Cartographic Generalization of Digital Terrain Models

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University Microfilms International 300 North Zeeb Road Ann Arbor, Michigan 48106 USA St. John's Road, Tyler's Green High Wycombe, Bucks, England HP10 SHR LQDM, JOSEPH COLM&N CÀRTDGRAPHTC GENERALIZATION OF DIGITAL TERRAIM MODELS. THE OHIO STATE UNiVERSITY, PH.D., 1976 " S m s IrrtematKXVU 300 n. zeeb road, ann arbor, mi asiob ® Copyright by Joseph Colman Loon 1978 CARTOGRAPHIC GENERALIZATION OF DIGITAL TERRAIN MODELS DISSERTATION Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University Joseph Colman Loon, B.Sc., M.Sc., M.S. * * * * The Ohio State University 1978 Reading Committee: Dr. U. A. Uotila, Chairman Dr. R. H. Rapp U y A . Uotila, ^ v i s e r Dr. J. N. Rayner Apartment of/ceodetic Science ACKNOWLEDGMENTS I am indebted to Dr. U. A. Uotila, for his support during the whole period of my graduate studies at the Ohio State University and for his encouragement and ideas which led to the study presented here; to Drs. I. I. Mueller, H. J. Steward and R. H. Rapp, for allowing me the use of their extensive personal libraries; to my reading committee, Drs. U. A. Uotila, R. H. Rapp and J. N. Rayner, for their patience and advice; to the Faculty, Staff and Students of the Department of Geodetic Science, for contributing to an atmos phere and experience which has made a lasting im pression on me; and to my wife, Zilla, for undertaking m m e r o u s difficult tasks including that of mother and budget director, while I immersed myself in the search. My thanks to Diana Howes, who typed this disserta tion with good humor and efficiency. November 2, 1931 . Born— Parys, South Africa 1954 ................... B.Sc. (Land Surveying), University of Cape Town, South Africa 1956 ................... L (S.A). Registered Land Surveyor of South Africa. 1956-1960............... Junior Lecturer and Assistant, Department of Land Surveying, University of Cape Town, South Africa 1961-1967............... Lecturer and Senior Lecturer, Division of Technicians, Cape Technical College, Cape Town, South Africa 1967 ................. Part-time Lecturer, Department of Land Surveying, University of Cape Town, South Africa 1967 ..... ........ M.Sc. (Land Surveying), University of Cape Town, South Africa 1969-1973............... Lecturer, Division of Geodesy, Technion— Israel Institute of Technology, Haifa, Israel 1974-1978. ....... Teaching and Research Associate, Department of Geodetic Science, The Ohio State University, Columbus, Ohio 1976 ................... M.S., The Ohio State University, Columbus, Ohio PUBLICATIONS "Isostasy." Journal of the University of Cape Town Engi neering and Scientific Society, Vol. 1, No. 3, 1955. "Photogrammetry." The Lens— Journal of the Cape Technical College, Cape Town, South Africa, 1961. Photogrammetry. Course Book, published by the Cape Technical College, Cape Town, South Africa. Surveying for the National Technical Certificate 3. Course Book published by the Cape Technical College, Cape Town, South Africa, 1963. "Gravimetric Geodesy." Proceedings of the Third South African National Survey Conference, Johannesburg, South Africa, 1967. "Survey Technicians." Proceedings of the Third South African National Survey Conference, Johannesburg, South Africa, 1967. With P. Yoeli. Map Symbols and Lettering; A Two Part Investigation. Part I— An examination of map symbols in their most elementary forms. Part II— The logic of auto mated map lettering. Final Technical Report. European Research Office of the United States Army. (AD-741" 834) , 1972. FIELDS OF STUDY Major Field; Geodetic Science Studies in Cartography. Professors H. J. Steward and H. Moellering Studies in Adjustments and Geodesy. Professors U. A. Uotila and I. I. Mueller Studies in Photogrammetry and Remote Sensing. Professors S. K. Ghosh, D. C. Merchant and 0. W. Mintzer Studies in Statistics and Numerical Methods. Professors W. A. T. Archambault, P. Feder, J. S. Rustagi, D. R. Whitney and R. LaRue iv TABLE OF CONTENTS Page ACKNOWLEDGMENTS...................................... Ü VITA ............................................. iii LIST OF TABLES .................... viii LIST OF FIGURES...................................... X LIST OF SYMBOLS AND NOTATION USED..................... xiv Chapter 1 CARTOGRAPHIC GENERALIZATION. 1.1 Introduc t ion......................... 1.2 Generalization of Topographic Maps. 1.2.1 Why Should Topographic Maps Be Generalized ............... 1.2.2 Generalization of Topographic Map Elements Other Than Relief 1.2.3 Generalization of Relief . 10 1.3 Purpose of This Study ............... 15 1.3.1 Computer-Assisted Cartography. 15 1.3.2 Problems of Generalization in Computer-Assisted Cartography. 16 1.3.3 Needed— A Flexible Method. 18 1.4 Hypothesis and Subsidiary Research Questions ............................ 1.4.1 The Least Squares Collocation Algorithm..................... 19 1.4.2 Subsidiary Research Questions. 20 1.5 Assumptions and Scope of This Study . 21 1.6 Organisation of This Study........... 24 Page Chapter 2 REVIEW OF RELATED RESEARCH AND METHODS . 26 2.1 State of the Art of the Cartographical Generalization of the Relief Continuum on Topographical M a p s ................. 26 2.1.1 Manual M e t h o d s ................. 28 2.1.2 Automated Methods............... 32 2.2 Summary and How This Study Will Make a Contribution.......................... 35 3 THE CHARACTER OF THE TERRAIN ............. 39 3.1 Introduction............................. 39 3.2 Some Terrain Descriptors................ 41 3.3 Description of DTM and Contouring Program Used in This Study............. 44 3.4 Double Fourier (Trigonometric) Series . 48 3.5 Harmonic Surfaces .................... 52 3.6 The Empirical Covariance Function .. 59 3.6.1 Theoretical Considerations .. 59 3.6.2 The Empirical Covariance F u n c t i o n ........................ 63 3.6.3 Reference surfaces ............. 66 3.6.4 Some Results ......... 77 3.7 Some Quantitative Measures Related to the Change in the Character of the T e r r a i n ........................ ... 84 3.8 Summary ................................. 93 4 LEAST SQUARES COLLOCATION. ............. 95 4.1 Introduct ion............................. 95 4.2 Overview of the Least Squares Collocation Method...................... 96 4.3 Proposed Use of Least Squares Collocation Concepts in Cartographic Generalization............................. 103 4.4 S u m m a r y ................................. 109 Page Chapter TESTING THE HYPOTHESIS........................ HO 5.1 Preliminary Investigations Using Diagonal Matrices Only.................... HO 5.2 Using the Least Squares Collocation Algorithm— With a Limited Distance of Influence............................... 116 5.3 Constraints and Varying Degrees of Generalization.......... 124 5.4 S u m m a r y ...................................128 DESIGN OF A GENERALIZATION FILTER..............133 6.1 The Nines Filter.......................... 133 6.2 Requirements of a Filter................. 137 6.3 Design of Nines Filter Using the Gaussian Function ...................... 138 6.4 The Gaussian Function Nines Filter Compared With Other Filters ........... 143 6.5 Frequency Response........................ 150 6.6 Results and Analysis of Experiments . 154 6.7 S u m m a r y ...................................165 PROPOSED SYSTEM FOR THE CARTOGRAPHIC GENERALIZATION OF THE RELIEF CONTINUUM ON TOPOGRAPHIC MAPS................... 7.1 Outline of the System ............... 7.1.1 Filter Selection and Generalization ............... 164 7.1.2 Analysis of the Generalized Map 169 7.2 Proposed System Applied to a Digitized Portion of a Topographic

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