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FRACTAL ANALYSES OF SATELLITE DATA WITH GEOGRAPHIC INFORMATION SYSTEMS IN LAND USE CLASSIFICATION By BRUCE ERNEST MYHRE A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 1996 ACKNOWLEDGMENTS The author wishes to acknowledge and recognize the people involved with this project. As with any task of this scope, there are many people without whose help this work could not have been accomplished. Gratitude is extended to the author's committee members, Dr. Kenneth L. Campbell, Dr. Allen R. Overman, Dr. Donald J. Pitts, Dr. Byron E. Ruth, Dr. Fedro S. Zazueta, and especially to Dr. Sun Fu "Tony" Shih for support, advice, and, when needed, prodding to continue this arduous journey. Also, many thanks go to Orlando Lanni, Jack Jordan, Yurong Tan, and ChiHung Tan of the Remote Sensing Lab in the Agricultural and Biological Engineering Department. Their comments, suggestions, and general discussions on this research are greatly appreciated. Special thanks go to my father, Dr. Donald L. Myhre, for his assistance, not only in this project, but throughout my life; he gave me the inspiration and confidence to set high goals. Additional special thanks go to my mother, Donna Myhre, for her assistance and guidance throughout my life. Lastly, and most important of all, gratitude goes to my wife, Cynthia Silvestre, for all her support, love, patience, and friendship. TABLE OF CONTENTS ACKNOWLEDGMENTS ............................................... ii LIST OF TABLES............. ............................. vii LIST OF FIGURES ..................................... .......... . ... ix ABSTRACT ...................................... .......... xvi CHAPTERS 1 INTRODUCTION................................... ...... 1 Importance of Land Use Determination ............... .1 Classification of Satellite Images...... ............ 2 Combining Geographic Information System Applications with Satellite Images...... ......... 5 Applications of Fractal Research................... 7 Waveband Combinations ............................... 8 2 OBJECTIVES............................................. .... 9 3 REVIEW OF LITERATURE ................................ 10 Conventional Land Use Classification Methods....... 10 Satellitebased, Land Use Classification Methods............ .... .... ........ .... .... 10 Traditional Satellite Image Classification Methods ....................................... 10 Land Use Classification Systems................. 11 Integration of Remote Sensing and Geographic Information Systems ............ ................ .12 Use of Fractals in Remote Sensing and Satellite Imagery ................. ....................... 20 Waveband Combinations.............................. .24 4 MATERIALS AND METHODS..................... ..... ...... ..... 26 SPOT Images ................................... ..... 26 Study Areas........................................ .............. 29 Image Processing System............................ 34 Geographic Information System...................... 34 Maximum Likelihood Classification Method........... 35 Fractal Dimension Calculation....... .............. 36 Variograms ...................................... 38 Fourier Power Spectrum......................... 40 WalkingDivider............. ............. ............ 41 Triangular Prism Surface........................ 41 Robust Fractal Estimator.................... ...42 Fractal Shape Calculation..................... ..46 Statistical Analyses.................... ......... 48 Use of Different Pixel Groupings................... 49 Unique AreaPerimeter Combinations .............. 49 Using Different Cell Sizes...................... 50 Spectral Reflectance and Waveband Combinations.....50 Normalized Difference Vegetation Index.......... 50 Proposed Fractal Analyses............................ 53 Historical Fractal Analyses.................... 53 New Fractal Analyses ........................... 54 5 RESULTS AND DISCUSSION ................................ 55 Conventional Classification of SPOT Images......... 55 Spatial Distribution of Land Uses............... 62 Fractal Dimension by Class and Land Use............ 66 Class Analysis .................................. 66 Land Use Analysis............................... 70 Fractal Shape by Class and Land Use................ 82 Class Analysis.................................. 82 Land Use Analysis ............................... 83 Unique AreaPerimeter Combinations................. 90 Fractal Dimension Analysis...................... 90 Fractal Shape Analysis.......................... 99 Using Different Cell Sizes........................ 107 Fractal Dimension Analysis..................... 107 Fractal Shape Analysis......................... 114 Mean Spectral Reflectance versus Fractal Parameters ..................................... 118 Waveband Combinations versus Fractal Parameters...128 Normalized Difference Vegetation Index......... 128 Other Band Combinations........................ 137 6 CONCLUSIONS, RECOMMENDATIONS, AND FUTURE WORK....... 146 Conclusions......................................................... 146 Recommendations....................................... 150 Future Work................................. ....... 151 GLOSSARY.................................................. 153 REFERENCES ................................. 999. ....... 155 APPENDICES A ELAS SPECTRAL CLASSIFICATION CALCULATIONS........... 163 B ELAS RESAMPLING METHODOLOGY......................... 168 C FRACTAL DIMENSION VERSUS FRACTAL SHAPE FOR THE HASTINGS, PALATKA, AND SEVILLE STUDY AREAS..... 171 D FIGURES SHOWING THE EFFECT OF CELL SIZE ON FRACTAL PARAMETERS FOR PALATKA AND SEVILLE STUDY AREAS............................................... ... 178 E FIGURES OF SPECTRAL REFLECTANCE VERSUS FRACTAL PARAMETERS FOR PALATKA AND SEVILLE STUDY AREAS...... 191 F FIGURES OF WAVEBAND COMBINATIONS VERSUS FRACTAL PARAMETERS FOR PALATKA AND SEVILLE STUDY AREAS...... 204 BIOGRAPHICAL SKETCH....................................................229 LIST OF TABLES Tables Page 11 A comparison of Landsat, SPOT, NOAA, GOES, and TIROS satellite characteristics............................ 3 31 Florida land use, cover, and landform classification scheme for remote sensing data....................... 13 41 Universal Transverse Mercator (UTM zone 19) boundary coordinates for Hastings, Palatka, and Seville study areas .......................................... 33 42 Fractal dimension by Landsat band for three land uses ................................................. 45 43 Waveband combinations and ratios ..................... 52 51 Land use descriptions for SPOT images................ 56 52 Land use spectral classes for SPOT image 619290.....58 53 Land use spectral classes for SPOT image 619291.....59 54 Spatial distribution of land use areas for SPOT image 619290....... .................................. 63 55 Spatial distribution of land use areas for SPOT image 619291............................................ 64 56 Spatial distribution of land use areas for combined SPOT images 619290 and 619291......................65 57 Fractal dimension and fractal shape for 59 spectral classes for Hastings, Palatka, and Seville study areas ........................................... .... 68 58a Fractal dimension and fractal shape for eight land uses for the Hastings study area.....................71 58b Fractal dimension and fractal shape for eight land uses for the Palatka study area ...................... 72 58c Fractal dimension and fractal shape for eight land uses for the Seville study area......................73 59 Area and perimeter statistics for Hastings, Palatka, and Seville study areas.................... 77 510a Fractal dimensions for eight land use categories using areaperimeter combinations which include either all data, unique data, or data of areas greater than three pixels for the Hastings study area......................... ................. 91 510Ob Fractal dimensions for eight land use categories using areaperimeter combinations which include either all data, unique data, or data of areas greater than three pixels for the Palatka study area .......................................... 92 50lOc Fractal dimensions for eight land use categories using areaperimeter combinations which include either all data, unique data, or data of areas greater than three pixels for the Seville study area.......................................... 93 511a Fractal shape for eight land use categories using areaperimeter combinations which include either all data, unique data, or data of areas greater than three pixels for the Hastings study area....................... ..................... 100 5lib Fractal shape for eight land use categories using areaperimeter combinations which include either all data, unique data, or data of areas greater than three pixels for the Palatka study area................................................. 101 5lic Fractal shape for eight land use categories using areaperimeter combinations which include either all data, unique data, or data of areas greater than three pixels for the Seville study area.............................................. 102 512 Mean reflectance of channel 1 (green), channel 2 (red), and channel 3 (infrared) for eight land uses in the Hastings area ..........................119 513 Normalized difference vegetation index (standard, revised, and modified revised) for eight land uses in the Hastings area.......................... 129 514 Comparison of three waveband combinations for enhancement of the spectral image of land use in the Hastings study area..................... 138 viii LIST OF FIGURES Figure Page 41 Location of SPOT images............................. 27 42 Hastings, Palatka, and Seville quadrangle locations.28 43 Photograph of Hastings quadrangle map (reduced scale) ............................................... .30 44 Photograph of Palatka quadrangle map (reduced scale) ..............................................31 45 Phtograph of Seville quadrangle map (reduced scale) ........................................ 32 51 SPOT Image 619290 land use classes.................60 52 SPOT Image 619291 land use classes .................61 53 Fractal dimension versus land use for the Hastings study area ......................................... 74 54 Fractal dimension versus land use for the Palatka study area .....................................................75 55 Fractal dimension versus land use for the Seville study area..................................... ......76 56 Fractal shape versus land use for the Hastings study area ........................................ 84 57 Fractal shape versus land use for the Palatka study area............................................. 85 58 Fractal shape versus land use for the Seville study area......................................... 86 59 Fractal dimension for unique areaperimeter combinations for the Hastings study area............95 510 Fractal dimension for unique areaperimeter combinations for the Palatka study area.............96 511 Fractal dimension for unique areaperimeter combinations for the Seville study area.............97 512 Fractal shape for unique areaperimeter combinations for the Hastings study area...........103 513 Fractal shape for unique areaperimeter combinations for the Palatka study area............ 104 514 Fractal shape for unique areaperimeter combinations for the Seville study area............ 105 515a Fractal dimension versus minimum number of pixels for the Hastings study area for pine and hardwoods land use ........................................... 110 515b Fractal dimension versus minimum number of pixels for the Hastings study area for pasture, clearings, and row crop land use.............................. 111 515c Fractal dimension versus minimum number of pixels for the Hastings study area for urban, water, and marsh/shadehouse land use .......................... 112 516a Fractal shape versus minimum number of pixels for the Hastings study area for pine and hardwoods land use.......................................... 115 516b Fractal shape versus minimum number of pixels for the Hastings study area for pasture, clearings, and row crop land use.............................. 116 516c Fractal shape versus minimum number of pixels for the Hastings study area for urban, water, and marsh/shadehouse land use .......................... 117 517 Fractal dimension versus mean reflectance of band 1 (green) for the Hastings study area................. 120 518 Fractal dimension versus mean reflectance of band 2 (red) for the Hastings study area................... 121 519 Fractal dimension versus mean reflectance of band 3 (infrared) for the Hastings study area.............. 122 520 Fractal shape versus mean reflectance of band 1 (green) for the Hastings study area ................. 125 521 Fractal shape versus mean reflectance of band 2 (red) for the Hastings study area ...................126 522 Fractal shape versus mean reflectance of band 3 (infrared) for the Hastings study area.............. 127 523 Fractal dimension versus normalized difference vegetative index (NDVI) for the Hastings study area.130 524 Fractal dimension versus revised normalized difference vegetative index (NDVI) for the Hastings study area ................................... 131 525 Fractal dimension versus modified revised normalized difference vegetative index (NDVI) for the Hastings study area ....................................... .... 132 526 Fractal shape versus normalized difference vegetative index (NDVI) for the Hastings study area .......................................... 134 527 Fractal shape versus revised normalized difference vegetative index (NDVI) for the Hastings study area .......................................... 135 528 Fractal shape versus modified revised normalized difference vegetative index (NDVI) for the Hastings study area ............................................ 136 529 Fractal dimension versus infrared/red (IR/R) for the Hastings study area ............................. 139 530 Fractal shape versus infrared/red (IR/R) for the Hastings study area................................. 140 531 Fractal dimension versus infrared red (IRR) for the Hastings study area ............................. 141 532 Fractal shape versus infrared red (IRR) for the Hastings study area ............................. 142 533 Fractal dimension versus red/green for the Hastings study area..................................... 143 534 Fractal shape versus red/green for the Hastings study area......................... .......... 144 Ci Fractal dimension versus fractal shape for the Hastings study area using 59 class image............ 172 C2 Fractal dimension versus fractal shape for the Palatka study area using 59 class image.............173 C3 Fractal dimension versus fractal shape for the Seville study area using 59 class image............. 174 C4 Fractal dimension versus fractal shape for the Hastings study area using 8 land use image.......... 175 C5 Fractal dimension versus fractal shape for the Palatka study area using 8 land use image........... 176 C6 Fractal dimension versus fractal shape for the Seville study area using 8 land use image........... 177 D1 Fractal dimension versus minimum number of pixels for the Palatka study area for pine and hardwoods land use........................................... 179 D2 Fractal dimension versus minimum number of pixels for the Seville study area for pine and hardwoods land use....................... .. ........................ 180 D3 Fractal dimension versus minimum number of pixels for the Palatka study area for pasture, clearings, and row crop land use..................... .............. 181 D4 Fractal dimension versus minimum number of pixels for the Seville study area for pasture, clearings, and row crop land use....................................... .. 182 D5 Fractal dimension versus minimum number of pixels for the Palatka study area for urban, water, and marsh/shadehouse land use ........................... 183 D6 Fractal dimension versus minimum number of pixels for the Seville study area for urban, water, and marsh/shadehouse land use.......................... 184 D7 Fractal shape versus minimum number of pixels for the Palatka study area for pine and hardwoods land use............................................ 185 D8 Fractal shape versus minimum number of pixels for the Seville study area for pine and hardwoods land use ..................................... .......... 186 D9 Fractal shape versus minimum number of pixels for the Palatka study area for pasture, clearings, and row crop land use................................... 187 D10 Fractal shape versus minimum number of pixels for the Seville study area for pasture, clearings, and row crop land use........................ ....... ..... 188 D11 Fractal shape versus minimum number of pixels for the Palatka study area for urban, water, and marsh/shadehouse land use ........................... 189 D12 Fractal shape versus minimum number of pixels for the Seville study area for urban, water, and marsh/shadehouse land use........................... 190 E1 Fractal dimension versus mean reflectance of band 1 (green) for the Palatka study area..................192 xii E2 Fractal dimension versus mean reflectance of band 1 (green) for the Seville study area.................. 193 E3 Fractal dimension versus mean reflectance of band 2 (red) for the Palatka study area.................... 194 E4 Fractal dimension versus mean reflectance of band 2 (red) for the Seville study area................... 195 E5 Fractal dimension versus mean reflectance of band 3 (infrared) for the Palatka study area .............. 196 E6 Fractal dimension versus mean reflectance of band 3 (infrared) for the Seville study area............... 197 E7 Fractal shape versus mean reflectance of band 1 (green) for the Palatka study area.................. 198 E8 Fractal shape versus mean reflectance of band 1 (green) for the Seville study area.................. 199 E9 Fractal shape versus mean reflectance of band 2 (red) for the Palatka study area..........................200 E10 Fractal shape versus mean reflectance of band 2 (red) for the Seville study area......................... 201 E11 Fractal shape versus mean reflectance of band 3 (infrared) for the Palatka study area............... 202 E12 Fractal shape versus mean reflectance of band 3 (infrared) for the Seville study area...............203 Fi Fractal dimension versus normalized difference vegetative index (NDVI) for the Palatka study area..205 F2 Fractal dimension versus normalized difference vegetative index (NDVI) for the Seville study area..206 F3 Fractal dimension versus revised normalized difference vegetative index (NDVI) for the Palatka study area .......................................... 207 F4 Fractal dimension versus revised normalized difference vegetative index (NDVI) for the Seville study area .......................................... 208 F5 Fractal dimension versus modified revised normalized difference vegetative index (NDVI) for the Palatka study area .......................................... 209 xiii F6 Fractal dimension versus modified revised normalized difference vegetative index (NDVI) for the Seville study area .......................................... 210 F7 Fractal dimension versus infrared/red (IR/R) for the Palatka study area..................... ............. .. 211 F8 Fractal dimension versus infrared/red (IR/R) for the Seville study area......... ................... .. 212 F9 Fractal dimension versus infrared red (IRR) for the Palatka study area............................. 213 F10 Fractal dimension versus infrared red (IRR) for the Seville study area .............................. 214 Fli Fractal dimension versus red/green for the Palatka study area.......... ....................... 215 F12 Fractal dimension versus red/green for the Seville study area................................ .216 F13 Fractal shape versus normalized difference vegetative index (NDVI) for the Palatka study area.............217 F14 Fractal shape versus normalized difference vegetative index (NDVI) for the Seville study area............. 218 F15 Fractal shape versus revised normalized difference vegetative index (NDVI) for the Palatka study area .......................................... 219 F16 Fractal shape versus revised normalized difference vegetative index (NDVI) for the Seville study area.............. ............ ......... ....... 220 F17 Fractal shape versus modified revised normalized difference vegetative index (NDVI) for the Palatka study area .......................................... 221 F18 Fractal shape versus modified revised normalized difference vegetative index (NDVI) for the Seville study area....................... .................. 222 F19 Fractal shape versus infrared/red (IR/R) for the Palatka study area..................................... 223 F20 Fractal shape versus infrared/red (IR/R) for the Seville study area........... *............. .... 224 F21 Fractal shape versus infrared red (IRR) for the Palatka study area.................... .......... 225 xiv F22 Fractal shape versus infrared red (IRR) for the Seville study area................................... 226 F23 Fractal shape versus red/green for the Palatka study area......................................... 227 F24 Fractal shape versus red/green for the Seville study area .......................................... 228 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy FRACTAL ANALYSES OF SATELLITE DATA WITH GEOGRAPHIC INFORMATION SYSTEMS IN LAND USE CLASSIFICATION by Bruce Ernest Myhre December 1996 Chairman: SunFu Shih Major: Agricultural and Biological Engineering The major objective of this research was to apply the conventional fractal dimension technique and new fractal shape technique using old and new pixel groupings for improvement of land use classification of satellite images. Relationships were developed for mean reflectance and waveband combinations/ratios with fractal parameters. Two SPOT scenes from May 1988 were selected for analysis. Three subsets were selected for study areas to show the range of different land uses for the three quadrangle areas of Hastings, Palatka, and Seville, Florida. The SPOT images were classified by use of ELAS software. The fractal dimension and fractal shape were used to distinguish 59 different spectrally separate classes and eight land uses which resulted from the maximum likelihood classification. The fractal dimension and fractal shape for a set of areas were statistically calculated. The mean, standard deviation xvi (SD), and coefficient of variation (CV) were used to compare the fractal dimension and fractal shape of the spectral classes and land uses. First, differentiating among land uses was improved by using eight land uses instead of 59 classes. Second, an inverse relationship existed between the fractal dimension and the fractal shape. Third, when using all the area perimeter data combinations, the fractal dimension technique was successful in differentiating among most land uses. Fourth, the fractal dimension technique was improved by using either an areaperimeter combination only once (unique data) for a given land use, or by using areas greater than three pixels. Fifth, the newly developed fractal shape technique maximized differentiation among land uses, and was further improved by using unique data as compared with the fractal dimension. Sixth, the relative rank among land uses is identical for green and red wavebands, with reflectance highest for urban and lowest for water. Seventh, the red channel may be the superior channel for differentiating among land uses. Eighth, the new revised normalized difference vegetation index (NDVI) methods are slightly better than the standard NDVI method for land use classification. Ninth, the new revised NDVI and the infrared band minus red band with fractal shape are superior for maximizing differentiation among land uses. xvii CHAPTER 1 INTRODUCTION Importance of Land Use Determination The need for land use determination is wide and varied. Land use is an important parameter in environmental studies. These studies include water quantity and quality management research which has gone into the modeling and quantifying of nonpoint source pollution (Beasley, 1977; Haan et al., 1982; Marani and Delluer, 1986; and Zhang et al., 1990). In general, land use and land use activities can be partially correlated to nonpoint source pollution (Novotny and Chesters, 1981). Therefore, a strong need exists to identify the amount and spatial extent of different land uses for hydrologic analysis. Many existing hydrologic/water quality models (CREAMS, AGNPS, and others) use the Soil Conservation Service runoff equations (SCS, 1972). Additionally, the Universal Soil Loss Equation (USLE) is very popular for erosion modeling. Both of these equations are dependent on land use; therefore, to successfully predict water quantity or quality land use must be determined. Other environmental studies requiring land use information include wetland assessment (Still and Shih, 1991), ecotone analysis (Johnson and Bonde, 1989), and temporal shifting of agriculture (Williams and Shih, 1989; and Tan and 2 Shih, 1990). Soil moisture estimates using Landsat data have been in part based on land use (Shih and Jordan, 1992 and 1993). Land use information is also very important in forestry applications. Locations of clear cut areas, forest inventories, deforestation of developing countries and the spatial extent of forest fires have been studied with land use playing a very important role. These studies include Lachowski et al., 1979; Strahler, 1981; Johnston, 1987; and Hudson, 1991. Land use classification systems include the United States Geological Survey system (Anderson et al., 1976); Florida Department of Transportation system (Kuyper et al., 1981); and Florida Land Use/Cover Classification system (FLUCCS). The latter two are designed for applications in Florida. Classification of Satellite Images The beginning of using satellites for remote sensing devices began in 1972 with the launch of what was to become the United States Landsat series. Since then other satellites have been used for different types of remote sensing systems (see Table 11). The Landsat and French Systeme Probatoire Table 11. A comparison of Landsat, SPOT, NOAA, GOES, and TIROS satellite characteristics. Band Spectral Spatial Satellite Sensor designation Range Resolu tion 2 ym m Landsat Return Beam Band 1 0.4750.575 76 1,2 Vidicom (RBV) Band 2 0.5800.680 76 Band 3 0.6900.830 76 Multispectral Band 4 0.50.6 76 Scanner (MSS) Band 5 0.60.7 76 Band 6 0.70.8 76 Band 7 0.81.1 76 Landsat 3 RBV MSS Landsat Thematic 4,5 Mapper (TM) Two Cameras 0.5050.750 Band 4 0.50.6 Band 5 0.60.7 Band 6 0.70.8 Band 7 0.81.1 Band 8 10.412.6 Band 1 0.450.52 Band 2 Band 3 Band 4 Band 5 Band 6 Band 7 0.530.61 0.620.69 0.780.91 1.571.78 10.4211.66 2.082.35 40 76 76 76 76 234 30 30 30 30 30 120 30  continued. Satellite Sensor Band Spectral Spatial designation Range Resolu tion Lam mn MSS Band 1 0.50.6 76 Band 2 0.60.7 76 Band 3 0.70.8 76 Band 4 0.81.1 76 SPOT Panchromatic 0.510.73 10 Band 1(green) 0.500.59 20 Band 2(red) 0.610.68 20 Band 3 0.790.89 20 (infrared) GOES E/W Visible 0.660.7 7000 Thermal 10.512.6 7000 IR TIROS 9 APT AVHRR 1 0.550.90 4000 14 AVHRR 2 0.7251.10 4000 AVHRR 4 10.5011.50 4000 Table 11. 5 pour l'Oberservation de la Terre (SPOT) satellites are most frequently used in land use classification. Traditional methods of satellite classification include supervised and unsupervised classification schemes. The methods usually involve statistically manipulating raw and/or processed satellite digital numbers. The most popular of these methods encompass minimum distance to means, parallelepiped, and maximum likelihood classifiers. These classification systems provide the link between the satellite reflectance data and land use classification. The importance of satellite classification is its ability to spatially determine land use (and/or other important environmental factors such as soil moisture or geologic substratum). Combining Geographic Information System Applications with Satellite Images The ability to integrate different types of data from many sources can be a very powerful tool. One area of importance for water resources studies is the link between remotely sensed data and geographical information systems (GIS). Currently the interface between remote sensing systems and GIS is still weak, and many problems must be solved before the combination becomes widely available. 6 The term GIS is relatively new. However, the concepts GIS employs are both old and new. The concept of GIS is to relate spatial data to informational databases. The modern component of the GIS is the computer system. A complete GIS should have computer hardware, application software, and a proper organizational context (Burrough, 1986; and Shih, 1988). The hardware components include a digitizer (for input), a CPU, disk and/or tape drives, a monitor, and a plotter (for output). The software should be capable of manipulating the various hardware components. An efficient organization will have a management system that effectively communicates with the rest of the GIS. The data structure of a GIS can be based on either a raster or vector format. A raster format is a simple matrix of "x" and "y" coordinates with an appropriate relational database for each pixel. A vector format consists of lines (or arcs), points, and areas (or polygons). Lines are often used to represent roads, canals, etc., while areas are used to represent regions that are homogeneous for a single attribute. Points can be used to represent wells, sewer holes, etc. Database files are used to relate the geographic and attribute data. The attributes are artificial descriptors assigned by the user or others (i.e., soil type, land use, elevation, tax status, etc.). Applications of Fractal Research The concept of fractals is relatively new, being defined by Mandelbrot in 1967. Simply stated, the fractal dimension of a phenomena is a measure of randomness or variability. This dimension is different from the traditional dimension of Euclidian geometry. Application of fractals range from stream networks (Tarboton et al., 1988) to economics (Mandelbrot, 1970; and 1977) to satellite images (Lovejoy, 1982; and Lam, 1990). From this one can see the variety of applications possible with fractals. Another property of fractals is selfsimilarity. This means that the fractal dimension does not vary with scale, thus the fractal dimension will be the same regardless of the unit of measure. In the area of hydrology this concept was applied to a drainage basin area and main river length (Hack, 1957). This study showed the ratio of (length/area)06 to be consistent over a large range of scales. The use of fractals in satellite classification of land use has been sparse to date (Ramstien and Raffy, 1989; De Cola, 1989; and Lam, 1990). These studies and others represent a beginning upon which this research will start. Thus, a need exists to further develop fractal applications. Waveband Combinations The use of waveband combinations and/or ratios (CR) is done for spectral and spatial enhancement and separability of remote sensing images. Many different combinations have been devised (Lillisand and Keifer, 1987; Lo, 1986; Huete and Jackson, 1988; and Kidwell, 1991). These combinations are often trial and error procedures with some combinations being used more widely, most notably the normalized difference vegetation index (NDVI). The NDVI is used for enhancement of different types of vegetation (Lillisand and Keifer, 1987; and Shih, 1994). The relationship between waveband CR and fractal parameters has not been explored to this point. This research will examine this area. CHAPTER 2 OBJECTIVES The main objective of this research is to apply fractal techniques for land use classification of a SPOT satellite image. The specific objectives are as follows: 1. To classify a SPOT image using conventional methods for land use classification; 2. To determine the conventional fractal parameter (i.e., the fractal dimension) for different land uses; 3. To define a new fractal parameter (i.e., the fractal shape) for different land uses and to compare it with the fractal dimension; 4. To evaluate the impact of using different pixel groupings on the fractal dimension and fractal shape; 5. To develop a relationship between mean reflectance and fractal parameters for improving land use classification; 6. To develop a relationship between existing and new waveband combinations and/or ratios (CR), and fractal parameters for further improving land use classification; 7. To evaluate the performance of methods in objectives 5 and 6. CHAPTER 3 REVIEW OF LITERATURE Conventional Land Use Classification Methods Traditionally land use is classified by aerial photographs, ground surveys or a combination of both. This involves creating a mosaic of the aerial photographs (often color infrared photographs are used) and relating this to known land uses (Baker et al., 1979; and Campbell, 1983). This is done through use on ancillary information such as field checks, soils maps, tax documents, and similar literature. The resultant land use areas are then transferred to a base map through the use of a zoom transfer scope or digitizer. Areas for each land use can then be determined by a planimeter or computer programs. Satellitebased, Land Use Classification Methods Traditional Satellite Image Classification Methods Image processing methods have been available since the development of environmental satellites such as Landsat, and have included many applications in land use classification. The advantages of satellites over aerial photography are the 11 availability of repetitive coverage, wide coverage area, and cost effectiveness (Lo, 1986). The classification process involves geometric correction, radiometric manipulations, and statistical classification. Geometric corrections are needed to adjust for the spacecraft movement and tilt and the earth's movement. Radiometric manipulations are done to enhance certain features or bands within the images. The statistical classifications are minimum distance to means, parallelepiped, and maximum likelihood classifier. These different methods group the image pixels together into different classes. Apriori information is assigned to the data through training sets. The classes are then combined by a supervised or unsupervised (or a combination of both) methods. This allows the classes to be based solely on spectral separability. Land Use Classification Systems Classification of remote sensing data by land use is commonly through the use of the Anderson classification system (Anderson et al., 1976). This system, devised for the United States Geological Survey, divides land use into different levels of increasingly specific land use. While this system is used on many remote sensing applications, many projects use modifications of the Anderson system. 12 The Anderson system was developed to meet the following criteria: (1) 85% classification accuracy; (2) equal accuracy for each class; (3) repeatability; (4) applicable over extensive areas; (5) categorization permitting land cover to be used as a surrogate for activity; (6) usable with satellite data from different times; (7) integration with ground survey data or large scale remote sensor data possible through use of subcategories; (8) aggregation of categories; (9) comparison with future data; and (10) multiple uses of land recognizable. The Anderson system is the most widely used classification scheme and its adaptation to Florida by Kuyper, et al. (1981) is shown for Levels I and II in Table 31. Integration of Remote Sensing and Geographic Information Systems The merging of photogrammetry, remote sensing, GIS, and related technologies was addressed by the International Society for Photogrammetry and Remote Sensing (ISPRS) (Welch, 1988; and Shih, 1990). The working group for the ISPRS was formed in 1985 and held its first symposium in conjunction with the American Society of Photogrammetists and Remote Sensors/American Congress on Surveying and Mapping (ASPRS/ACSM) convention in April 1987. Table 31. Florida land use, cover, and landform classification scheme for remote sensing data (Kuyper et al., 1981). Major Land Use Land Use Land Use Description Number Urban And BuiltUp 110 Residential, Low Density 120 Residential, Medium Density 130 Residential, High Density 140 Commercial and Services 150 Industrial 160 Extractive 170 Institutional 180 Recreational 190 Open Land Agricultural 210 Cropland and Pastureland 220 Tree Crops 230 Feeding Operations 240 Nurseries and Vineyards 250 Specialty Farms 260 Other Open Lands Rangeland 310 Herbaceous 320 Shrub and Brushland 330 Mixed Rangeland Forestland 410 Coniferous Forest 420 Hardwood Forest 430 Hardwood Forest (continued) 440 Tree Plantation Water 510 Streams 520 Lakes 530 Reservoirs 540 Bays and Estuaries 550 Major Springs 560 Slough Waters Wetlands 610 Hardwood Forest 620 Coniferous Forest 630 ForestedMixed 640 Vegetated NonForested 650 NonVegetated Barren Lands 710 Beaches other than Swimming Beaches 720 Sand other than Beaches 730 Exposed Rock 740 Disturbed Lands Transportation, 810 Transportation Communication, and 820 Communication Utilities 830 Utilities 14 The merging of remotely sensed data into GIS can be accomplished by three different methods (Curran, 1985). The first method converts all data (remotely sensed and otherwise) into polygon layers. These layers are then overlaid for importation into the GIS. The second method keeps the remotely sensed data in a raster format. The data are converted into georeferenced thematic maps and inserted with other necessary data into the geographically registered GIS database. The third method omits the conversion of remotely sensed data into thematic maps and inserts input data directly into the registered GIS. Systems that at present attempt to use one of these three methods to merge remotely sensed data and GIS include ODYSSEY, GIRAS, IBIS, and ARC/INFOERDAS (Lo, 1986). Several problems exist when integrating remotely sensed data and GIS. One problem involves regions of high topographic relief. In this case, displacement of polygons from the remotely sensed data will occur and thus a digital terrain model (DTM) must be employed (Goodenough, 1988). Another possible problem is distortion/displacement due to the conversion of raster satellite data to GIS vector data. Also, attributes associated with the GIS vector database present a problem. Thus, should one simply let the GIS determine the appropriate attribute assignments, or should the user manually determine these assignments through a given 15 procedure? Another solution is to let the spatial attribute values at the center of the raster cell determine the characteristics. Barker (1988) illustrates this rasterto vector and vectortoraster problem. The overlaying of data sets with different scales presents a problem somewhat similar to that caused by raster tovector conversion. The similarity comes from the fact that distortions can occur, but the solution to this problem involves the choice of automatic or manual rectification. Finally, the classification accuracy and positional accuracy of the remote sensing data are often not comparable with those of other data in the GIS (Marble and Peuquet, 1983; Ehlers et al., 1989; and Ehlers, 1989). Thus, for any calculations made within the GIS, the largest errors will be attributable to the remote sensing data. However, the larger the study area, the less influence these errors will have on GIS calculations. The calculation of SCS runoff curve numbers was the focus of a study by Berich and Smith (1985). Two Landsat scenes taken 10 years apart were used as the basis for land cover analysis. ERDAS software was used to resample the landcover data (originally 60 m x 80 m) to 61 m x 61 m. This was done in order to match the soiltype and zoning data which were also used. The GIS in that study was IRIS, which is a 16 raster format system. Thus, each cell in GIS was set to correspond with the resolution of the soils/zoning data. Williams and Shih (1989) studied the land use change within the Florida Everglades Agricultural Area (EAA) using Landsat images captured 13 years apart. They achieved a Level I classification of the data and used the Earth Resources Laboratory Applications Software (ELAS) GIS to analyze the data. They discerned that agricultural development was moving southeast toward the water conservation area of the EAA. In another study, Shih (1989) was able to achieve a Level I classification of land use from Landsat data using the ELAS GIS. A 100 m2 cell size was used in that analysis. The classification of SPOT imagery in conjunction with a GIS was used by Jadkowski and Ehlers (1989) to study the growth of an urban/suburban area. They used a rasterbased GIS to overlay SPOT land use/land cover with zoning maps. Vegetation change detection using Landsat data was performed by Jakubauskas (1989). He used images from 1973 and 1982 to analyze the impact of a forest fire on the spatial extent of different tree species. The raster based GIS used matrix manipulations to analyze the classified digital data for changes that occurred over time. Jampoler and Haack (1989) used aerial photography, Landsat and SPOT imagery within a GIS framework to analyze land use change, deforestation, slope failures, and soil 17 suitability. Their use of the remotely sensed data was particularly important due to a lack of other data sources. The study was conducted for the Kathmandu, Nepal, area which does not have the historical databases that are available in more developed countries. The ERDAS rasterbased GIS used a 70 m grid cell size. One problem they encountered was in comparing historical land use (from 1972 and 1979) from aerial photography with recent land use (March and October, 1987) from SPOT digital data. Walsh et al.(1990) stressed the importance of using a digital elevation model (DEM) with Landsat TM within the GIS. This was performed to enhance the satellite data where topography is an important factor. They also used the GIS for spatial rectification of the Landsat data during image processing. Wilkening (1987) used a Landsat/GIS merger for regional water resource management. The software packages were ELAS and ARC/INFO. Hydrologic subbasins were manually determined and input into the GIS in vector format and then converted to raster format (60 m2 cell size). This enabled the overlaying of the subbasins with Landsat landcover data. Other data (soils, hydrologic, etc.) were also entered into the system and were used in water resource management. One study (Johnston and Bonde, 1989) analyzed the boundaries between adjacent ecosystems using Landsat TM data 18 (bands 2, 3, and 4). A normalized difference vegetation index (NDVI) was calculated within the GIS using brightness values from bands 2 and 4. A 3 pixel x 3 pixel scan was used to enhance the difference among the vegetation classes. They concluded that the GIS helped in determining subtle differences between ecosystems. A study by Tan and Shih (1990) was conducted by overlaying digitized aerial photographs and a classified Landsat image at the Remote Sensing Application Laboratory (RSAL) in the Department of Agricultural and Biological Engineering, University of Florida. This study (performed on St. Lucie County, Florida) was done to compare historical agricultural land use. Aerial photographs from 1958 were digitized and input as polygon data into the ELAS GIS. These data were then overlain on a 1973 classified Landsat MSS image. This study showed a slight decrease in agricultural land use between 1958 and 1973. The merging of remotely sensed data with GIS has many applications. As mentioned earlier, there are many possible uses for their combination in water resource studies. Land use and land cover analysis are obtainable from classified Landsat and SPOT digital data and can serve as input to a GIS. Most researchers have used a raster GIS with cell sizes ranging from 60 m2 to 00 2. This eliminates the need for conversion from 60 m to 100 M This eliminates the need for conversion 19 to a vectorbased GIS. However, to overlay this data with vector data, a transformation must be performed. Lam et al. (1987) analyzed the errors involved with vectorrastervector transformations. They concluded that for their set of test areas, the maximum error increases as the raster grid cell size increases. However, this could be due to the fact the starting and ending vector area values were kept equal. One area that needs to be studied further is raster vector conversion error. One would suspect that the more irregular the perimeter the greater the error. Problems with rastervector conversions include the "stairstep" look of the resulting polygon layer and small polygons which produce a "saltandpepper" appearance in the image (Bury, 1989). The resulting polygons do not have a "realistic" appearance. The processing required user interaction with the program to decide if any errors had occurred. The results of Bury (1989) were within National Map Accuracy Standards for 1:24,000 scale maps. Another concept that should encourage the merging of remote sensing with GIS is the use of multitemporal data (Xiao et al., 1989). Thus, satellite (or other remotely sensing) data from different dates would be used to increase the effectiveness of the GIS. For example, the GIS manager would then be able to overlay different "snapshots" of 20 landcover with static data (such as soils information) and dynamic data (such as zoning and ownership). Use of Fractals in Remote Sensing and Satellite Imagery The use of fractals to study natural phenomena has only recently begun. The concept of fractals was first introduced by Mandelbrot, who based his work on Hausdorf and Besicovitch (Mandelbrot, 1977). Fractals can be defined as an entity for which the HausdorfBesicovitch dimension exceeds the topological dimension. The use of fractals in satellite classification of land use has been sparse to date (Krummel, 1987; Ramstien and Raffy, 1989; De Cola, 1989; Lam, 1990; and La Gro, 1991). These will be examined in greater detail later. Fractals have been applied to terrain surfaces (real and digital elevation models, DEM) by Shelburg et al. (1983); Burrough (1983); Mark and Aronson (1984); Roy et al. (1987); and Clarke (1988). Other studies include coastline analysis (Mandelbrot, 1967), particle shape analysis (Clark, 1986), coral reefs (Mark, 1984), and stream networks (Tarboton et al., 1988; and La Barbera and Rosso, 1989). Presently, the applications to satellite data include 1) determination if rain and cloud areas are scaleindependent (Lovejoy, 1982; Lovejoy and Schertzer, 1990; and Cahalan, 1990); 2) using 21 fractals and a chaos model as a forecasting tool (Brammer, 1989); 3) describing different satellite bands in terms of texture (Ramstein and Raffy, 1989); and 4) classifying land use (De Cola, 1989; and Lam, 1990). These studies will be briefly reviewed and their relationship to the present study will be shown. Lovejoy (1982) first examined the fractal dimension of rain areas (determined from radar images) and cloud areas (determined from geostationary operational satellite [GOES] images). The resolution of the radar images was 1 km x 1 km, while the GOES resolution was 4.8 km x 4.8 km. The fractal dimension of the rain and cloud areas were determined using the areaperimeter method. The fractal dimension (D) was 1.35 for both areas. The correlation coefficient from the regression analysis was 0.99. To take into account these different resolutions the GOES perimeter data were "corrected" by the ratio of the two resolutions taken to the power of one minus the fractal dimension of the radar data. Thus the GOES perimeters were multiplied by (1/4.8) 1.35 = 1.73. Even more interesting was that this analysis was done over a range from 1 km2 to 106km2. The work of Brammer (1989) concentrated on using fractals and a chaos model to simulate GOES satellite images. The simulations were short range (6 to 48 hours) and required 22 the use of temperature, pressure, humidity, and wind fields (speed and direction). Ramstein and Raffy (1989) used fractals and variograms to analyze Landsat TM and NOAA7 images. This study was able to distinguish urban, field, and forested areas from texture analysis alone. However, no spectral analysis was included. De Cola (1989) used the areaperimeter method described earlier to determine fractal dimensions of a classified Landsat TM image. The image was classified into eight classes with ranges of D from 1.35 to 1.82. De Cola concluded that it was possible to associate land cover patterns with fractal measurement. The remote sensing data were considered a form of a spatial surface by Lam (1990). The objective of the study was to determine land use/land cover for a Landsat TM image. Lam calculated the fractal dimension for surfaces using an algorithm developed by Shelburg et al. (1983), but calculated the surface fractal dimension as D = 2 B (the slope of the regression line). The study only calculated fractal dimensions for each band and neglected the band combinations which are very important in land use classification. Thus, one objective of the present study is to calculate the fractal dimension for the condition of band combinations. Olsen et al. (1993) used a modified fractal dimension to measure landscape diversity. The research evaluated the 23 diversity of landscapes at various scales (e.g., with various changes of extent and/or grain size) and how to evaluate the distribution of diversity over a landscape (i.e., what areas within a given landscape are more diverse than others). The modified fractal dimension combined the number of landscape patches, their distribution, and shape into an overall measure of landscape diversity. Olsen et al. (1993) concluded that the modified fractal index can provide a simple measure of diversity which can be related to land management practices, wildlife/habitat interactions, and biodiversity; however, the index can not be used as a tool for land use classification. Vasil'yev and Tyuflin (1992) analyzed ecosystems spatial structure and its fractal characteristics. They indicated that the spatial structure of geosystems is reflected primarily by the nature of land uses. This was examined by determination of whether fractal properties of spatial structures exist and, if so, interpretation of the fractal in a geometric sense. They concluded that agroengineering geosystems have a fractal character, the dimension of which should be used in the spatial differentiation of the land use system. The main limitation of their research is that only variations between different agricultural systems were analyzed. Thus, no comparison was made between urban, forested (hardwood or conifer), marsh, etc. land uses. 24 De Jong and Burrough (1995) used variograms and coefficients of variation of satellite image pixels, and a triangular prism surface area method to estimate the fractal dimension. This work is similar to that of Clarke (1986) and Lam (1990), but was applied to Mediterranean vegetation types. They classified a given rectangular area by land use and then calculated the fractal dimension versus the percentage of pixels in the study area of that particular land use. They did not conclusively relate the fractal dimension to land use, but indicated that the fractal dimension could be used as ancillary information to the classification process. Waveband Combinations The use of waveband combinations (mainly waveband ratios) began almost as soon as digital imagery was available. However, the integration of waveband combinations with fractal analysis for processing images in land use classification is a totally new field, which the present study will research. A brief background for the range of NDVI values is given below. Shih (1994) studied the vegetation distribution in the Everglades Agricultural Area using the High Resolution Picture Transmission (HRPT) data from the NOAA weather satellite. The NDVI values varied from 0.05 to 0.341 with an average of 0.183 and a standard deviation of 0.054. In 25 the current study the revised NDVI was used to eliminate the negative values. Lillesand and Kiefer (1987) reported that in highly vegetated areas the NDVI typically ranges from 0.1 to 0.6 in proportion to the density and greenness of the plant canopy. CHAPTER 4 MATERIALS AND METHODS SPOT Imaces Two SPOT satellite scenes were selected from northeast Florida which cover the Lower St. Johns River Basin (LSJRB) and the Lake George Basin (LGB). Figure 41 shows the location of the SPOT images in northeastern Florida. Two SPOT scenes (#619290 and #619291) from May, 1988 were selected for analysis. The portions of the LSJRB and LGB covered by these two scenes are shown in Figure 42. Each image covers an area 2 of approximately 5400 km2. The SPOT satellite has three high resolution visible (HRV) spectral bands: green (0.500.59 pm); red (0.610.69 pm); and near infrared (0.790.89 gm), with a resolution of 20 m x 20 m, and one panchromatic band (0.51 0.73 pm) with a resolution of 10 m x 10 m. The near infrared band is sensitive to reflective and not to thermal infrared wavelengths. The near infrared band is useful in determining spectral signatures of similar vegetation types and water bodies. OW SCm E 62o 9M SCENM w=B Figure 41. Location of SPOT images. Figure 42. Hastings, Palatka, and Seville quadrangle locations. Study Areas The primary ecosystem of the basins is southern Florida flatwoods (hyperthermic zone). The soils in the area are mainly Spodosols, which are nearly level, somewhat poorly drained sandy soils. Smaller areas of Histosols (level, poorly drained organic soils underlain by marl and/or limestone) and Entisols (level to sloping, excessively drained thick sands) also exist in the two basins (Fernald and Patton, 1984). The land use in the basins historically included forest (conifers and hardwoods), agriculture (citrus, potatoes, cabbage, corn, onion, and improved pasture), wetlands, rangeland, urban, barren, and water. In recent years, fern operations and improved pasture areas have increased. For our purposes of examining the fractal dimension, three subsets were selected to show the range of different land uses and correspond to USGS quadrangle areas of Hastings, Palatka, and Seville. Figure 42 shows the location of these areas, while Figures 43, 44, and 45 illustrate the Hastings, Palakta, and Seville quadrangles, respectively. The coordinates of the boundaries for each of the three quadrangles used to extract subimages for analysis are given in Table 41. Figure 43. Photograph of Hastings quadrangle map (reduced scale). * 1 MINUTC *cmei irwicinwci Figure 44. Photograph of Palatka quadrangle map (reduced scale). Figure 45. Photograph of Seville quadrangle map (reduced scale). Table 41. Universal Transverse Mercator (UTM zone 19) boundary coordinates for Hastings, Palatka, and Seville study areas. Quadrangle/ XUTM YUTM Study Area m m Hastings 439,567 3,291,068 439,493 3,277,218 451,594 3,277,159 451,654 3,291,009 Palatka 427,481 3,291,140 427,391 3,277,289 439,493 3,277,218 439,567 3,291,068 Seville 451,475 3,249,459 451,416 3,235,610 436,562 3,235,565 436,606 3,249,414 Image Processing System The Earth Resources Laboratory Analysis System (ELAS, 1989) classification software was used to classify the SPOT images. This program was originally developed by NASA for analyzing Landsat and other remote sensing data. ELAS has many image processing capabilities including image enhancement, registration, rectification, and classification. Additionally, ELAS can perform basic GIS manipulations. Geographic Information System Geographic Information Systems are a recent interactive mapping technology with widespread applications. Originally developed on main frame computers, GIS's are now readily available in versions for the personal computer (PC) and mini computer such as the Sun Sparc computer. The Remote Sensing Applications Laboratory (RSAL) of the Agricultural and Biological Engineering Department at the University of Florida uses the Arc/Info GIS package developed by Environmental System Research Institute (ESRI, 1992). Arc/Info is a vector based system that can perform overlays, analysis, and graphic output of spatial databases. A digitizing tablet (CalComp 9100) is used for entering map related data and a Hewlett Packard Proplot plotter and laserjet printer are used for output. Maximum Likelihood Classification Method ELAS spectrally classifies satellite imagery using a maximum likelihood classifier which utilizes a Bayesian statistical procedure (ELAS, 1989). The two satellite images were classified using the Normal Variation (NVAR), Thematic Mapper Trainer (TMTR), and Maximum Likelihood Classifier (M234) modules in ELAS. The NVAR module determines the normal variation of the data for each of the three HRV spectral bands. The module fits the data to a parabola (assuming a Gaussian distribution of the data) for each band. Curve fitting coefficients are the outputs for use in the TMTR module. Training sets are developed in the TMTR module, by use of a 3 pixel x 3 pixel window to search for nearhomogeneous spectral classes. The output of this module is a set of spectral classes (the number of which is determined by the user) and their associated statistical parameters and apriori values. The M234 module classifies all the pixels in the scene. The digital number for each pixel of each band is compared to the spectral classes determined by TMTR. Each pixel is then assigned a spectral class based on the Bayes' Rule decision making algorithm. The result of this pixel assignment process is a one channel image. This procedure used an unsupervised classification process which was done without prior knowledge 36 of the actual ground landuse information. Specifics of these ELAS modules are given in Appendix A. Fractal Dimension Calculation There are varied ways to calculate the fractal dimension depending on the dataset and purpose of the analysis. Following is a brief overview of fractals and different fractal analysis techniques. The dimension of an object in Euclidian geometry can be either 1 (line), 2 (plane), or 3 (volume). These dimensions are often described in terms of X, Y, and Z coordinates. However, interdimension values for entities can be described through use of the fractal dimension. A curve possesses a fractal dimension between 1 and 2, while a surface possesses a fractal dimension between 2 and 3. The fractal dimension of a line may be calculated as: D = log(N)/log(l/r) = fractal dimension............(41) where: N = number of steps and 1/r = similarity ratio. In practice D for a curve is often calculated by using different step sizes and can estimated by the following equation: log(L) = C + B(log(G)) ........ ..........(42) D = 1 B.............................(43) where: L = length of the curve, G = step size, and B,C = regression coefficients. This can be simply demonstrated (Lam, 1990): II I I I N = 4, I/r = 4 N = 8, 1/r = 4 D = log(4)/log(4) = 1 D = log(8)/log(4) = 1.5 For areas the fractal dimension may be calculated using area and perimeter measurements (De Cola, 1989): P = C (A0 5)D ......................(4 4) where: P = perimeter, A = area, and C = fractal shape D = fractal dimension. Similar to the calculations for the fractal dimension of a line, the fractal dimension for a set of areas is often calculated using a regression equation: ln(P)= ln(C) + D(ln(A05 )) ................. ...... ...(45) There are five methods for measuring the fractal dimension of surfaces: variograms, Fourier power spectrum, the walkingdivider (boxcounting or gridoverlay) method, triangular prism surface method, and the robust fractal estimator. For further discussion on measuring D see Shelburg et al. (1982 and 1983), Shelburg and Moellering (1983), Muller (1987), Roy et al., (1987), or De Cola (1989). Varioqrams The basis for using variograms in estimating the fractal dimension lies in fractional Brownian motion. This may be described (using elevation as an example) as (Roy et al., 1987): E[(zi + Zi+h)2] = ......................... (46) where: zi = elevation at point i, zi+h = elevation at point i + distance h, h = distance between points, H = coefficient to be calculated (0 < H < 1). For lines the fractal dimension is computed as D = 2 H........................ ............... (47) and for surfaces D = 3 H..........................................(48) or D = E + 1 H.............................. ..... (49) where E = Euclidian dimension (Voss, 1988). Now let S = E[(zi + Zi+h)2] .................... ....... (410) where S = expected value of the squares of the elevation points. To calculate D from actual data we take logs for both sides of the equation 46 and perform a regression analysis which leads to: log(S) = log(b) + 2 H log(h)......................(411) In this equation b is the intercept of the regression equation. If the mean of the squared height differences (variance) is computed for different distances, then D can be estimated from the slope of a loglog plot of variance against distance by D = 3 (b/2)......................................(412) Mark and Aronson (1984) applied this variogram method by picking independent random points (32,000) on a map. However, the map was restricted to an area which could be drawn by the 40 largest circle completely within the map. The measurements were made for 100 equally spaced distances using pseudorandom numbers generated by an algorithm developed by Tausworthe (1965). For 17 study areas used by Mark and Aronson (1984) only one was selfsimilar over all scales. However, all of the other areas did show selfsimilarity over certain ranges, often with sharp breaks between scales. This led them to conclude different processes were working to shape the landscape at different scales. Fourier Power Spectrum The use of Fourier analysis to calculate the fractal dimension has been performed by Burrough (1981), Fournier et al., (1982), Pentland (1984), Pfiefer (1984), and Clarke (1988). The basis of Fourier analysis is using sines and cosines, with characteristic wavelengths and amplitudes, to estimate a certain parameter. The analysis may be either continuous (in which the function is integrated) or discrete (in which a summation is performed). The discrete method is used for fractal analysis. The fractal dimension is determined by performing a log log regression of the power spectrum versus distance. The slope of the regression line, b, is used to calculate D as, D = 3 (b/2) .....................................(413) Note the similarity of this equation and the one used in the variogram analysis. WalkingDivider The Walkingdivider method (WDM) is based on work originally developed by Richardson (1961) and later expanded by Mandelbrot (1967). Richardson measured the length of a line with a pair of dividers of different lengths, producing pairs of divider length versus total line length. He plotted the loglog relationship between these two measurements to examine the variation between total length and divider length. Mandelbrot (1977) extended this concept by performing a regression of the loglog plots and relating the slope in the regression (b) line with the fractal dimension. D = 1 b...................... ..... ............ (414) The walking divider method can be applied to both area and surface fractal calculations. Triangular Prism Surface The triangular prism surface method (TPS) was developed by Clarke (1986a). This method is designed for grid elevation data (from Digital Elevation Models) and is calculated from the known geometry. 42 The method uses four elevation points, which form a square, to calculate an average center elevation. Using the center point, four triangular prisms are created and their areas are computed. The surface area for sides of increasing powers of two are calculated and summed for each side size area. A loglog regression of surface area versus the side area (i.e., lxl = 1; 2x2 = 4; 4x4 = 16; etc.). The slope of the regression line, b, is then used to calculate the fractal dimension, D, as D = 2 b. Note that as the resolution measurement area increases, the computed surface area decreases and thus, b will be negative. Robust Fractal Estimator The robust fractal estimator (RFE), developed by Clarke and Schweizer (1991), is based on the Walkingdivider method. Profiles are taken in eastwest and northsouth directions for each pixel of a matrix (this method designed for use with 7.5 minute digital elevation models). This was done based on the assumption that changes occur gradually in one (or two) of these directions. The walking divider method is applied in both directions for pixel, thus a m x n matrix will have 2(m x n) estimates of D. The surface fractal dimension is then calculated as the average of the D values plus one. The addition of one is due to the walkingdivider method being a line estimate. 43 De Cola (1989) used a Landsat Thematic Mapper image of northwest Vermont to compare fractal dimensions for different land uses. IDIMS image processing software was used to perform a supervised classification of the image into eight land uses. Fractal numbers were calculated for each class using areaperimeter regression techniques. The equation used is : in(pj) =lIn(C) + D*lin(sj05( ln(pj) = ln(C) + D ln(sj.5).................... (415) where: pj = th perimeter for a given land use sj = j th area for a given land use C = fractal shape D = fractal dimension. The dominant land use in De Cola's image are hardwoods (39.5%), hayland (12.8%), and softwoods (12.2%). Other land uses are water, brush/wetland, grassland, bare ground/corn, and urban. This research used classes which had previously been determined by a supervised classification procedure. The fractal dimensions were an end product and not used as part of the classification process. Lam (1990) used Landsat TM images from Louisiana to compare fractal dimensions for different land uses. Fractal analysis was applied to a 5 km by 5 km area for three 44 different images. Each area represented one of three land uses: urban, rural, or coastal. An isarithmic line algorithm was used on the digital numbers of each TM band for each area. Thus, each land use had seven fractal dimensions (one for each band of the TM image). Table 42 gives the results of the fractal dimension calculations. The problem with this research is applying the methods to classify other areas in the image. This is not readily possible using the techniques given. Also, the between band difference of the fractal dimensions is greater than the difference between the land uses. Bands 1, 2, and 3 had the highest fractal dimension for each land use. Bands 4, 5, and 7 were next highest with band 6 (thermal IR) having the lowest fractal number. This is to be expected since the range of digital numbers is so small for thermal IR. La Gro (1991) used aerial panchromatic and color infrared photography to classify forest areas within the Finger Lakes National Forest area of New York. The forest areas included both deciduous and coniferous trees. The fractal dimension was calculated using areaperimeter methodology (see discussion on De Cola, 1989). The fractal dimension was calculated for 1938 and 1988 forest areas, with resulting values of 1.222 and 1.243 respectively. No other land uses were analyzed, thus this Table 42. Fractal dimension by Landsat uses (Lam, 1990). band for three land Land Use Landsat Band Fractal Dimension Urban 1 2.698 2 2.715 3 2.726 4 2.672 5 2.592 6 2.208 7 2.653 Rural 1 2.709 2 2.615 3 2.607 4 2.587 5 2.540 6 2.176 7 2.536 Coastal 1 2.866 2 2.737 3 2.671 4 2.604 5 2.562 6 2.157 7 2.583 46 work can not be compared with other research into classifying land use with fractals. Krummel et al. (1987) used NASA UR/RB57 high altitude aerial photography to study the fractal dimension of forest areas. Their study area was the USGS Natchez, Mississippi quadrangle (1:250,000). The forest areas were deciduous trees, with conifer areas eliminated. The standard area perimeter methodology used by De Cola (1989) was also used by Krummel et al. (1987). They divided the forest areas into small (< 55.7 ha) and large (>100.4 ha) areas and performed the fractal analysis on each set of areas. The results show the fractal dimension to be smaller (D=1.20 +/ 0.02) for the smaller areas than for larger areas (D=1.52 +/0.1). They theorized that there are separate constraints which influence the fractal dimension based on forest area size. The smaller areas are affected more by nearby agricultural activity and thus are more rectangular than the larger areas. Fractal Shape Calculation The relationship between the fractal dimension and fractal shape can be best understood by examining the regression equation. The regression model takes the form (Haan, 1977) : Y = a + b*X + e...................................(416) where: Y = dependent variable X = independent variable a = intercept b = slope e = error term Solution of this equation for a and b using least squares is: b = I(xi*yi)/. (xi2) ............................... (417) a = Ymean b*Xmean ..............................(418) where: xi, Yi = sample points Mean = mean of y observations Xmean = mean of x observations. Thus, a and b are related through the mean of the x and y data points, which in our case are the ln(sqrt(area)) and ln(perimeter); respectively. For this study the fractal dimensions will be calculated using the areaperimeter method. A loglog regression on the area and perimeter data will be performed using equation (4 5). In addition to the fractal dimension, which is the slope of the regression equation, the intercept, called the fractal shape, will be used to distinguish the different classes and land uses which result from the maximum likelihood 48 classification. These data will be used to combine the 59 classes into different land uses. Statistical Analyses Three parameters will be used to compare the fractal dimension with the fractal shape and other comparisons for use in land use classification. First, the mean is used to locate the center of the distribution. The mean is an important factor for analysis. For example, if the fractal dimension is large it implies more irregularity of the land use, while if the fractal shape is large it implies a more regular shape of the land use. Second, the standard deviation (SD) is used to measure the spread or range of the individual measurements which is very important in image processing. A parameter associated with a larger SD implies that it has a greater capability to differentiate the land use conditions. Third, the coefficient of variation (CV) affords a relative measure of dispersion so that variation can be compared in features expressed in different units of measurement. In other words, this parameter is ratioing the above two parameters in a percentage basis for quantifying the variation. This also implies that a parameter associated with a larger CV is better in image processing for differentiating the land use conditions. Use of Different Pixel Groupings Often after classification of satellite images there are land use areas which consist of only a few pixels which results in "peppering" of the final image. These small areas often are the majority of the total number of land use areas. This effect could unduly affect the value of the fractal dimension and fractal shape. To resolve this dilemma two methods are employed, the use of unique areaperimeter combinations and the use of successively increasing minimum pixel areas. Unique AreaPerimeter Combinations The results of the fractal dimensions in the previous sections were based on using all areaperimeter information available for each study area. However, to eliminate the effect of multiple areaperimeter combinations for each land use, the fractal dimension was calculated using only the unique areaperimeter combinations. The reason for doing this is to examine the types of shape that occur for each type of land use. For example, the water land use areas would generally be long areas with narrow widths that meander, typical of rivers, while the urban land use would contain areas which are more rectangular. Using Different Cell Sizes To examine the use of different cell sizes, the fractal parameters will be calculated by successively increasing the minimum number of pixels for any land use group. For example, if the standard method of fractal calculation includes land use areas which consist of only one pixel of a 2 SPOT image, an area is only consisting of 400 m For this analysis the fractal number is calculated eliminating the land use areas below a given minimum size. This is then done for increasing number of pixels (and corresponding land use areas). The results of this will be a relationship between the fractal dimension and a given minimum pixel land use area. Spectral Reflectance and Waveband Combinations The mean spectral reflectance data were obtained for channel 1 (green), channel 2 (red), and channel 3 (infrared) for the Hastings, Palatka, and Seville study areas. These data will be compared with the different fractal parameters. Normalized Difference Vegetation Index The NDVI is calculated for each pixel in the SPOT image as follows (Price, 1987): NDVI = (DN3 DN2)/(DN3 + DN2) ....................(419) where : DNi = digital number (reflectance value) for channel i. To correlate NDVI with the fractal dimension for each class and land use the following equation was used: NDVI = (MR3 MR2)/(MR3 + MR2) .................. (420) where : MRi = mean reflectance for channel i. To apply a NDVI to an AVHRR scene a ratio is applied to each pixel as follows (Price, 1987 and Shih, 1994): NDVI = (DN2 DN1)/(DN2 + DNj) ................... (421) where terms are the same as before, except the wavelength ranges are different for the AVHRR than the SPOT image. The use of different waveband combinations and ratios is used for enhancement of spectral images. Table 43 lists the different combinations used. A study conducted by Shih (1994), using AVHRR data to analyze the NDVI within the EAA, showed negative NDVI values in the noncropped areas such as water and cleared land. These negative values are mainly due water having a lower spectral response in the near infrared region than in the visible region. In order to avoid this negative value image which may influence the image processing, 0.5 and 0.3 were added to the NDVI and called the revised NDVI and the modified revised NDVI, respectively (Table 43). Table 43. Waveband combinations and ratios. Band Ratio Name Definitiona Status Normalized Difference Vegetative Index (NDVI) (B3B2)/(B3+B2) Old Revised Normalized Difference Vegetative NDVI + 0.5 Index (RNDVI) New Modified Revised Normalized Difference Vegetative Index (MRNDVI) NDVI + 0.3 New Infrared/Red B3/B2 Old Infrared Red B3 B2 Old Red/Green B2/B1 Old aBand 1 = green waveband Band 2 = red waveband Band 3 = infrared waveband Proposed Fractal Analyses Historical Fractal Analyses Historically the fractal dimension was not calculated on an unsupervised maximum likelihood classification image. DeCola (1989) used a supervised classification in Vermont and thus started with only eight classes. He only postulated using fractals as part of the classification scheme. However, this method is also implemented with unsupervised classification techniques in this study for examining its applicability for Florida conditions. Although significant and interesting progress has been made by recent researchers, problems of existing fractal analysis are evident. Lam (1990) calculated fractal dimension for each band, but did not calculate fractal dimension for band combinations which are very important in land use classification. Vasil'yev and Truflin (1992) concluded that agroengineering geosystems have a fractal character, but they made no comparisons between urban, forested (hardwood or conifer), marsh, etc. land uses. Olsen et al. (1993) used a modified fractal dimension to measure landscape diversity, but the index cannot be used as a tool for land use classification. De Jong and Burrough (1995) did not conclusively relate the fractal dimension to land use. 54 Therefore, the new fractal analyses are proposed in the following section. New Fractal Analyses 1. Use of the fractal shape along with the fractal dimension for land use classification. 2. Use unique areaperimeter combinations greater than three pixels for fractal parameter calculations. 3. Use of different cell sizes by eliminating the land use areas below a given minimum size for fractal calculations. 4. Use of mean reflectance values and fractal parameters for land use classification. 5. Use of different waveband combinations and/or ratios with fractal parameters for land use classification. CHAPTER 5 RESULTS AND DISCUSSION Conventional Classification of SPOT Images The ELAS image processing system classified each SPOT scene into 59 unrelated classes using the maximum likelihood methodology discussed in Chapter 4. These 59 separate classes were assigned a land use by "sliding through" the classes. This was done by assigning each spectral class of interest a color and viewing it on the computer monitor. The location and spatial pattern (straight line, rectangular, sinuous, etc.) were noted and compared with quadrangle maps and through extensive groundtruthing. Finally, the 59 classes were grouped into eight land use categories which are described in Table 51. This is a modification of the Anderson classification system. These eight land uses are conifers, hardwoods, marsh, pasture, row crops, urban, water, and clearings. The marsh/shadehouse land use grouping was based on similar reflectance and included reed, rush, bullrush, flag, cattail, and some asphalt and shadehouse used in fern operations. Pastures were both improved and unimproved. Urban areas included pavement, buildings, quarries, and landfills. Water included lakes, ocean, intercoastal waterways, and rivers. Clearings included Table 51. Land use descriptions for SPOT images. Land Use Description Urban Water Clearings Pavement Buildings Quarries Landfills Ocean Intercoastal Waterway Rivers Ponds/Lakes Fresh Silviculture ClearCuts Beach Bare Sand Hills Conifers Primarily Plantation Pine. Pine Wetland Pine Scrub Fired Pine Scrub Sapling Pine Red Cedar Stands Hardwoods Live Oak Oak Scrub Oak/Tupelo Mixed Hardwoods Marsh Treeless Wetlands with Growths of: Reed Rush Bullrush Flag Cattail Also includes some Fresh Asphalt and Shade Houses. Pasture Improved Pasture (Tended Pasture, Lawns, Golf Courses) Unimproved Pasture (Weedy/Neglected Pasture, Brush Rangeland, Grassy Fallow Areas. Roadside Grass). Row Crops Potato Fields Corn Cabbage Onion OrnamentalsGladiolus and Canna OrnamentalsGladiolus and Canna 57 mainly silviculture clearcuts and some beach, and bare sand hills. Seven distinct classes for the top scene are shown in Table 52 mainly because the clearings class was not shown in the original 59 classes; and eight distinct classes for the bottom scene were determined and are shown in Table 53. The spatial distribution of land uses is shown in Figures 51 and 52 for images 619290 and 619291, respectively. For our purposes only black and white are shown, while the land uses can be color coded for ease in identification of their spatial distribution. This final processing step consisted of entering ground control points (GCPs), followed by image geocorrection and resampling. GCPs were brought into ELAS using a digitizing tablet and USGS 7.5 Minute Series quadrangle sheets. These GCPs included intersections of twolane, paved roads. Dirt roads and ditchlines were not used, because they are often rerouted. Multilane highways, utility easements, and urban road intersections were also not used, since they are usually too large to pindown as GCPs. Once a sufficient GCP set with a sufficient number of points (3+ per quadrangle) and with an acceptable accuracy (rms error < 10 m for entire image) was entered, the image could be geocorrected and resampled. Because the project Table 52. Land use spectral classes for SPOT image 619290. Land Use/Cover Conifers Hardwoods Marsh Pasture Row Crops Urban Water ELAS Spectral Class Numbers 1, 2, 6, 7, 9, 13, 15, 16, 19, 23, 27, 33, 38,43, 45 4, 8, 18, 41 17, 22, 34, 35, 36 5, 24, 26, 28, 29, 32, 40, 44, 47, 48, 53, 57, 58 39, 42, 46, 49, 55, 56, 59 31, 50, 52 3, 10, 11, 12, 14, 20, 21, 25, 30, 37, 51, 54 Table 53. Land use spectral classes for SPOT image 619291. Land Use/Cover Conifers Hardwoods Marsh Pasture Row Crops Clearings Urban Water ELAS Spectral Class Numbers 1, 2, 9, 10, 11, 17, 21, 23, 29, 33, 40, 45, 54, 55 3, 4, 6, 7, 12, 26, 46, 47 15, 38, 57 5, 8, 20, 22, 24, 25, 34, 35, 36, 39, 42, 48, 52, 59 13, 16, 18, 19, 27, 28, 32, 37, 41, 43, 50, 51,56 30, 44, 49 31, 53 14, 58 Figure 51. SPOT image 619290 land use classes. Figure 52. SPOT image 619291 land use classes. 62 area contained reasonably lowrelief terrain, the firstorder global polynomial surface model was selected. The nearest neighbor resampling method was then applied to the images. This resampling method should be the one chosen for all land cover images, since the other resampling methods are limited in application to singlechannel, nonclassified images. The resampling size was chosen to be identical to the original SPOT pixel size (20 m x 20 m). Spatial Distribution of Land Uses The acreages and landarea percentages of the eight landuse types distinguished within the two SPOT images are given in Tables 54, 55, and 56. Several conclusions can be drawn from these tables. It is evident that most (75.6%) of the project land area (Table 56) is under forested land use, and that pines comprise 70.8% of forest component. Agriculture (including pasture and row crops) forms the second largest land use (19.8% of project land area). The largest agricultural sub type is shown to be pasture (80.0% of agriculture). Marsh, clearings, and urban land use types, although important for watermanagement purposes, are relatively small components of the project land area. It should also be noted that the total area belonging to the Ocala National Forest clearcuts is divided into four 63 Table 54. Spatial distribution of land use areas for SPOT image 619290. Land Use Area Total Area Land Area ha % % Conifers 142,337 38.6 58.4 Hardwoods 37,066 10.1 15.3 Marsh 5,178 1.4 2.1 Pasture 42,979 11.6 17.6 Row Crops 9,609 2.6 3.9 Urban 6,621 1.8 2.7 Water 125,204 33.9  Clearings    Total land 243,790 66.1 100.0 Total 368,994 100.0  64 Table 55. Spatial distribution of land use areas for SPOT image 619291. Land Use Area Total Area Land Area ha % % Conifers 185,422 45.0 50.3 Hardwoods 98,281 23.8 26.7 Marsh 4,128 1.0 1.1 Pasture 53,846 13.1 14.6 Row Crops 14,613 3.5 4.0 Urban 986 0.3 2.7 Water 43,812 10.6  Clearings 11,132 2.7 3.0 Total land 368,408 89.4 100.0 Total 412,220 100.0  65 Table 56. Spatial distribution of land use areas for combined SPOT images 619290 and 619291. Land Use Area Total Area Land Area ha % % Conifers 327,759 42.0 53.5 Hardwoods 135,347 17.3 22.1 Marsh 9,306 1.2 1.5 Pasture 96,825 12.4 15.8 Row Crops 24,222 3.1 4.0 Urban 7,607 1.0 1.3 Water 169,016 21.6  Clearings 11,132 1.4 1.8 Total land 612,198 78.4 100.0 Total 781,214 100.0  66 of the above landuse classes. Those clearcut areas which were freshly cut in 1988 fell within the clearing class, while those with 12 years of natural regrowth fell within the pasture or row crops classes, those with 35 years of natural regrowth fell within the conifer or hardwoods classes, and those with 35 years of pure pine regrowth fell within the conifer class. Fractal Dimension by Class and Land Use Class Analysis Images resulting from the maximum likelihood classification process yielded a 59 class image, which was first analyzed for fractal properties. As discussed previously, three subsets of the SPOT image No. 619290 were used in this research. The areas are the Hastings, Palatka, and Seville USGS 7.5 minute quadrangle areas. These areas were selected since they included all land uses and contained the larger urban areas found in the SPOT image. For purposes of discussion, the word "study area" will refer to the quadrangle area (i.e., the Hastings study area refers to the study area encompassed by the geographic location of the Hastings USGS quadrangle). After extraction of these smaller images the fractal dimension was calculated using the loglog regression 67 techniques discussed earlier (equation 45). This method uses the log of the perimeter and the log of the square root of the area. The results of the fractal dimension are given in Table 57 for the 59 classes of the three study areas. The statistical analyses of the mean, standard deviation (SD), and coefficient of variation (CV) are also given in Table 57. Several observations can be made from Table 57. First, of the 59 class images, 13 are for each of three land uses (pasture, pine, and row crops), eight are for hardwoods, three each for marsh/shadehouse and clearings, and two each for urban and water. Second, the mean fractal dimensions for the 59 class image for each study area show similar results: 1.325 for Hastings and Seville, and 1.324 for Palatka. Third, the standard deviations are 0.042, 0.036, and 0.031 and coefficients of variation are 3.2%, 2.7%, and 2.3% for Seville, Hastings, and Palatka, respectively. This indicates that the spread or variation of individual class measurements for the fractal dimensions are similar for the three study areas. Furthermore, from this small range of SDs and CVs it is difficult to differentiate the land use conditions within a study area using fractal dimension techniques for analyzing the original 59 classes, in other words, a further modification is needed. Table 57. Fractal dimension and fractal shape for 59 spectral classes for Hastings, Palatka, and Seville study areas. Class Land Use Hastings Palatka Seville FDa FS b FD FS FD FS 1 Pine 1.351 1.377 1.392 1.199 1.353 1.363 2 Pine 1.345 1.399 1.339 1.427 1.340 1.425 3 Hardwoods 1.383 1.237 1.372 1.285 1.387 1.221 4 Hardwoods 1.374 1.272 1.369 1.298 1.378 1.257 5 Pasture 1.327 1.482 1.333 1.453 1.331 1.461 6 Hardwoods 1.326 1.491 1.330 1.473 1.317 1.534 7 Hardwoods 1.369 1.295 1.363 1.319 1.347 1.392 8 Pasture 1.344 1.404 1.324 1.498 1.339 1.427 9 Pine 1.373 1.280 1.346 1.394 1.365 1.314 10 Pine 1.314 1.547 1.319 1.523 1.349 1.383 11 Pine 1.335 1.441 1.322 1.499 1.333 1.445 12 Hardwoods 1.392 1.202 1.394 1.193 1.377 1.264 13 Row Crops 1.313 1.548 1.322 1.511 1.336 1.439 14 Water 1.243 1.932 1.308 1.584 1.198 2.278 15 Marsh/ 1.308 1.579 1.323 1.509 1.301 1.614 Shadehouse 16 Row Crops 1.341 1.421 1.290 1.669 1.351 1.380 17 Pine 1.327 1.485 1.336 1.443 1.345 1.400 18 Row Crops 1.321 1.511 1.317 1.534 1.324 1.497 19 Row Crops 1.350 1.377 1.303 1.606 1.368 1.309 20 Pasture 1.326 1.489 1.308 1.579 1.330 1.472 21 Pine 1.341 1.419 1.347 1.388 1.359 1.341 22 Pasture 1.313 1.555 1.308 1.579 1.301 1.611 23 Pine 1.316 1.535 1.331 1.465 1.340 1.422 24 Pasture 1.306 1.585 1.300 1.613 1.345 1.401 25 Pasture 1.316 1.535 1.292 1.658 1.349 1.380 26 Hardwoods 1.396 1.186 1.390 1.205 1.397 1.186 27 Row Crops 1.354 1.356 1.269 1.779 1.301 1.617 28 Row Crops 1.317 1.520 1.233 1.986 1.173 2.384 29 Pine 1.319 1.521 1.320 1.514 1.312 1.549 30 Clearings 1.307 1.580 1.321 1.512 1.333 1.456 31 Urban 1.290 1.661 1.340 1.418 1.319 1.517 32 Row Crops 1.358 1.335 1.336 1.445 1.338 1.429 33 Pine 1.360 1.330 1.378 1.261 1.366 1.302 34 Pasture 1.320 1.520 1.303 1.598 1.347 1.392 35 Pasture 1.324 1.499 1.319 1.524 1.344 1.404 Table 57.  continued. Class Land Use Hastings Palatka Seville FDa FS b FD FS FD FS 36 Pasture 1.292 1.656 1.316 1.535 1.273 1.744 37 Row Crops 1.330 1.467 1.324 1.506 1.326 1.491 38 Marsh/ 1.290 1.672 1.301 1.607 1.221 2.070 Shadehouse 39 Pasture 1.336 1.440 1.295 1.633 1.319 1.519 40 Pine 1.324 1.497 1.315 1.541 1.354 1.364 41 Row Crops 1.325 1.493 1.295 1.642 1.312 1.552 42 Pasture 1.315 1.539 1.336 1.438 1.339 1.425 43 Row Crops 1.339 1.420 1.300 1.618 1.332 1.458 44 Clearings 1.297 1.632 1.291 1.662 1.315 1.541 45 Pine 1.338 1.433 1.337 1.438 1.344 1.407 46 Hardwoods 1.353 1.366 1.338 1.431 1.352 1.370 47 Hardwoods 1.293 1.648 1.334 1.430 1.341 1.399 48 Pasture 1.297 1.627 1.272 1.761 1.281 1.710 49 Clearings 1.319 1.522 1.312 1.555 1.363 1.324 50 Row Crops 1.272 1.759 1.302 1.611 1.299 1.617 51 Row Crops 1.237 1.969 1.374 1.267 1.290 1.663 52 Pasture 1.329 1.475 1.313 1.549 1.318 1.526 53 Urban 1.230 2.006 1.309 1.551 1.287 1.665 54 Pine 1.303 1.603 1.327 1.490 1.245 1.915 55 Pine 1.322 1.504 1.314 1.545 1.275 1.744 56 Row Crops 1.306 1.579 1.297 1.628 1.304 1.592 57 Marsh/ 1.248 1.906 1.321 1.514 1.315 1.542 Shadehouse 58 Water 1.402 1.168 1.389 1.209 1.374 1.272 59 Pasture 1.352 1.373 1.310 1.570 1.312 1.560 Mean 1.325 1.503 1.324 1.503 1.325 1.504 SD 0.036 0.175 0.031 0.148 0.042 0.223 CV, % 2.7 11.7 2.3 9.8 3.2 14.8 a FD = fractal dimension b FS = fractal shape 70 Fourth, since the 59 class image is the first output of the unsupervised classification and the similarity of fractal dimension among the three study areas, it is difficult to differentiate actual land use conditions. Thus, after ground truthing and class combinations, the original 59 classes were regrouped into eight land uses (see Table 51 for a description) which are analyzed in the following section. Land Use Analysis The fractal dimensions for the eight land use image for each quadrangle are given in Tables 58a, 58b, and 58c and plotted in Figures 53, 54, and 55 for Hastings, Palatka, and Seville, respectively. A complete listing of the statistical results (number of areas, mean area and perimeter) used in the fractal analysis is given in Table 59. Several observations can be made from Tables 58a, 58b, 58c, 59 and Figures 53, 54, and 55. First, the pasture land use has the highest fractal dimension for all three study areas and varied from 1.396 to 1.414. This implies that boundaries are more irregular in pastures than in other land uses. This increased complexity of the boundaries may be partially due to "tree islands" in pastures. Also, pastures include rangeland, grassy areas, and roadside grassed areas. The border of some unimproved pastures have irregular perimeters due to migration of hardwood and Table 58a. Fractal dimension and fractal shape for eight land uses for the Hastings study area. Land use FDa FSb CVc Pine 1.344 1.402 1.6 Hardwoods 1.313 1.536 1.8 Pasture 1.396 1.176 1.9 Row Crops 1.311 1.556 1.8 Marsh/ 1.309 1.569 1.0 Shadehouse Clearings 1.344 1.405 1.2 Urban 1.264 1.799 1.5 Water 1.139 2.664 1.6 Mean 1.303 1.638 SD 0.076 0.451 CV, % 5.8 27.5 a FD = fractal dimension using all data. b FS = fractal shape using all data. c CV = Coefficient of Variation within each land use. Table 58b. Fractal dimension and fractal shape for eight land uses for the Palatka study area. Land use FDa FSb CV, Pine 1.344 1.398 1.6 Hardwoods 1.316 1.522 1.8 Pasture 1.414 1.110 1.9 Row Crops 1.396 1.191 1.5 Marsh/ 1.353 1.364 1.4 Shadehouse Clearings 1.353 1.364 1.3 Urban 1.290 1.646 1.6 Water 1.189 2.333 2.5 Mean 1.332 1.491 SD 0.070 0.380 CV, % 5.3 25.5 a FD = fractal dimension using all data. b FS = fractal shape using all data. c CV = Coefficient of Variation within each land use. Table 58c. Fractal dimension and fractal shape for eight land uses for the Seville study area. Land use FDa FSb CVc Pine 1.371 1.229 2.2 Hardwoods 1.331 1.396 2.3 Pasture 1.410 1.063 2.2 Row Crops 1.320 1.475 1.6 Marsh/ 1.204 2.218 2.1 Shadehouse Clearings 1.382 1.181 1.8 Urban 1.304 1.540 1.9 Water 1.085 3.540 2.3 Mean 1.301 1.705 SD 0.107 0.821 CV, % 8.2 48.2 a FD = fractal dimension using all data. b FS = fractal shape using all data. c CV = Coefficient of Variation within each land use. 1.400 + row crops marsh/ shadehouse 1.300  clearing urban 1.200 + water 1.100 + 1.000 1L _ Land Use Fractal dimension versus land use for the Hastings study area. Figure 53. row rcrnnc pine marsh/ shadehouse clearing 1.100 1.000  Figure 54. Land Use Fractal dimension versus land use for the Palatka study area. 1.400 1.300 1.200 hardwoods urban water pasture clearing Dine hardwoods row crops marsh/ shadehouse 1.100 1 1.000 _1  Land Use Fractal dimension versus land use for the Seville study area. 1.400 1.300 1.200 I urban water Figure 55. Table 59. Area and perimeter statistics for Hastings, Palatka, and Seville study areas. Study Land Use No. of Average Average Area Areas Aria Perimeter m m Hastings Pine 4,320 4,731 258 Hardwoods 2,228 11,774 387 Pasture 3,137 7,664 392 Row Crops 1,885 9,180 339 Marsh/Shadehouse 794 1,246 134 Clearings 3,382 1,344 152 Urban 392 3,148 219 Water 12 2,066,066 5,393 Palatka Pine 4,774 13,589 364 Hardwoods 2,240 19,058 462 Pasture 4,370 5,916 370 Row Crops 3,082 2,439 215 Marsh/Shadehouse 953 1,825 173 Clearings 4,375 1,580 166 Urban 506 3,533 237 Water 78 211,087 1,130 Seville Pine 1,984 32,103 751 Hardwoods 1,165 46,917 946 Pasture 1,317 23,424 812 Row Crops 916 4,699 304 Marsh/Shadehouse 319 6,792 322 Clearings 787 4,823 332 Urban 70 4,331 317 Water 48 172,712 948 78 conifers into old pasture areas. This increases the complexity of the pasture areas. Second, water has the lowest fractal dimension which implies a high regularity of perimeter of the water bodies in all three study areas. Third, the greatest range (highest minus lowest value) of fractal dimensions among land uses occurred between pasture and water land uses at all three study areas (Table 58). For example, the fractal dimension at Seville for pasture compared with water is 30% higher. Fourth, the fractal dimension technique clearly separates water from urban land use at all locations (Table 5 8). For example, the fractal dimension for urban compared to water land use at Seville is 20% higher. Fifth, the pine and clearings have similar fractal dimensions in each study area. This similarity could be due to the high correlation between clearings and pine land use areas. For example, after harvest of pines, areas become clearings, or vice versa. Sixth, the fractal dimensions for pine and clearings are higher, i.e., more perimeter irregularity, for Seville than for Hastings and Palatka. This could be due to the more interior location of Seville which contains less water bodies as shown in Table 59, which can contribute to less regular boundaries. Also, pine and clearing areas are less likely to 79 be adjacent to water bodies in the Seville area than in the other two areas, thus causing a higher fractal dimension at Seville. Seventh, the fractal dimensions are similar for hardwoods at all study locations. However, the fractal dimensions for row crops and hardwoods are similar in the Hastings and Seville study areas, but the fractal dimension for row crops is higher than for hardwoods in the Palatka area. This could be due to the row crops in the Palatka area being of smaller size per number of row crop areas, i.e. about 2 2 2,400 m compared to about 4,700 m or higher for the other two areas (Table 59). This could contribute to the higher fractal dimension for row crops in the Palatka area. Eighth, fractal dimension was slightly but consistently higher for pines compared to hardwood land use for all three study areas (Table 58). For example, the fractal dimension at Seville for pine compared to hardwood is 3% higher. Both pine and hardwood have natural boundaries which are non rectangular, but the reason for the slightly lower fractal dimension for hardwoods may be due to hardwoods being located near water bodies, which have a lower fractal dimension, and pines are located in upland sites. Ninth, the lower fractal dimension for marsh/shadehouse land use in the Seville area compared to Hastings and Palatka areas may be due to a larger sized marsh/shadehouse area in 2 2 the Seville area (6,800 m2 compared to 1,800 m2 or less for the other areas). This feature creates a more regular shaped marsh/shadehouse area for the Seville area. Additionally, the lower fractal dimension for Seville could be due to more shadehouses present in the Seville area compared to the Hastings and Palatka areas. These shadehouses are rectangular and thus would lower the fractal dimension. Tenth, the higher overall mean fractal dimension (1.332) for the Palatka area could be mainly due to the higher fractal dimension (1.396) for row crops and the higher fractal dimension (1.414) for pasture as mentioned above. Eleventh, after comparing Table 57 with Table 58, it is evident that the SDs and CVs for fractal dimensions in eight land uses are higher than in the 59 classes. This implies, as mentioned in the statistical analysis section, that the eight land uses are better for differentiating land use conditions than the 59 classes. Twelfth, as Table 58 shows, the CVs for fractal dimensions for all three study areas only varied from 5.3% to 8.2%. This small magnitude of CVs still makes it difficult to differentiate among land uses using fractal dimensions. In other words, another parameter which has a higher CV is urgently needed. Thirteenth, the coefficients for fractal dimensions and fractal shapes are given in Tables 58a, 58b, and 58c for 81 Hastings, Palatka, and Seville, respectively. These results afford a relative measure of dispersion within a given land use. The CVs among land uses ranged from 1.0 to 1.9% for Hastings, 1.3 to 2.5% for Palatka, and 1.6 to 2.3% for Seville. These relatively low CVs suggest validity of the experimental method and that the spectral signatures were similar within a given land use. The CV is ratioing the standard deviation and the mean in a percentage basis for quantifying the variation. This implies that a parameter with a smaller CV is better for the unsupervised maximum likelihood classification within a given land use. In summary, application of the fractal dimension technique for differentiating among land uses is only partially successful. The technique separates pasture from other land uses, water from other land uses, urban from water, and pine from hardwood. However, clearings, hardwoods, and row crops may have similar fractal dimensions at some locations. The above shortcomings or disadvantages suggest the need for a different parameter to differentiate among land uses. This leads to an analysis of fractal shape. Fractal Shape by Class and Land Use Class Analysis Three observations pertaining to fractal shape can be made from Table 57. First, the mean fractal shapes for the 59 class image show similar results for each study area: 1.503 for Palatka and Hastings; and 1.504 for Seville. This close relationship among study areas also was shown previously for the fractal dimension. Second, the SDs for fractal shape for the 59 classes are 0.148, 0.175, and 0.223 for Palatka, Hastings, and Seville, respectively. Whereas the SDs for fractal dimensions only range from 0.031 to 0.042, these four times larger SDs for fractal shape are desirable in image processing for differentiating among land uses. Third, the CVs for fractal shape for the 59 classes are 9.8%, 11.7%, and 14.8% for Palatka, Hastings, and Seville, respectively. Whereas the CVs for fractal dimension only range from 2.3% to 3.2%, these four times larger CVs for fractal shape are desirable in image processing for differentiating among land uses. In other words, using the fractal shape technique is better than the fractal dimension technique in land use classification. The fractal shape is the intercept of the loglog regression. The fractal shape versus the fractal dimension is 83 plotted in Figures Cl, C2, and C3 in Appendix C for the 59 class images for Hastings, Palatka, and Seville, respectively. These figures show a negative linear relationship between the intercept (fractal shape) and the slope (fractal dimension), i.e., the higher the fractal dimension, the lower the fractal shape. Land Use Analysis The fractal shapes for the eight land use image for each study area are given in Tables 58a, 58b, and 58c and plotted in Figures 56, 57, and 58 for Hastings, Palatka, and Seville, respectively. Several observations can be made as follows. First, pasture land use has the lowest fractal shape for all three study areas and varies from 1.063 for Seville to 1.176 for Hastings. This implies that boundaries are more irregular, or less regular, for pastures compared with other land uses. A similar conclusion was reached based on the high fractal dimension for the pasture land use. However, the difference based on fractal dimension among three areas was only 1%, whereas the difference based on fractal shape was 11%. This means that the pasture land use among land uses is similar based on fractal dimension, whereas there is a large difference based on fractal shape analysis. This could be due to the smaller farms (Table 59) with more improved pasture in 