I I 71-18,006 GARDNER, Steyen Ray, 194-2- A GENERALIZED TEMPLATE MATCHING ALGORITHM FOR PICTORIAL PATTERN RECOGNITION. The Ohio State University, Ph.D., 1970 Computer Science University Microfilms, A XEROX Company , Ann Arbor, Michigan . THIS DISSERTATION HAS BEEN MICROFILMED EXACTLY AS RECEIVED A GENERALIZED TEMPLATE MATCHING ALGORITHM FOR PICTORIAL PATTERN RECOGNITION DISSERTATION Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Steven Ray Gardner, B.E.E., M.S.E.E, ^ * * * * The Ohio State University 1970 Adviser Department of Electrical Engineering PLEASE NOTE: Some pages have small and indistinct type. Filmed as received. University Microfilms A GENERALIZED TEMPLATE MATCHING * ALGORITHM FOR PICTORIAL PATTERN RECOGNITION By Steven Ray Gardner, Ph.D. The Ohio State University, 1970 Professor H, Hemami, Adviser The research undertaken in this dissertation is con­ cerned with the following problem. Given a two-dimensional image of an unknown object, it is desired to develop an algorithm for a digital computer which will determine the class to which the image belongs as well as its size, translation and rotation in the field of view with respect to some coordinate system. The major portion of the research is concerned with the estimation of the size, translation and rotation parameters associated with the image, while the classification problem is only a minor objective. The algorithm which is developed uses the coordinates of a set of discrete points on the boundary of the image for both estimation and classification. The data acquisition system is simulated for testing the algorithm since it is 1 2 not vital in the development of the algorithm. The images which are presented to the algorithm include ellipses, rectangles, convex.crescents, and concave crescents. These images were chosen from a practical viewpoint (physical objects possess these images) and from a theoretical viewpoint (the images are not representable by an analytical equation except for the ellipse). The algorithm which is developed solves the stated problem in the following manner. First of all, a template for each of the four patterns is generated by the computer and stored; that is to say, if the computer is given a set of parameters it can produce the corre­ sponding template for each pattern. The algorithm next fits each stored template to the data points of the incoming image, automatically adjusting the parameters in such a manner that an appropriate error function is minimized. The parameters are adjusted by making use of nonlinear regression analysis. After each of the templates has been fitted to the data points, the template is chosen which yields the smallest least squares fit. ‘A total of three different error functions are investigated in this research, one of which is found to give very good recognition capabilities (good parameter estimates), even in the presence of moderate levels of noise. The estimates for the rotation parameter are especially good, a quality not common to many pattern recognition systems. \ ACKNOWLEDGEMENTS The author gratefully acknowledges the encouragement, advice, and guidance provided to him throughout the course of this research by his adviser, Professor H. Hemami. Professors R, B. McGhee and K. J. Breeding are also to be thanked for their many helpful suggestions and for serving as readers of this manuscript. This research was supported in part by the National Aeronautics and Space Administration under Grant No. NGR-36-008-076 and in part by the United States Air Force Office of Scientific Research under Grant No, AFOSR-70-1901. The experimental results reported in the work were obtained on the IBM 360/75 Computer located at the Instructional and Research Computer Center, The Ohio State University. The author would like to take this opportunity to thank his wife, Karen, for her patience and understanding during the course of his graduate studies. He is especially indebted to her for typing this manuscript. ii VITA September 15, 1942 . Born - Columbus, Ohio 1965 B.E.E., The Ohio State University, Columbus, Ohio 1966 M.Sc,, Electrical Engineering, The Ohio State University, Columbus, Ohio 1968 Teaching Associate, Mathematics Department, The Ohio State University, Columbus, Ohio 1969 - 1970 Research Associate, The Ohio State University Research Foundation, Communications and Control Systems Laboratory, Department of Electrical Engineering, Columbus, Ohio FIELDS OF STUDY Major Fields Electrical Engineering Studies in Control Systems: Professors H, Hemami, F. C. Weimer, and J. Bacon Studies in Network Synthesis and Communication Theory: Professors W, C. Davis and C. E. Warren Studies in Coding Theory: Professor R. Lackey Studies in Physics: Professor W. H. Shaffer Studies in Mathematics: Professor S, Drobot iii f TABLE OF CONTENTS Page ACKNOWLEDGMENTS ii VITA iii LIST OF TABLES Vi LIST OF FIGURES viii LIST OF PLATES X Chapter I. INTRODUCTION 1 1*1 Formulation of the Problem 1 1.2 Organization 6 II. SURVEY OF PATTERN RECOGNITION 8 2.1 Introduction 8 2.2 The Pattern Recognition Process 9 2.3 Related Pattern Recognition Techniques 21 2.4 Summary 22 III. NONLINEAR REGRESSION ANALYSIS 24 3.1 Introduction 24 - 3.2 Representation of the Ellipse Pattern 24 3.3 Parameter Estimation Problem 33 3.4 Summary 50 IV. RECOGNITION OF ELLIPSES 51 4.1 Introduction 51 4.2 Statement of Problem 52 4.3 Implementation of the Parameter Estimation Schemes 54 4.4 Results 59 4.5 Fitting an Ellipse Template to Ellipse Data Points 63 4.6 Implementation of the Ellipse Template 69 4.7 Summary 69 Page V. RECOGNITION OF RECTANGLES 83 5.1 Introduction 83 5*2 Fitting an Ellipse to a Rectangle 84 5.3 Parameter Estimation for Noise-Free Rectangular Patterns 86 5.4 Parameter Estimation for Noisy Rectangular Patterns 92 5.5 Fitting a Rectangle Template to Rectangle Data Points 96 5.6 Implementation of the Rectangle Template 103 5.7 Summary 103 VI. RECOGNITION OF CRESCENTS 122 6.1 Introduction 122 6.2 Recognition of Convex Crescents 123 6.3 Recognition of Concave Crescents 129 6.4 Implementation of the Crescent Templates 135 6.5 Summary 136 VII. CONCLUSIONS, SUMMARY OF RESULTS, AND EXTENSIONS 140 APPENDIX A. Generation of Data Points 149 B. Discussion of Criterion Functions 158 C. Parameter Estimation Using First and Second Moments 163 D. Regression Matrix for Template Matching Algorithm 172 E. Computer Program 183 BIBLIOGRAPHY 215 v LIST OF TABLES Table Page 1. Ellipse Parameter Estimates Obtained by the One Step Minimization Method 74 2. Ellipse Parameter Estimates Obtained by the Iterative Minimization Scheme 75 3. Ellipse Parameter Estimates Obtained by the Template Matching Method 76 4. Parameters of Ellipses Fitted to Rectangles by the One Step Minimization Method (8 Data Points) 107 5. Parameters of Ellipses Fitted to Rectangles by the One Step Minimization Method (20 Data Points) 108 6* Parameters of Ellipses Fitted to Rectangles by the One Step Minimization Method (48 Data Points) 109 1* Parameters of Ellipses Fitted to Rectangles by the One Step Minimization Method (100 Data Points) 110 8, Parameters of Ellipses Fitted to Rectangles by the Iterative Minimization Method (8 Data Points) 111 9. Parameters of Ellipses Fitted to Rectangles by the Iterative Minimization Method (20 Data Points) 112 10* Parameters of Ellipses Fitted to Rectangles •by the Iterative Minimization Method (48 Data Points) 113 vi Table Page 11. Parameters of Ellipses Pitted to Rectangles by the Iterative Minimization Method (100 Data Points) 114 12. Rectangle Parameter Estimates Obtained by the Template Matching Method 115 13. Convex Crescent Parameter Estimates Obtained by the Template Matching Method 138 14. Concave Crescent Parameter Estimates Obtained by the Template Matching Method 139 15. Values for the Sum-Squared Error Criterion Function Obtained by Matching Each Template to an Ellipse Image (48 Data Points) 145 16. Values for the Sum-Squared Error Criterion Function Obtained by Matching Each Template to a Rectangle Image (48 Data Points) 146 17. Values for the Sum-Squared Error Criterion Function Obtained by Matching Each Template to a Convex Crescent Image (48 Data Points) 147 18. Values for the Sum-Squared Error Criterion Function Obtained by Matching Each Template to a Concave Crescent Image (48 Data Points) 148 19. Comparison of Sum-Squared Error Criterion Functions Associated with the One Step Minimization Method and the Iterative Minimization Scheme 162 vii LIST OF FIGURES Figure Page 1. Components of a Pattern Recognition System 10 2. Example of an Ellipse 26 3. Example of a Rotated and Translated Ellipse 26 4. Relation of 6 and p 26 5. Parameters of a Rotated and Translated Ellipse 53 6. Determination of Ellipse Model Point Associated with a Given Data Point 64 7. Parameters of a Rotated and Translated Rectangle 85 8. Determination of Rectangle Model Point Associated with a Given Data Point 97 9* Example of a Convex Crescent 124 10, Determination of Convex Crescent Model Point Associated with a Given Data Point 124 11, Example of a Concave Crescent 130 12, Determination of Concave Crescent Model Point Associated with a Given Data Point 130 13, Example of an Ellipse 151 14, Data Points Associated with an Ellipse Having No Rotation or Translation 151 15, Data PojLnts Associated with a Rotated and Translated Ellipse 151 16, Example! of a Rectangle 154 * % viii Figure Page 17. Example of a Concave Crescent 154 IB. Example of a Convex Crescent 154 19. Principal Axes for an Ellipse 168 20. Principal Axes for a Rectangle 168 21. Principal Axes for a Concave Crescent 170 22. Principal Axes for a Convex Crescent 170 LIST OF PLATES Plate Page I. Ellipses Fitted to Data Points by the Iterative Minimization Method (a = 0.0) 77 II. Ellipses Fitted to Data Points by the Iterative Minimization Method (a = 0.1) 78 III.