. This also holds true for a plane having FD = 2 approach a 3-dimensional volume with increasing complexity. An object will fill more space when it becomes increasingly irregular and have higher value of FD. (Lam, 1990; Sun et al., 2006)

2.2. Natural fractals - statistical self-similarity

The notion of self-similarity is the basic property of fractal objects. A mathematical fractal has an infinite number of identical versions of itself and can be made by the iteration of a certain rule. In principle, a theoretical or mathematically generated fractal is self-similar over an infinite range of scales, while natural fractals have a limited range of self-similarity. The similarity method for calculating fractal dimension works for a mathematical fractal, which is composed of. It is not completely true for natural objects. Such objects show only statistical self-similarity. In non-fractals, however, the size always stays the same, no matter of applied magnification. Unlike mathematical fractals, natural objects do not always display exact self-similarity, therefore the fractal dimension for natural objects can only be found out empirically and not analytically.

2.3. Fractals in remote sensing of land-cover

Remotely sensed images are not only spectrally and spatially complex, but often exhibit certain similarities at different spatial scales and the relevance and use of fractal geometry comes in solving these remote sensing problems (Sun et al., 2006). The use of FD as a texture measure to segment and classify remote sensing images have been tried and tested. Fractal techniques are well suited for the analysis of texture in remote sensing images as the environmental feature that are captured in the images are often complex and fragmented. It can be supposed that different kind of terrain can have different texture or roughness and can be expressed in terms of different FD. While computing the fractal dimension, an image is considered to be a 3D surface where the complexity of the surface is


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expressed as its variability over space and it is a function of its vertical variability of pixel values (Qiu et al., 1999). It has been suggested by (Pentland 1984, Keller et. al. 1987) cited in (Sun et al., 2006) that local variation in FD can be used as texture measures to segment images. This is based on the idea that different land-cover types have characteristic texture or roughness and can have different FD values. Therefore a local fractal analysis of images can reveal information on patterns of vegetation and rock outcrops much better than pixel-per-pixel procedures (Jong and Burrough, 1995). In their study De Jong and Burrough ((Jong and Burrough, 1995)) proposed a ‘local D- algorithm’ for Triangular Prism Surface Area method (TPSAM) which gave results as a new image file with the FD values. This new layer was used in classification procedure. They used their proposed method to classify six types of Mediterranean vegetation with Landsat TM and GER images. Although they were able to distinguish 5 out of 6 vegetation types, in their study area, with the Landsat image but the results were not satisfactory with the GER images for their poor image quality. They concluded that though FD values for TM images reflected different land cover types but they alone are not enough to classify the imagery. Roach and Fung (Roach and Fung, 1994) applied two techniques, the power spectrum method and fractional Brownian motion (fBm) method, for quantifying fractal scaling characteristics to texture within spectrally-classified segments of Landsat TM and MEIS images of a logging area in South-East British Columbia. From their study they concluded that fractal geometry can be a useful tool in the study of remote sensing forestry texture but a ‘blind’ application of fractal techniques to non-fractal anisotropic textures can result in characteristic fractal plots which can be falsely interpreted as fractal. Lam, (Lam, 1990) used two methods, isarithm and variogram, to measure the spatial complexity of three Landsat TM images consisting of three different land-cover types of coastal Louisiana. She found that the calculated fractal dimension of these TM surfaces were higher than real-world terrain. Read and Lam (Read and Lam, 2002) compared performances of selected pattern recognition methods for characterizing different land-cover types using unclassified Landsat TM data of lowland site NE Costa Rica. They used fractal dimension, calculated from Isarithm and TPSAM, and other spatial auto-correlation and landscape indices to represent land-cover types of forest, agriculture, pasture and scrubs. They found that fractal dimension from TPSAM and Moran’s I index of spatial auto-correlation were useful for characterizing spatial complexity of imagery whereas the landscape indices failed.

2.4. Fractal models

There are several proposed methods to compute the fractal dimension of natural objects, which use different ways to approximate N given in equation 2-1 but most of the methods have the following three common steps:

• Measure the quantities of the object using different step sizes. • Plot log- log graph of measured quantities versus step sizes and fit a least square regression

line through the data points. • Use the slope of regression line to derive the FD

Different computational methods, however, have their own practical, and theoretical limitations, or both. Past researches used fractals as a spatial measure for describing and analyzing remotely sensed imagery emphasizing more on spatial relationship between adjacent cells. Hence they are different from traditional spectral methods, which either perform pixel-by-pixel comparison between two images or matrix of from-to classes during classification (Kulkarni, 2004). Pixel-by-pixel classifier do


9

not take into account the spatial content of the pixels (Jong and Burrough, 1995) and therefore cannot exploit all the information in the data (Cihlar, 2000). Main problems that hinder the widespread use of fractals in remote sensing are the lack of standardized tools and algorithm details in research papers. (Sun et al., 2006) pointed out the lack of review papers which summarizes and evaluates different fractal methods and applications are widely scattered in the literature. A number of methods for calculation of fractal dimension have been developed for application in various spatial problems and variety of image processing and pattern recognition problem and several researchers have applied fractal techniques to describe image textures and used segmentation of various types of images (Sun et al., 2006), but most of the methods have their own limitations of assumption and certainty. Studies by several researchers (Lam et al., 2002; Sun et al., 2006; Tate, 1998) reveal the fact that different methods bring out significantly different FD values, for the same feature/ surface. Apart from method induced errors, factors such as input parameter values, quality of image data also influences the output FD value (Sun et al., 2006). Studies have been done comparing different fractal estimators. As cited in (Zhou and Lam, 2005), Klinkenberg and Goodchild (1992) tested seven methods on 55 real topographic data sets that yielded mixed results. (Tate, 1998) analyzed several estimators using nine simulated surfaces and also concluded that indeed different estimators gave different results. (Lam et al., 2002) used 25 simulated surfaces in three methods TPSAM, Isarithm and Variogram methods and found that Isarithm and TPSAM performed better than Variogram method. The methods have been well described and documented in (Goodchild, 1980; Jaggi et al., 1993; Kolibal and Monde, 1998), the detailed algorithm is given in (Jaggi et al., 1993). The software package, ICAMS, contains all these methods along with other spatial descriptors (Quattrochi et al., 1997) (Sun et al., 2006), in their review paper stated that most of the research till date has suggested that real remotely sensed images are not true fractals, which clearly contradicts the fundamental assumption underlying the theory of fractal descriptors. Some researchers (Lam et al., 2002) argued that this should not be taken as a drawback instead could be used positively. They pointed out that FD value which is stable over limited ranges of scale can be used to study the effect of scale changes on image properties. Emerson in (Emerson et al., 1999) pointed out that no one scale is optimal for different geographical processes, therefore further investigation is required to determine how the fractal dimension can be used as an indicator of the trade-off between scale, resolution and spatial extent of the input imagery. Some of the methods that are used in FD calculation are as follows:

• TPSAM • Isarithm method • Variogram method • Differential Box counting method • Robust Fractal estimator • Power spectrum method etc.

From the above mentioned methods, the first three methods will be used in this study. The reason is that these three methods are extensively used in remote sensing images and are easily applicable Apart from this, these methods have their own advantages, like TPASM uses raster representation of elevation of the earth’s surface and is computationally simple method. Isarithm method can be used to estimate FD of non self-similar surfaces, it is robust, accurate and relatively lacks sensitivity to input parameters and returns good result for images with medium-ranged complexity. Variogram method is easy to use and can be applied to both regular and irregular data (Sun et al., 2006).


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2.4.1. Isarithm method

The isarithm or line-divider method calculates the fractal dimension using an extension of the one dimensional line-divider method (Jaggi et al., 1993). It uses the walking-divider logic by using different ‘step-sizes’, that represent the segments necessary to cross a curve, to calculate the fractal dimension. For an irregular curve, as the step sizes become smaller, the complexity and the length of the stepped representation of the curve increase. If the logarithm of the number of step or segments needed to traverse the curve for a range of step-sizes is plotted against the length of the curve, we get the D of the isarithm line from the slope of the regression line as:

LogrCLogL β+= β−=1D Equation 2-2

where, L is the length of the curve or the number of boundary cells, β is the slope of the regression line and C is a constant.

Figure 2-1: Estimation of FD using isarithm method

Source: (Weng, 2003)

The figure above shows a self affine fractal with a nominal length of λ0 having discreet intervals of ‘r’ and a standard deviation of heights δ. Therefore the total length of the line α as a function of r is approximately

( ) 2/1220 δλα += rr

Equation 2-3

For a self affine fractal over distance r, the standard deviation of heights is

D

brb

−

⎟⎠⎞

⎜⎝⎛=

2

δ Equation 2-4

Where b is the crossover length, which is the horizontal sampling interval, above which the method breaks down. Replacing δ in equation 2 we get


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2/1)1(2

0 1⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛+=

−D

brλα Equation 2-5

For r > b, then α ≈ λ0. (Weng, 2003). The algorithm used in this study is elaborately given in (Jaggi et al., 1993).For remotely sensed images, this method uses contours of equal z values as the object of measurement for which the fractal dimension is estimated. Multiple passes are taken in the image using different isarithm values (iso-spectral reflectance curve). These values are generated by dividing the range of pixel values of the image into a number of equally spaced intervals with the following parameters given by the user:

• Number of step sizes • Isarithm interval and • Direction of computation (row, column or both).

To calculate the fractal dimension, the image is divided into two regions – one with values equal to or greater than the isarithm and the other with values less than the isarithm value. The whole image is transformed into a binary set of 1 and 0 by setting ‘off’ the pixels below the threshold and setting ‘on’ the pixels above the threshold. By comparing every pixel, an edge is detected and counted whenever it contains a value different from the threshold. These boundary cells are then counted at different step sizes, pre-defined by the user. In the absence of boundary cells for a given step-size, the isarithm line is excluded from the analysis to avoid regression using fewer points than the given number of steps (Sun et al., 2006). The log of the number of edges is regressed against the log of step-sizes producing a fractal plot, which is used to calculate the FD using D = 1- β. This process is repeated for every isarithm line and the FD of the entire image is obtained by averaging the FD values of all the isarithm lines that have R2 ≥ 0.9. The slope of the regression line is always negative as when the step-sizes increases, the details in the line decreases and the length of the line decreases (Read and Lam, 2002). The isarithm method provides a measure of the pixel correlation which determines the distance over which fluctuation in one region of the image are correlated or affected by those in another region.

2.4.2. Triangular Prism Surface Area method

The triangular prism surface area method is a computationally simple method, put forward by Clarke (1986) cited in (Sun et al., 2006), to calculate the dimension of topographic surface. It has been applied extensively to remote sensing images (Sun et al., 2006). It makes use of a raster representation of the elevation of the Earth’s surface as in a DEM. The image is seen as a grid of ‘x’ and ‘y’ coordinates and the value of the pixel is taken as the ‘z’ value, providing a vertical dimension for the cell. Taking the value of the pixels that constitute the four corners of the square (side of the square equals to the step size), the mean is calculated. A vertical line equal to the mean value is drawn from the centre of the square grid. Straight lines are drawn joining the top of each corner lines and with the centre line (figure 2-2). This defines the four triangular surfaces comprising the triangular prism. The area of the top of this prism is calculated using trigonometric formulae.


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Figure 2-2: Pictorial representation of the Triangular prism surface area method

Source : (Jong and Burrough, 1995; Sun et al., 2006)

This procedure is repeated for every step-size. Each succeeding computation takes a cell area which is exponentially larger than the previous one. This process continues till the whole image area is calculated as a single cell area. But doing this the image resolution diminishes and information is lost when individual pixel values are replaced by the mean at the centre. As this method needs square grids of different sizes, the square grid with the largest step is computed first. If, for example, an image is made entirely of the same digital number, then the resulting 3D structure would be a cuboid and would give a fractal dimension of 2.0. On the other hand if an image has entirely uncorrelated brightness value, then it would give a fractal dimension of 3.0. A typical image has a fractal dimension between 2 and 3.(Jaggi et al., 1993) TPSAM unlike the Isarithm method compares area with grid cell length. Considering the basic equation for defining a fractal curve as given in Mandelbrot (1967) [see (Lam et al., 2002)]

( ) DKdN −= δ Equation 2-6

( ) ( ) DKNdL −== 1δδδ Equation 2-7 Where: δ = step size; N(δ) = number of steps: L(δ) = length of the curve: and K = constant For extending this definition of curve to area, the expression for fractal dimension of an object of area A and step size δ can be deduced as follows:

( ) ( ) DKNA −== 22 δδδδ Equation 2-8 Rearranging the above equation in logarithmic form we get:


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( ) δLogDKLogA −+= 2 Equation 2-9 Where: β = (2-D), the slope of the regression: K = constant, therefore:

β−= 2D Equation 2-10 The log of the total surface areas (sum of all triangular prisms) is plotted against the log of the step-size. Fractal dimension is calculated by taking the slope of the regression line and substituting it in equation 2-10. As total surface area decrease with the increase of step-size, the β of the regression line is negative hence the resultant D ranges from 2.0 to 3.0

2.4.3. Variogram method

The Variogram method is a widely used technique for computing D of surfaces (Sun et al., 2006) This method is based upon the statistical Gaussian modeling of images (Jaggi et al., 1993)which states that given a fractal dimension, it is possible to use the fractional Brownian motion (fBm) modeling to create an image corresponding to the given fractal dimension. The Variogram method attempts to solve the inverse of the Gaussian modeling problem. It states that if an image is given, its fractal dimension can be calculated assuming that the surface under consideration is a fractional Brownian surface. The fractional Brownian motions says that there exists a distinct statistical relationship between two pixels and the variance of the difference in their pixel values or

HdisVar 2)2,1()2,1( ∝

Where, )2,1(dis is the distance between two pixels 1 and 2, H represents the ruggedness of the surface. H ranges between 0 and 1, where small value of H corresponds to rugged surface, while a larger value of H exhibits smoother surface. The fractal D of the fBm surface is calculated by:

HD −= 3 Equation 2-11 To calculate the fractal dimension, the log of the variance between all the pixel pairs is plotted against log of the distance between them as shown in the figure above. The distance is partitioned into clusters and the variance is calculated for each of the cluster formed. To each cluster, the difference and the square of the difference between the pixel values is added and repeated for all pixel pairs. Using this, the variance for all data pairs that fall in each of the cluster or distance interval is calculated by

( ) ( ) ( )[ ]2

112

1 ∑=

+−=n

idi zzndγ Equation 2-12

Where: n = total number of data pairs that fall in distance interval d, z = DN values or surface values (Lam et al., 2002) D is estimated from the slope of the regression line as follows:


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2/3 β−=D Equation 2-13

Where β is the slope of the regression line.(Jaggi et al., 1993)

Figure 2-3: The log-log plot of variance and distance as used in variogram method

Source: (Sun et al., 2006) The Variogram method uses the Variogram function to estimate the fractal dimension. The Variogram function describes how variance in surface height between data points is related to the spatial distance between them. The only difference between the traditional Variogram and that used in fractal estimation is that distance and variance are portrayed in double-log form. So to derive the Variogram function for a surface, variance of all data pairs which fall into a specific distance interval are calculated (Lam et al., 2002) The above mentioned three fractal dimension estimators represent a collection of easily applied techniques used for remote sensing images. These are two-dimensional fractal measurement techniques mostly used for analyzing image textures and surface roughness. Perimeters and outlines are one-dimensional also used for forest studies but are not considered because in this study we are more concerned with the features delineated in areas and surfaces, like texture and roughness, rather than those with boundaries of forests. The summary of the methods, their formula and relation used are tabulated below: METHOD RELATION USED BASIC FORMULA ESTIMATE OF FD Isarithm Length of contour line

vs. step size Dr −∝ 1α For each contour line, plot

log α(δ) versus log (δ), slope = (1-D)

TPSAM Total area of the tops of prisms vs. side length of analysis windows

DA −∝ 2)( δδ Plot log A(δ) versus log(δ), slope = (2-D)

β−= 2D Variogram Mean squared elevation

(or DN) difference vs. distance

HdisVar 2)2,1()2,1( ∝ Plot log(var) vs log(dist) Slope = 2H

2/3 β−=D Table 2-1: Summary of methods for computing fractal dimension

Refined and adapted from (Sun et al., 2006)


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The detailed flowchart for all the methods used in this study and the source code is given (Jaggi et al., 1993). The present study requires understanding of different fractal models and their response to different remote sensing datasets. Fractal dimension which is the central construct of any fractal model holds the same importance in this research. Here we are mostly concerned with natural fractals and the change of fractal dimension with the change of vegetation, resolution, spectral resolution, season as well as well altitude.


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3. Materials and methods

This chapter briefly describes the different materials used in the study and the methodology followed in this study. The importance of study area is also described.

3.1. Study area and field investigation

Uttarakhand is among the northern states of India and covers an area of about 53,500 km2. It incorporates the entire Himalayan part and the adjoining parts of the Indo – Gangetic Plain falling in the Haridwar and Udham Singh Nagar districts. Dehradun is the provisional capital of the state situated in district of Dehradun, while Haldwani is located in the district of Nainital (Kumar, 2005).

3.1.1. Location of study area

Figure 3-1: Location and extent of study areas.

3.1.2. Reasons for selecting the study area

The study area is rich in forest cover and diversity of forest types. It was chosen as it had a large diversity of vegetation as well as a considerable elevation gradient. The chosen area has about 2225.17 Ha of land under plantation (2005-06), where different species of trees like teak, shisham and poplar are grown as plantation forests. To the north of Haldwani the study area approaches the Himalayas, gaining an elevation of more than 2000m within a distance of about 50km. This relatively small area is


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thus convenient to address issues of elevation differences and corresponding changes in vegetation type as shown in the figure 3-1 below

Figure 3-2: Altitudinal distribution of forests in western Himalayas

Source: (Negi, 2000)

3.1.3. Vegetation in the study area

The study area is extremely rich in vegetation, which comprises mainly of forests. The following forest regions are found in this area spanning different altitudes (figure 3-2): 1. Sub-montane or Sub-tropical region forests – It is found in the elevation range from 500m to 1500m. The main vegetation of this area being dominated by Sal (Shorea robusta), Khair (Acacia catechu), Shisham (Dalbergia sissoo), Chir pine ( Pinus roxburghii) and varieties consisting of deciduous species. Out of all these species of this region, Sal and Chir pine is taken in the study as they are seldom intermixed and found at different altitudes. Sal – Sal is a small to medium sized tree. Crown is moderately developed and has fairly long trunk. Generally the bark is dirty green or ash grey. When young, the leaves are oblong or elliptical, dark green and dense but become glabrous and coriaceous when mature. Flowering occurs during April and May while fruiting takes place in the winter season. Although Sal exhibits concentrated leaf drop in summer but the simultaneous leafing-out never renders their population naked. However the canopy becomes markedly thin during the summers. Pine – Pine is a fairly large-sized tree with not so well developed crown. The tree attains a height of about 30-35m. Pine has brownish bark which is moderately thick. Leaves are in the form of needles, light green in colour and found in bundles of three. Flowering takes place between February and April and fruiting occurs in April- May of next year.


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2. Montane or Temperate region forests: This region extends from an elevation of about 1500m to 3500m. The main forests occurring in this area are Oak forests (Quercus leucotricophora), Deodar (Cedrus deodara), Kail and Fir and Spruce forests. Among all these, Oak is chosen for the study as it is at a lower navigable altitude than other and easily accessible. Oak- Oak is found at an altitude of more than 2000m. It is generally a medium to large sized tree. Its bark is highly fissured, dark grey or blackish in colour. Leaves are oblong or lanceolate, are spinous and tooted in young trees. Flowering occurs in April to early June while fruiting occurs fifteen to seventeen months after (Negi, 2000; Singh and Singh, 1992).

3.1.4. Field visit

In order to gain knowledge about the study area and its vegetation, a field visit was carried out from 1st October to 5th October 2007. The main objective of the field visit was to collect ground truth for the different vegetation types found in the area. The base camp for the first two days was at Tanda forest guest house; south of Haldwani while the remaining was at Nainital. Forest survey was done with the help of local forest officials. Tree species, GPS reading and age of the forest was noted where possible. Field work for Dehradun area was undertaken after the first field work and similar investigation and collection of ground truth was done. Figure 3-3 and 3-4.

Figure 3-3: Image showing field points and elevation values in Haldwani.


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Figure 3-4 DEM showing field points in Haldwani


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3.2. Image data

For studying the variation of fractal dimension with the change in spectral and spatial resolution along with the change in season, a variety of remotely sensed images, from different sensors, offering a range of spatial and spectral resolution, has been taken. We considered two different seasons for dealing with existing temporal variation. Images from the months of March-April and October-November are taken. LISS IV, ASTER and LISS III images, offering resolutions of 5.8m, 15m and 23.5m respectively were used.

LISS IV

LISS (Linear Imaging Self Scanner) IV on board IRS-P6 (ResourseSat) is a multi spectral high resolution sensor with a spatial resolution of 5.8m. This sensor was chosen for its high resolution and easy availability in India. The spectral characteristic of the sensor is given in the table below. (www.nrsa.gov.in)

BAND WAVELENGTH RESOLUTION SWATH WIDTH

REVISIT TIME

1 (green) 0.52 µm to 0.59 µm 5.8m 23.9 km 5 days 2 (red) 0.62 µm to 0.68 µm 5.8m 23.9 km 5 days 3 (NIR) 0.77 µm to 0.86 µm 5.8m 23.9 km 5 days

Table 3-1: Spectral characteristics of LISS IV

ASTER

The Advanced Spaceborne Thermal Emission and Reflection Radiometer obtains high-resolution (15 to 90 m2 pixel-1) images of the Earth in 14 different wavelengths of the electromagnetic spectrum, ranging from visible to thermal infrared light. ASTER is the only high spatial resolution instrument on the Terra platform. ASTER's ability to serve as a zoom lens for the other Terra instruments is particularly important for change detection, calibration/validation and land surface studies. Unlike the other instruments aboard Terra, ASTER does not collect data continuously; rather, it does it on an average of 8 minutes of data per orbit. All three ASTER telescopes (VNIR, SWIR, and TIR) can be pointed in the cross-track direction. (http://terra.nasa.gov/About/ASTER/about_aster.html)


REVISIT TIME

1 (green) 0.52 µm to 0.60 µm 15m 60 km 16 days 2 (red) 0.63 µm to 0.69 µm 15m 60 km 16 days 3 (NIR) 0.76 µm to 0.86 µm 15m 60 km 16 days

Table 3-2: Spectral characteristics of ASTER

LISS III

Spatial resolution of 23.5 m of IRS-1D and IRS-P6 LISS-III multi spectral sensor is considered suitable for this study because of its easy availability in India at relatively low costs. IRS ID and IRS P6 carry a medium resolution LISS-III camera operating in three visible spectral bands (B2, B3, B4), which are suitable for vegetation monitoring

http://www.nrsa.gov.in/http://terra.nasa.gov/About/ASTER/about_aster.html


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REVISIT TIME

1 (green) 0.52 µm to 0.59 µm 23.5m 140km 24days 2 (red) 0.62 µm to 0.68 µm 23.5m 140km 24days 3 (NIR) 0.77 µm to 0.86 µm 23.5m 140km 24days 4 (SWIR) 1.55 µm to 1.70 µm 23.5m 140km 24days

Table 3-3: Spectral characteristics of LISS III

3.3. Data generation

Several sites comprising patches of a varying homogeneity were selected for each type of recognized forest cover in the study area. Subsets of different sizes are generated for each of the sites. Three subset sizes of 750m by 750 m, 500m by 500m and 250m by 250 m for Global fractal approach could be generated for Sal forests as they have large extents of homogeneous cover over the study area. For other vegetation types, like the planted forests south and south-west of Haldwani, the number and size of the subset had to be reduced because of limitations in extent and homogeneity of the forest plots. This also applies for forest cover in the mountainous regions of the Nainital and Bhowali areas, having similar complexities in terrain feature. A uniform subset size of 1 km by 1km was generated for Local fractal approach. Criteria for selection of subset size were based on resolution, size of the regions, and a minimum number of pixels. Smaller subset size than those chosen here would not cover sufficient spatial or textural information to characterize the forest cover type. A larger subset size, however, would not be suitable as it would incorporate information from other vegetation types, thus leading to ineffective analyses. Since it is not possible to have all subset sizes for all vegetation types, it would be inappropriate to use different subset sizes for different forest covers as their comparison would become meaningless. Maximum effort was put to keep the same area of the subsets for different forest cover type similar, but it was not possible for all. NDVI (Normalized Difference Vegetation Index) is used as an indicator for vegetation vigour. It can be used to interpret urban, rural or vegetation/forest contrast and seasonal changes in vegetation patterns (Emerson et al., 1999). NDVI values are calculated for every image with similar subsets generated for all vegetation patches. The images are rescaled to an 8-bit format to facilitate the comparison between the different forest types. This can also help in illustrating how the computed fractal dimension varies with change in resolution and season. Fractal dimension for each subset are calculated globally and locally using the methods mentioned. The results are graphically plotted for different variables and further analyzed.

Detailed methodology:

The elaborate steps involved within the methods are described by a conceptual flow chart given below in Figure 3-5.


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LISS 3 LISS 4ASTER

Calculate Fractal dimension by Isarithm, TPSAM and Variogram methods

Subset generation

PREPROCESSING OF DATAIncludes import of raw images

and geometric correction and re-projection

NDVI

Convert to .lan format

Convert to .bsq format

Plot results graphically

Analysis andFinal results

Rescale to 8-bitASTER DEM

GROUND TRUTHDATA

Figure 3-5: Detailed methodology flow chart

Step 1. Procuring and importing of data Remote sensing data from different sensors were collected. Aster data were ordered from www.glovis.usgs.gov . The data are in Hierarchical data format (HDF-EOS). It is imported as IMG format through ERDAS Imagine™ import data module. IRS data which comprise of LISS III and LISS IV data were either available at Indian Institute of Remote Sensing (IIRS) or ordered through NDC of NRSA. The raw data from NDC are in generic binary form. Step 2. Pre-processing of data Pre-processing of the data involves cloud or haze removal, image geometric correction and re-projection of the data. For this study cloud free images were required, so that no masking of ground features occurs due to clouds. The ASTER and LISS images used here are either cloud free or existing clouds did not cover any part of the study area. Geometric correction:

• Image to map registration- Survey of India topo-sheets were used as reference data for image to map geometric correction. Permanent features like road crossings, bridges, railway lines, reservoir and dams which were easy to locate both on map and ASTER image of March 2004 were used as Ground control points (GCP) for geometric correction. Theoretically three GCPs are required for this but other 16 GCPs well distributed over the study area were taken for final geo-correction (Jenson, 1996). The Root Mean Square error on geo-correction was 0.676

http://www.glovis.usgs.gov/


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Pixels. The transformation projection selected for the geometric correction was Universal Transverse Mercator (UTM) and Datum as WGS84.

• Image to image registration - The geo-referenced Aster 2004 image was used to co-register the other images used in the study. The root mean square error (RMSE) on final image to image co-registration was kept as low as possible. During this process special care was taken in selecting well distributed GCPs as any mis-registration at this stage could give erroneous result. Through visual inspection of geo-linked pixels on both the images the geo-registration was ascertained to be within sub pixel level. The correctness of geo-registration was further cross verified by swiping and flickering in ERDAS Imagine™ 8.7.

Step 3. Computation of NDVI NDVI has been computed using the red and infrared bands. For the aster images bands 3a and 2 represent the infrared and red wavelength of the electro-magnetic spectrum, while for the LISS 3 and LISS 4 images they are band 3 and 2 respectively. NDVI is calculated in ENVI and the files are saved as ERDAS Imagine format. Mathematically the equation for NDVI can be defined as:

)/()( RNIRRNIRNDVI +−= , which for aster images becomes

)23/()23( bandabandbandabandNDVI +−= , and for LISS images

)23/()23( bandbandbandbandNDVI +−= . Step 4. Rescaling of NDVI The NDVI images are rescaled to an 8-bit format in ERDAS Imagine™ 8.7 by means of the module Interpreter in order to facilitate the comparison between the different forest types. This can also help in illustrating how the computed fractal dimension varies with change in resolution and season.

Step 5. Subset generation Subsets were mostly generated taking the field data points (Figure 3-3) as reference. This helped in taking pure samples of the concerned vegetation. Square subsets were generated using AOI tools in ERDAS Imagine™ Data Preparation module. A number of concentric squares of size 2)750( m , 22 )250(,)500( mm were used as AOIs for global approach and 2)1( km for local approach. These are used where the forest patches have large extent and homogeneity. Subsets were generated from images of ASTER and LISS for different vegetation types as well as the NDVI image. Similar subsets were generated from the DEM, for both the regions, using the same AOIs. The average elevation were then calculated from the DEM and used as a reference for altitude of the patches whose FD is to be calculated for further use in the study.


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SAL PLANTATION MIXED BROAD LEAF MOUNTAIN VEG. Figure 3-6: Some selected subsets of vegetations

Step 6. Conversion to LAN format All the subsets have to be converted to LAN format before being fed to ICAMS. ICAMS can only recognize images with LAN format, so the images are converted to LAN through Export option in ERDAS Imagine™ 8.7. Step 7. Conversion to BSQ Format LAN images have to be converted to BSQ Generic Binary format to do the data processing and calculations in ICAMS. So the subsets were first imported in ICAMS in BSQ format. Step 8. Calculation of fractal dimension Local (window based) and Global (entire image) FD by all the three methods are calculated in ICAMS through characterization tab (discussed in chapter 4). For Isarithm method, the software default ‘Isoline interval’ and ‘Number of steps’ are taken and for the Method option both rows and columns were chosen. This is done for all subset sizes and bands. All default options provided in the TPSAM window are taken for calculation, whereas parameters for the Variogram method are chosen after a careful examination of inputs and results. After a series of experiments the parameters that to be used were decided. Sampling method- Stratified random, Sample interval- 5, Group- 10, Break 1- 1, break 2- 5 were taken for further analysis. Other values for parameters either did not give any result at all or if it did, it was unacceptably erroneous.


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Step 9. Plotting of results graphically The results of the fractal models were fractal dimensions in the form of numerical values. These values were plotted in graphs to analysis so that they can be meaningfully interpreted. Graphs were plotted with the different variables used in the study and analyzed to achieve the objectives of the study and to subsequently answer the research questions. The output images of local fractal approach had FD values for every pixel. This pixel data were extracted from the image and the frequency of every FD occurring in the image were noted. The percentage of pixels for every FD present in the image was plotted against the values of FD. This gave curves for the different vegetation in the study area. These curves were further analyzed. Step 10: Statistical analysis To analyse the graphical results both visual and statistical approaches were taken. Standard deviation and R2 were taken as the statistical indicators. Graphs between FD - spectral bands, resolution, season and altitude were plotted and statistical inferences were made depending on the relation they gave indicated by R2 and standard deviation. Finally the inferences are integrated and presented.

3.4. Software used

ICAMS: The Image Characterization and Modeling System (ICAMS) is used in the study to calculate the fractal dimension of the remotely sensed images. Apart from calculating the fractal dimension, this integrated software package provides specialized spatial analytical functions for visualizing and interpreting remote sensing data, which includes Variogram, spatial autocorrelation, wavelet and texture analysis. It also has modules for calculating NDVI, land-water boundary and synthesis of artificial images. ICAMS has the ability to compute fractal dimension and spatial autocorrelation indices either in a global (whole image or subset) or local approach using a moving window filter (Emerson et al., 2005) Image file format conversions, image geometric correction, classification, calculating NDVI and other image processing were done in ERDAS Imagine™ version 8.6 (Leica Geosystems, 2002) and ENVI version 4.3 (RSI Inc, 2006).


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4. Results & Discussions

This chapter presents the results of the study analysed, to fulfil the research objective and answer the research questions. This study is mainly concerned with vegetation types in the study area. The spectral characteristics of vegetation play an important part in the experiments conducted. It is known that the spectral reflectance of vegetation canopy varies because of pigmentation, physiological structure and water content. In the visible wavelength, pigmentation dominates the spectral response of the plant wherein chlorophyll is especially important. Absorption by chlorophyll gives low reflectance in red and blue bands while a peak reflectance at about 0.5 µm is seen because of the green colour of the leaf. Apart from this, the morphological characters of the vegetation, i.e. shape, size, height and density also play an important role. The structure of the canopy and the light scattering between the leaves causes the spectral response of the canopy of the different vegetation types to vary. The seasonal state of maturity of a plant also influences its spectral reflectance by altering its proportion, or by controlling the presence or absence of some of its parts. Flowering usually occurs over a short period during the growth cycle of the vegetation. Evergreen trees shed their leaves regularly but the simultaneous leafing out never renders them leafless while on the other hand deciduous trees shed their leaves during peak winter which drastically change the appearance from summer. Because of these factors the spectral signature of a plant species may vary during a season and its life cycle. This study uses both the local and global approaches to calculate the fractal dimension of the vegetations. Local and global are generic terms in remote sensing, but in fractal calculations, these refer to two methods where the resultant FD is calculated by two different approaches. In global approach, resultant

comparing various fractal models for analysing vegetation ...vidya, nidhi, saurav, aditi, smita,...

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