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End-To-End Analysis of Hexagonal Vs Rectangular Sampling in Digital Imaging Systems

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End-To-End Analysis of Hexagonal Vs Rectangular Sampling in Digital Imaging Systems W&M ScholarWorks Dissertations, Theses, and Masters Projects Theses, Dissertations, & Master Projects 1993 End-to-end analysis of hexagonal vs rectangular sampling in digital imaging systems John Clifton Burton II College of William & Mary - Arts & Sciences Follow this and additional works at: https://scholarworks.wm.edu/etd Part of the Computer Sciences Commons Recommended Citation Burton, John Clifton II, "End-to-end analysis of hexagonal vs rectangular sampling in digital imaging systems" (1993). Dissertations, Theses, and Masters Projects. Paper 1539623834. https://dx.doi.org/doi:10.21220/s2-19ge-rt36 This Dissertation is brought to you for free and open access by the Theses, Dissertations, & Master Projects at W&M ScholarWorks. It has been accepted for inclusion in Dissertations, Theses, and Masters Projects by an authorized administrator of W&M ScholarWorks. For more information, please contact [email protected]. INFORMATION TO USERS This manuscript has been reproduced from the microfilm master. UMI films the text directly from the original or copy submitted. Thus, some thesis and dissertation copies are in typewriter face, while others may be from any type of computer printer. The q u a li t y of this reproduction Is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleedthrough, substandard margins, and improper alignment can adversely afreet reproduction. In the unlikely event that the author did not send UMI a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion. Oversize materials (e.g., maps, drawings, charts) are reproduced by sectioning the original, beginning at the upper left-hand corner and continuing from left to right in equal sections with small overlaps. Each original is also photographed in one exposure and is included in reduced form at the back of the book. Photographs included in the original manuscript have been reproduced xerographically in this copy. Higher quality 6" x 9" black and white photographic prints are available for any photographs or illustrations appearing in this copy for an additional charge. Contact UMI directly to order. University Microfilms International A Bell & Howell Information Com pany 300 North Z eeb Road. Ann Arbor, Ml 48106-1346 USA 313/761-4700 800/521-0600 Order Number 9403277 End-to-end analysis of hexagonal vs. rectangular sampling in digital imaging systems Burton, John Clifton, II, Ph.D. The College of William and Mary, 1993 Copyright ©1994 by Burton, John Clifton, IT. All rights reserved. UMI 300 N. Zeeb Rd. Ann Arbor, MI 48106 END-TO-END ANALYSIS OF HEXAGONAL VS. RECTANGULAR SAMPLING IN DIGITAL IMAGING SYSTEMS A DISSERTATION PRESENTED TO THE FACULTY OF THE DEPARTMENT OF COMPUTER SCIENCE THE COLLEGE OF WILLIAM AND MARY IN VIRGINIA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY By John C. Burton II April 1993 APPROVAL SHEET This dissertation, is submitted in partial fulfillment of the requirements of the degree of Doctor of Philosophy John C. Burton II, Author Approved, April 1993 Keith W. Miller, Dissertation Director Stephen K. Park ^Aa a c l v William L. Bynum Richard H. Prosl CXS SZfstA./ John H. Drew D edication This dissertation is dedicated to the memory of my father, John Burton, whose thirst for knowledge and curiosity about the world around him left a lasting impression on me. C ontents 1 Introduction 2 l.X Background ................................................................................................. 3 1.2 Hexagonal Sampling .............................................................................................. 4 1.3 Rectangular Sampling ........................................................................................... 5 1.4 C om parisons .................................. ........................................................................ 6 1.5 Chapter Description ................................................................................. 7 References ................................................................................................. 8 2 T h e Im aging S ystem M odel 11 2.1 Scene ............................................... 12 2.1.1 Synthetic Scenes .................................. 14 2.1.2 Digital Scenes ........................................................ 15 2.1.3 Comparison of Synthetic and Digital Scenes .......................................... 16 2.2 Image F orm ation ..................................................................................................... 17 2.3 S a m p lin g .................................................................................................................. 22 2.3.1 Arbitrary Sampling Geometries ............................................................... 23 2.4 Reconstruction . .................................................................................................. 26 2.4.1 Ideal Reconstruction Function ............................................................... 27 2.4.2 Display Reconstruction Function ............................... 27 2.5 Summary ...................... 28 References ................................................................................................ 32 3 Fidelity Loss Metrics 34 3.1 Imaging fidelity l o s s ............................................................................................... 35 3.2 Sample/scene phase averaging ............................................................................... 36 3.3 Sampling/reconstruction fidelity lo s s ................................................ 37 3.4 End-to-End Fidelity L o s s ..................................................................................... 39 3.5 Fidelity Loss Budget ............................................................................................... 40 3.6 Application to Periodic Scenes .................................................................... 41 References ............................ 43 iv 4 Experimental Results - Band-limited Scenes 44 4.1 Implementation D e ta il s ........................................................................................ 44 4.2 Experimental Design .............................................................................................. 44 4.2.1 Synthetic Band-limited Scene .................................................................. 45 4.2.2 Image Formation ............................................................................. 46 4.2.3 S a m p lin g .................................................................................................... 48 4.2.4 Reconstruction Function ................................................................. 49 4.3 Fidelity Loss Results ........................................................ 51 4.3.1 Imaging Fidelity L o s s .............................................................................. 51 4.3.2 Sampling and Reconstruction Fidelity L o ss ......................................... 52 4.3.3 End-to-End Fidelity L o ss .............................................. 58 References .................................. .......................................................................... ... 62 5 Experimental Results - Digital Scenes 63 5.1 Experimental Design ............................................................................................... 63 5.1.1 Digital Scenes .............................................................................................. 63 5.1.2 Image Formation ........................................................................................ 66 5.2 Fidelity Loss Results ........................................................................ 69 5.2.1 Imaging Fidelity L o s s .............................................................................. 69 5.2.2 Sampling and Reconstruction Fidelity L o ss ......................................... 78 5.2.3 End-to-End Fidelity L oss ........................................................................ 92 5.2.4 Reconstructed Im ages .............................................................................. 102 References .......................................................................................................................... 119 6 Summary and Conclusions 120 6.1 Summary of Results .............................................................................................. 121 6.2 Conclusions ............................................ 122 6.3 Future Efforts ................................................................................................. 122 References ......................................................................................................... 131 Bibliography 132 v Acknowledgments I am grateful to Professor Keith W. Miller for guiding me through the process of this research, and to Professor Stephen K. Park for providing valuable insights into this field. Portions of this work were supported by NASA Graduate Researcher Fellowship Grant NGT-50111 at the NASA Langley Research Center. I am indebted to my wife, Mala T. Conrad for her understanding and patience, and to my daughter Jordan for helping to keep my life in perspective. List of Tables 6.1 Range of Fidelity Loss Values List of Figures 1.1 Fourier Domain Representation of Sampling G rid s ....................................... 5 2.1 Typical Digital
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