Analysis of the Positional Accuracy of Linear Features

332 Pages·2007·8.63 MB·English

Analysis of the Positional Accuracy of Linear Features

Geoffrey John Lawford

Submitted in total fulfilment of the requirements of the degree of Doctor of Philosophy
September 2006
Department of Geomatics
The University of Melbourne
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Abstract

Although the positional accuracy of spatial data has long been of fundamental
importance in GIS, it is still largely unknown for linear features. This is compromising
the ability of GIS practitioners to undertake accurate geographic analysis and hindering
GIS in fulfilling its potential as a credible and reliable tool. As early as 1987 the US
National Center for Geographic Information and Analysis identified accuracy as one of
the key elements of successful GIS implementation. Yet two decades later, while there
is a large body of geodetic literature addressing the positional accuracy of point
features, there is little research addressing the positional accuracy of linear features, and
still no accepted accuracy model for linear features. It has not helped that national map
and data accuracy standards continue to define accuracy only in terms of “well-defined
points”. This research aims to address these shortcomings by exploring the effect on
linear feature positional accuracy of feature type, complexity, segment length, vertex
proximity and e-scale, that is, the scale of the paper map from which the data were
originally captured or to which they are customised for output.

The research begins with a review of the development of map and data accuracy
standards, and a review of existing research into the positional accuracy of linear
features. A geographically sensible error model for linear features using point matching
is then developed and a case study undertaken. Features of five types, at five e-scales,
are selected from commonly used, well-regarded Australian topographic datasets, and
tailored for use in the case study. Wavelet techniques are used to classify the case study
features into sections based on their complexity. Then, using the error model, half a
million offsets and summary statistics are generated that shed light on the relationships
between positional accuracy and e-scale, feature type, complexity, segment length, and
vertex proximity. Finally, auto-regressive time series modelling and moving block
bootstrap analysis are used to correct the summary statistics for correlation.

The main findings are as follows. First, metadata for the tested datasets significantly
underestimates the positional accuracy of the data. Second, positional accuracy varies
with e-scale but not, as might be expected, in a linear fashion. Third, positional accuracy
varies with feature type, but not as the rules of generalisation suggest. Fourth, complex
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features lose accuracy faster than less complex features as e-scale is reduced. Fifth, the
more complex a real-world feature, the worse its positional accuracy when mapped.
Finally, accuracy mid-segment is greater than accuracy end-segment.

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Declaration

This is to certify that

(i) the thesis comprises only my original work towards the PhD
(ii) due acknowledgement has been made in the text to all other material used
(iii) the thesis is less than 100,000 words in length, exclusive of tables, maps,
bibliographies and appendices
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Acknowledgements

The author gratefully acknowledges the following people and organisation. First,
Geoscience Australia for supporting the research associated with fractals and Fourier
and wavelet transformations. Second, Dr. Ole Nielsen, of Geoscience Australia, for
kindly providing the author with a wavelet transformation algorithm, and instructing the
author in its use and more broadly in wavelet technology. Third, the Statistical
Consulting Centre of the University of Melbourne, and in particular Dr. Ian Gordon, for
instruction on correlation and how its effect on the case study results could be
estimated. Dr. Gordon’s assistance extended to some data analysis, graph generation,
and script writing, all of which are acknowledged in the body of the thesis. Fourth, Dr.
Ewan Masters, of the University of New South Wales, for his encouragement to
commence this research and for his supervision of it until illness forced his untimely
retirement. Fifth, Dr. Bruce Harvey, also of the University of New South Wales, who
stepped into the breach following the retirement of Dr. Masters even though this
research was not in an area he specialised, for his enthusiastic supervision. Sixth, Dr.
Gary Hunter, of the University of Melbourne, who kindly supported the author’s
transfer to the University of Melbourne, for his ultimate supervision of this research,
and in particular his encouragement, feedback and friendship. Finally, Dr. Matt
Duckham for his support and co-supervision of this research.

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Table of Contents
ABSTRACT iii
DECLARATION v
ACKNOWLEDGEMENTS vi
TABLE OF CONTENTS vii
LIST OF TABLES xi
LIST OF FIGURES xvi
LIST OF ABBREVIATIONS xxvi
LIST OF PUBLICATIONS ARISING FROM RESEARCH xxvii
1 CHAPTER 1: INTRODUCTION 1
1.1 OVERVIEW 1
1.2 BACKGROUND 2
1.3 AIM, OBJECTIVES AND SIGNIFICANCE OF THE RESEARCH 7
1.4 THESIS STRUCTURE 8
1.5 CHAPTER SUMMARY 9
2 CHAPTER 2: REVIEW OF ACCURACY STANDARDS AND ERROR MODELS 11
2.1 INTRODUCTION 11
2.1.1 Terminology 11
2.2 MAP AND DATA ACCURACY STANDARDS 13
2.2.1 The US National Map Accuracy Standards 13
2.2.2 Other US map accuracy standards 15
2.2.3 The US National Standard for Spatial Data Accuracy 15
2.2.4 The Australian “Standards of Map Accuracy” 16
2.2.5 Criticism of accuracy standards 17
2.3 LINEAR FEATURE ERROR MODELLING RESEARCH 18
2.3.1 Epsilon bands and segment-generated “error” bands 18
2.3.2 Vertex-generated “error” bands 32
2.3.3 Area and offset models 43
2.4 CONCLUSION 56
3 CHAPTER 3: ERROR MODEL TRIALS AND DEVELOPMENT 59
3.1 INTRODUCTION 59
3.1.1 Terminology 60
3.2 HAUSDORFF DISTANCE MODEL 60
3.3 FRECHET DISTANCE MODEL 63
3.4 BACKGROUND TO THE FOURIER TRANSFORMATION 65
3.4.1 The complex series Fourier Transformation 65
3.4.2 Complex series Fourier Transformation and geographic data 72
3.5 FOURIER SPECTRAL SUBTRACTION MODEL 75
3.6 FOURIER CROSS CORRELATION MODEL 77
3.7 PROPORTIONAL DISTANCE POINT MATCHING MODEL 80
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3.8 SHORTEST DISTANCE POINT MATCHING MODEL 84
3.9 RASTER “CONSTRAINED DISTANCE” MODEL 87
3.10 TRIANGULATED IRREGULAR NETWORK (TIN) “STREAMFLOW” MODEL 88
3.11 PERPENDICULAR OFFSET POINT MATCHING MODEL 89
3.12 SUMMARY OF MODEL SHORTCOMINGS 94
3.13 TECHNICAL IMPLEMENTATION 95
3.14 CONCLUSION 101
4 CHAPTER 4: DEALING WITH POSSIBLE OFFSET CORRELATION 103
4.1 INTRODUCTION 103
4.2 CORRELATION AND THE EPOPM MODEL 103
4.2.1 Auto regressive time series model 107
4.2.2 Moving block bootstrap analysis 111
4.3 TECHNICAL IMPLEMENTATION 117
4.4 CONCLUSION 117
5 CHAPTER 5: MODELLING THE COMPLEXITY OF LINEAR FEATURES 119
5.1 INTRODUCTION 119
5.2 REVIEW OF LINEAR COMPLEXITY 119
5.3 WAVELET HISTORY 121
5.4 WAVELETS IN ONE DIMENSION 123
5.5 WAVELETS WITH SPATIAL DATA 127
5.6 WAVELETS AND LINEAR COMPLEXITY 133
5.6.1 Technique #1 133
5.6.2 Technique #2 135
5.7 TECHNICAL IMPLEMENTATION 137
5.8 CONCLUSION 138
6 CHAPTER 6: CASE STUDY DATASETS 139
6.1 INTRODUCTION 139
6.1.1 Terminology 139
6.2 DATASET DESCRIPTIONS 139
6.2.1 1:25K dataset 141
6.2.2 1:250K dataset 142
6.2.3 1:1M dataset 144
6.2.4 1:2.5M dataset 145
6.2.5 1:5M dataset 145
6.2.6 1:10M dataset 146
6.2.7 Summary of attributes 147
6.3 FEATURE TYPE SELECTION 148
6.4 PHENOMENA SELECTION 148
6.5 DATA PREPARATION 162
6.5.1 Method 163
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6.5.2 Interpretation changes 163
6.5.3 Retained anomalies 166
6.6 CONCLUSION 169
7 CHAPTER 7: EXPERIMENTAL CASE STUDY 171
7.1 INTRODUCTION 171
7.2 PROCEDURE 171
7.3 MODEL ENHANCEMENTS 172
7.3.1 Invalid intersections 173
7.3.2 Short offset precedence 181
7.3.3 Reference line omissions 183
7.4 EVALUATION 184
7.4.1 Coastlines 184
7.4.2 Waterbody boundaries 186
7.4.3 Watercourses 189
7.4.4 Roads 190
7.4.5 Railways 191
7.5 CONCLUSION 191
8 CHAPTER 8: CASE STUDY RESULTS 193
8.1 INTRODUCTION 193
8.2 EXPLANATION OF THE FORMAT OF THE FULL RESULTS 193
8.3 EXPLANATION OF THE FORMAT OF THE SUMMARY RESULTS 197
8.4 RESULTS EXTRACTS 198
8.4.1 E-scale dependence 201
8.4.2 Feature type dependence 202
8.4.3 Complexity dependence 203
8.4.4 Segment length dependence 208
8.4.5 Vertex distance dependence 212
8.4.6 Percent vertex distance dependence 216
8.5 CONFIDENCE INTERVALS 220
8.5.1 Auto-regressive time series model 220
8.5.2 Moving block bootstrap analysis 231
8.6 TECHNICAL IMPLEMENTATION 236
8.7 CONCLUSION 237
9 CHAPTER 9: DISCUSSION OF RESULTS 239
9.1 INTRODUCTION 239
9.2 ACCURACY APPRAISAL 239
9.3 ACCURACY DEPENDENCIES 241
9.3.1 E-scale 241
9.3.2 Feature type 242
9.3.3 Complexity 246
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9.3.4 Segment length 246
9.3.5 Vertex distance 247
9.3.6 Percent vertex distance 247
9.4 RESEARCH SHORTCOMINGS 249
9.5 FURTHER RESEARCH 251
9.6 CHAPTER SUMMARY 252
10 CHAPTER 10: CONCLUSIONS AND RECOMMENDATIONS 255
REFERENCES 259
A APPENDIX A: RESULTS FORMAT A.1
A.1 “OFFSETS” WORKSHEET A.1
A.2 “OFFSETS VS VERTEX DISTANCE” WORKSHEET A.3
A.3 “OFFSETS VS % VERTEX DISTANCE” WORKSHEET A.5
A.4 “CHORD LENGTH CATEGORIES” WORKSHEET A.7
A.5 “OFFSETS VS COMPLEXITY” WORKSHEET A.9
B APPENDIX B: SUMMARY RESULTS FORMAT B.1
B.1 “ABSOLUTE OFFSET LENGTH AND LEFT/RIGHT BIAS” TABLE B.1
B.2 “VERTEX PROXIMITY” TABLE B.2
B.3 “PERCENT VERTEX PROXIMITY” TABLE B.3
B.4 “CHORD LENGTH CATEGORIES” TABLE B.4
B.5 “COMPLEXITY CATEGORIES” TABLE B.5
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