Clifford E. Tiedemann
Geography Programs
University of Illinois at Chicago
1007 W. Harrison Street
Chicago, IL 60607-7138
312-996-3115; FAX: 312-413-8559; CLIFFT@UIC.EDU

CONTENTS
LIST OF FIGURES, LIST OF TABLES
ACKNOWLEDGEMENTS, ABSTRACT, KEY WORDS
INTRODUCTION
STEP 1: FEATURE DEFINITION
STEP 2: ARRANGEMENT COMPARISON
STEP 3: EVALUATION
PLAUSIBILITY
DISCUSSION
NOTES
REFERENCES
FIGURES & TABLES

LIST OF FIGURES
Figure 1. Comandra richardsiana: 1980 Cover Percentages
Figure 2. Comandra richardsiana: 1981 Cover Percentages
Figure 3. Aster laevis: 1980 Cover Percentages
Figure 4. Ambrosia artemesiifolia: 1980 Cover Percentages
Figure 5. Profiles of Some Simple "Macro-Features"
Figure 6. Two-By-Two Map Comparisons
Figure 7. SSD Computations
Figure 8. Assigning Value/Variation Classes
Figure 9. The Arrangement-Comparison Model
Figure 10. "Micro-Feature" Assignments
Figure 11. Complete Association Analysis...

LIST OF TABLES
Table 1. Local Variation Categories...
Table 2. Agreement Scores for "ALLCAN", 1980 Data
Table 3. Agreement Probabilities: Sequential Comparisons...

ACKNOWLEDGEMENTS
Access to the services and facilities of the Cartographic Laboratory and the Computer Center at the University of Illinois at Chicago are gratefully acknowledged. Similar recognition is accorded Dr. A. Rouffa, Director of the James Woodworth Prairie Preserve, and Mr. S. Apfelbaum, consulting ecologist for the Preserve, for their cooperation and encouragement.

ABSTRACT
A computational model is developed for comparing arrangements of features gleaned from spatial data and applied to data gathered in a small ecological preserve. A key aspect of the procedure is that it implements the presumption of maximum possible similarity between map-feature arrangements identified for pairs of mappings, thereby yielding a distance-measure of pattern agreement. Though quite simple by itself, extensive computation is required to set up necessary conditions and evaluate outcomes. Following arrangement comparisons for all possible pairings of numerous species, a commonly available grouping algorithm is employed to guide selection of image pairs for visual inspection to assess consistencies among agreement statistics. That exercise, incidentally, suggests progress toward recognizing geographic associations among sets of spatial data.

KEY WORDS
IMAGE COMPARISON, HEURISTICS, FEATURE DEFINITION, MONTE CARLO METHODS, SPATIAL ASSOCIATION, COORDINATION ANALYSIS, INTROSPECTIVE MODELING

Under Construction
coming: reproductions of figures 1 through 4, which are referred to below

INTRODUCTION

Consider Figures 1 through 4--each a map of a single, relatively widespread plant species noted during recent cover-percentage surveys of the James Woodworth Prairie Preserve. Visual inspection reveals that species' arrangements displayed on some pairings are quite similar in appearance, while other combinations exhibit considerable dissimilarity. The pairings 1 with 2, 1 with 3, and 2 with 3 are judged to be very similar by the author, at least, but neither Figure 1, 2 nor 3 resembles Figure 4 insofar as data mappings are concerned. These assessments of similarity are based on ad hoc, manual procedures, but all agree with outcomes from a programmed heuristic for comparing arrangements of features identified in mapable data.

The strategy followed in the automated map comparisons involves three major steps, the first and third of which are computationally intensive Monte Carlo procedures, while the second introduces an approach to pattern analysis accommodating operations not inconsistent with manual activity. The first step devises definitions of nominal feature classes from simple numerical data and ascribes them to observation points. The second assesses actual feature coincidences using a model reflecting the expectation of maximum possible agreement between arrangement pairs that produces a polarized comparison statistic. The third step evaluates comparative measures in light of the assumption of only random association between arrangement pairs. After completing numerous three-step arrangement comparisons, grouping algorithms are employed to demonstrate outcome plausibilities.

Stated as probability approximations, the following pairwise assessments hold for these four mappings. The probability of randomly repositioning features extracted from 1981 cover percentages for Comandra richardsiana (see Figure 2) into arrays that agree more closely than their original arrangement with the 1980 pattern of the same species (see Figure 1) is estimated to be less than 0.0005. Like manipulations of features developed for 1980 Comandra richardsiana data imply a comparably high level of agreement between their original pattern and that for Aster laevis cover percentages for the same year (see Figure 3). Conversely, fractions of patterns generated randomly using features obtained from 1980 cover percentages for Comandra richardsiana or Aster laevis that resemble the feature pattern of Ambrosia artemesiifolia (see Figure 4) more closely than their original arrangements exceed ninety-five and ninety-six percent, respectively. The arrangement of features extracted from data displayed in Figure 2 was not compared with that from data portrayed in Figures 3 and 4 because different species and surveys are involved.

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