A Probabilistic Approach to Geometric Hashing using Line Features

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CHAPTER 3. NOISE IN THE HOUGH TRANSFORM 35 image-8: ***************.********.****..***.*.****.*.*.....*..*................ image-9: ***********.**********.****..*.**...*.*..****.**.*..*...*..*...**..... ç ç = 1.938883 èdegreeè or 0.033840 èradianè; ç r = 2.519878 èpixelè; ç çr = -0.357589 èdegree.pixelè or -0.006241 èradian.pixelè. æ case 5: 20è negative noise, along with no positive noise image-0: ***********************************************.***................... image-1: ********************************.***..******.**.*.*....**........*...* image-2: ****************************************.***********.*..*.*....*...... image-3: ********************************.******.*.***..*.....**.*...*.*.*...*. image-4: *********************.****.**.*****.**.******.**.*...........**...*... image-5: ********************************************..*.....*.**.....*........ image-6: **********************************************************.*..*....... image-7: ************************************.***************.*.*.*..*......*.. image-8: **********************************************.*.......*........*..... image-9: ******************.*.******.********.*.*..*******.***.**.*.*.*..*.*... ç ç = 1.563745 èdegreeè or 0.027293 èradianè; ç r = 1.913004 èpixelè; ç çr = 0.219434 èdegree.pixelè or 0.003830 èradian.pixelè. æ case 6: 20è negative noise, along with 200 pieces of random dot noise and 200 pieces of segment noise image-0: *************.****************.*..**.*.*.*.*..*......................* image-1: ******************************.*..***...**..**.*...........*.....*..*. image-2: ****************************.*****.*.**.**.......**.....****.*........ image-3: **************************************.**.***.***.....*.......*...*... image-4: *******************.****.***..**.***...***..........................*. image-5: ***********************************.*.**.***..*....................*.. image-6: **********************.***************..***...**.*..*...**.....*.*.*.* image-7: ******************************.****..***...****.*..*...*..*..*.*...... image-8: *********************************.**..*.**.***.*..........*........... image-9: ***********.*****.*.******.**.*****...*...***......*......*..*.*.**.*. ç ç = 1.754688 èdegreeè or 0.030625 èradianè; ç r = 2.144938 èpixelè; ç çr = 0.349338 èdegree.pixelè or 0.006097 èradian.pixelè. æ case 7: 20è negative noise, along with 400 pieces of random dot noise and 400 pieces of segment noise image-0: *********.*****************.*.***.*...*.......*...*............*....*. image-1: **********************.*.**..**.*****..*.*.*****...................... image-2: *******************.**.*****..*...*.**.*....*..**..................... image-3: ***************************.**.*.**......*.........**...*........*.... image-4: ******************..**..*..**..*****..**...*.*............*.*......... image-5: *****************.************.**.*........***.*............*........* image-6: **********************..*******.*********.......*.**....*.***..*..*... image-7: ****************************.*.*.***.*.***..........**.*.*....*.**.... image-8: *********************..*******.*.*****.*..*..**...*..*.......*..*..... image-9: ***************..*.**.*.*.***.**.**..****....*.*.*........*...*.*..... ç ç = 1.880869 èdegreeè or 0.032827 èradianè; ç r = 2.397261 èpixelè; ç çr = -0.113044 èdegree.pixelè or -0.001973 èradian.pixelè. æ case 8: 20è negative noise, along with 800 pieces of random dot noise and 800 pieces
CHAPTER 3. NOISE IN THE HOUGH TRANSFORM 36 of segment noise image-0: ***********.****.******...*.****..*.....*.*...........**......*..*.... image-1: ***..**.***.**.**.***.**..*.*.*.*.**...*.*.*.....*.................... image-2: ******.*.****.**.**........***....**.....*........**.**.....*......... image-3: **********.****.*..*****..*.*.*..**..*.*........*.*...............*..* image-4: *************.*.*.*.......*.*..*.....*.........*..***...*.*.........** image-5: ********.**********.*****...*...*....*.*........*..**...........**.*.* image-6: ****************...*.*********...*....*.**...*....*.......*.*.....***. image-7: *************.***.***.*..*.*.***.**.**.***.*...*.........*.**.......*. image-8: ******.******....*.*****..*.....*.*.*.*...*.*.....*....*.............* image-9: ********..*******..**..*....**.**.*******...*.....*......*.....**..... ç ç = 2.168774 èdegreeè or 0.037852 èradianè; ç r = 2.503542 èpixelè; ç çr = -0.396545 èdegree.pixelè or -0.006921 èradian.pixelè. 3.4 Some Additional Observations Concerning the Accuracy of Hough Data For the case when there is no noise imposed, we can see that true lines dominate the front of the list èthose with high votesè and spurious lines are at the rear of the list. Note that some of the true lines are detected multiply. This can happen when a line is slanting, because its edgels become dispersed in ladder fashion, and two parallel lines are often detected. Negative noise is more devastating <strong>to</strong> the Hough transform than positive noise. Positive noise, unless very intense, does not make true lines disappear; Negative noise subtracts signals and can seriously aæect the accuracy of the line parameters detected. This is especially true of short lines with a small slope. For example, given negative noise the edge map can turn in<strong>to</strong> something like or
Page 1 and 2: A Probabilistic Approach to Geometr
Page 3 and 4: Dedication This dissertation is ded
Page 5 and 6: Abstract One of the most important
Page 7 and 8: 2.2.1 A Brief Description : : : : :
Page 9 and 10: List of Figures 3.1 A comparison of
Page 11 and 12: CHAPTER 1. INTRODUCTION 2 1.1 Model
Page 13 and 14: CHAPTER 1. INTRODUCTION 4 texture a
Page 15 and 16: CHAPTER 1. INTRODUCTION 6 reconstru
Page 17 and 18: CHAPTER 1. INTRODUCTION 8 Both synt
Page 19 and 20: CHAPTER 2. PRIOR AND RELATED WORK 1
Page 33 and 34: CHAPTER 3. NOISE IN THE HOUGH TRANS
Page 43: CHAPTER 3. NOISE IN THE HOUGH TRANS
Page 49 and 50: CHAPTER 4. INVARIANT MATCHING USING
Page 69 and 70: Chapter 5 The Eæect of Noise on th
Page 71 and 72: CHAPTER 5. THE EFFECT OF NOISE ON T
Page 83 and 84: Chapter 6 Bayesian Line Invariant M
Page 85 and 86: CHAPTER 6. BAYESIAN LINE INVARIANT
Page 87 and 88: CHAPTER 6. BAYESIAN LINE INVARIANT
Page 89 and 90: Chapter 7 The Experiments In this c
Page 91 and 92: CHAPTER 7. THE EXPERIMENTS 82 j det
Page 93 and 94: CHAPTER 7. THE EXPERIMENTS 84 Speci
Page 95 and 96:
CHAPTER 7. THE EXPERIMENTS 86 Figur
Page 97 and 98:
CHAPTER 7. THE EXPERIMENTS 88 èaè
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CHAPTER 7. THE EXPERIMENTS 90 èaè
Page 101 and 102:
CHAPTER 7. THE EXPERIMENTS 92 èeè
Page 103 and 104:
CHAPTER 7. THE EXPERIMENTS 94 of li
Page 105 and 106:
CHAPTER 8. CONCLUSIONS 96 We have a
Page 107 and 108:
Appendix A Given a correspondence b
Page 109 and 110:
Appendix B The components of the ma
Page 111 and 112:
Bibliography ë1ë A. Aho, J. Hopcr
Page 113 and 114:
BIBLIOGRAPHY 104 ë23ë W. E. L. Gr
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BIBLIOGRAPHY 106 ë47ë I. Rigoutso
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A Probabilistic Approach to Geometric Hashing using Line Features

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