Master Thesis - Fachbereich Informatik

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4.3. CAMERA CALIBRATION 61 Figure 4.8: Extracted grid corners at subpixel accuracy. The upper right corner is defined as origin O of the world reference frame. The directions of the X and Y axis are also visualized while the Z axis is perpendicular to the chessboard plane in direction to the camera. 20 11 0 20 40 20020 O c Z X c c Y c 0 Extrinsic parameters (camera centered) 50 100 150 15 14 6 312 516 217 4 1079 81 13 Figure 4.9: Reconstructed extrinsic location of each calibration pattern relative to the camera. The working distance of approximately 250mm is detected very well. 200
62 CHAPTER 4. LENGTH MEASUREMENT APPROACH Figure 4.10: Visualization of the resulting radial distortion model. The computed center of distortion indicated by the ‘◦’ is slightly displaced from the optical center (‘×’). The image area of interest considered in this application lies in between the red lines. Perspective Warping One possibility to compute a synthetic fronto-orthogonal view of an image is based on the extrinsic relationship of the camera plane and a particular world plane (e.g. conveyor plane) that can be extracted in a calibration step. With the extrinsic parameters it is possible to describe the position and orientation of the world plane in the camera reference frame. Finally, one can compute a transformation that maps the world plane into a plane parallel to the image plane or vice versa, and warp the image to a synthetic fronto-orthogonal view. This approach has a significant drawback. First of all, the accuracy of the results is closely related to the calibration accuracy. Furthermore, the extrinsic parameters of a camera change if the camera is moved even slightly compared to the intrinsic parameters that can be assumed constant as long as the focus is not changed. Thus, one has to recalibrate the extrinsic parameters as well as the transformation parameters every time the camera is moved, which seemed to be not practicable in this particular application. There are other methods that can be used to compute a fronto-orthogonal view of an perspective image, which are based on characteristic image features such as parallel or orthogonal lines, angles, or point correspondences and do not need any knowledge on the interior or exterior camera parameters [30]. One common approach is based on point correspondences of at least 4 points xi and x ′ i with x′ i = Hxi (1 ≤ i ≤ 4) and ⎡ H = ⎣ h1 h2 h3 h4 h5 h6 h7 h8 h9 ⎤ ⎦ (4.2) the projective transformation matrix representing the 2D homography. The unknown parameters of H can be computed in terms of the vector cross product x ′ i × Hxi = 0 using a Direct Linear Transformation (DLT) [30]. To correct the perspective of an image one has to find four points in the image that lie on the corners of a rectangle in the real world, but are perspectively distorted in the image. These points xi have to be mapped to points x ′ i that represent the corners of a rectangle in the image. Then, after H
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Fachbereich Informatik Department o
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Acknowledgments First of all, I wou
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Contents Acknowledgments iii Abstra
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Contents ix 5.3.7. TubeLength .....
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List of Tables 1.1. Rangeoftubetype
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List of Figures 2.1. AccuracyandPre
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1. Introduction Heat shrinkable tub
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1.2. PROBLEM STATEMENT 3 hazards, r
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1.4. RELATED WORK 5 Length [mm] Tol
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1.5. THESIS OUTLINE 7 The vision pa
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2. Technical Background 2.1. Visual
Page 26 and 27: 2.1. VISUAL MEASUREMENTS 11 (a) Fig
Page 28 and 29: 2.1. VISUAL MEASUREMENTS 13 Figure
Page 30 and 31: 2.1. VISUAL MEASUREMENTS 15 � xd
Page 32 and 33: 2.2. ILLUMINATION 17 tubes alternat
Page 34 and 35: 2.2. ILLUMINATION 19 effect of comp
Page 36 and 37: 2.3. EDGE DETECTION 21 i 2 i 1 0 (a
Page 38 and 39: 2.3. EDGE DETECTION 23 N × 1 kerne
Page 40 and 41: 2.3. EDGE DETECTION 25 These operat
Page 42 and 43: 2.3. EDGE DETECTION 27 (a) 0 ◦ (b
Page 44 and 45: 2.4. TEMPLATE MATCHING 29 accuracy
Page 46 and 47: 3. Hardware Configuration This chap
Page 48 and 49: 3.2. CAMERA SETUP 33 3.2. Camera se
Page 50 and 51: 3.2. CAMERA SETUP 35 eachcolorchann
Page 52 and 53: 3.2. CAMERA SETUP 37 Figure 3.4: Co
Page 54 and 55: 3.2. CAMERA SETUP 39 adjusting scre
Page 56 and 57: 3.2. CAMERA SETUP 41 further distan
Page 58 and 59: 3.3. ILLUMINATION 43 f V 12mm 129mm
Page 60 and 61: 3.3. ILLUMINATION 45 (a) (b) (c) Fi
Page 62 and 63: 3.3. ILLUMINATION 47 (a) (b) Figure
Page 64 and 65: 3.4. BLOW OUT MECHANISM 49 A light
Page 66 and 67: 4. Length Measurement Approach Whil
Page 68 and 69: 4.2. MODEL KNOWLEDGE AND ASSUMPTION
Page 74 and 75: 4.3. CAMERA CALIBRATION 59 4.2.7. B
Page 78 and 79: 4.3. CAMERA CALIBRATION 63 is compu
Page 80 and 81: 4.4. TUBE LOCALIZATION 65 (a) (b) F
Page 82 and 83: 4.4. TUBE LOCALIZATION 67 � 1 Psm
Page 84 and 85: 4.4. TUBE LOCALIZATION 69 Global Th
Page 86 and 87: 4.4. TUBE LOCALIZATION 71 but also
Page 88 and 89: 4.4. TUBE LOCALIZATION 73 Global Re
Page 90 and 91: 4.5. MEASURING POINT DETECTION 75 f
Page 92 and 93: 4.5. MEASURING POINT DETECTION 77 T
Page 94 and 95: 4.5. MEASURING POINT DETECTION 79 -
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Page 100 and 101: 4.5. MEASURING POINT DETECTION 85 (
Page 102 and 103: 4.5. MEASURING POINT DETECTION 87 w
Page 104 and 105: 4.6. MEASURING 89 side of the tube,
Page 106 and 107: 4.6. MEASURING 91 fcor(x) =−(c1x
Page 108 and 109: 4.7. TEACH-IN 93 inthemeasuringplan
Page 110 and 111: 4.7. TEACH-IN 95 The pair of a pixe
Page 112 and 113: 5. Results and Evaluation 5.1. Expe
Page 114 and 115: 5.1. EXPERIMENTAL DESIGN 99 between
Page 116 and 117: 5.1. EXPERIMENTAL DESIGN 101 where
Page 118 and 119: 5.1. EXPERIMENTAL DESIGN 103 Ground
Page 120 and 121: 5.2. TEST SCENARIOS 105 enough, the
Page 122 and 123: 5.3. EXPERIMENTAL RESULTS 107 The t
Page 124 and 125: 5.3. EXPERIMENTAL RESULTS 109 Detec
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5.3. EXPERIMENTAL RESULTS 111 Lengt
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5.3. EXPERIMENTAL RESULTS 113 GTD [
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5.3. EXPERIMENTAL RESULTS 115 gray
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5.3. EXPERIMENTAL RESULTS 119 (a) (
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5.3. EXPERIMENTAL RESULTS 121 (a) (
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5.3. EXPERIMENTAL RESULTS 125 Total
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5.3. EXPERIMENTAL RESULTS 127 Color
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5.3. EXPERIMENTAL RESULTS 129 Task
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5.4. DISCUSSION AND FUTURE WORK 131
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6. Conclusion In this thesis a func
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Appendix 135
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138 APPENDIX A. PROFILE ANALYSIS IM
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140 APPENDIX A. PROFILE ANALYSIS IM
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142 APPENDIX B. HARDWARE COMPONENTS
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144 APPENDIX B. HARDWARE COMPONENTS
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146 Bibliography [18] C. Demant, B.
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148 Bibliography [51] K.K. Pingle.
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Master Thesis - Fachbereich Informatik

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