Master Thesis - Fachbereich Informatik

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4.5. MEASURING POINT DETECTION 87 where ψmax and ψmin indicate the overall maximum and minimum curvature a template can have. Hence, one has to compute Nψ,total × k templates for each side. This can be done in a preprocessing step to reduce the computational load. During inspection one has to determine which templates have to be checked at a given position defined by the center of the local ROI around a predicted tube edge. For an efficient implementation a look up table (LUT) is used for this task. 4.5.4. Subpixel Accuracy The maximum accuracy of the template based edge localization so far is limited by the discrete pixel grid. The templates are shifted pixelwise within the local ROIs to find the position that reaches the maximum correlation score. Following the assumptions of tubes under perspective (see Section 4.2.3) the measuring is performed between the most outer points of the convex tube edges. The way the templates are defined the template center corresponds always to the most outer point of the generated ridge. This is consistent to template rotation, since the rotation is performed around the template center. In the special case that the template is not curved, the template center is still the valid measuring point. With the knowledge of this point within the template and the position where this template matches best in the underlying image, the position of the measuring point in the image can be easily computed. However, pixel grid resolution is not accurate enough in this application. For example one pixels represents about 0.12mm in the measuring plane ΠM in a typical setup for 50mm tubes. The allowed tolerance for 50mm tubes is ±0.7mm. As a rule of thumb for reliable results, the measuring system should be as accurate as 1/10thofthetolerance, i.e. 0.07mm in this example. To reach that accuracy one has to apply subpixel techniques to overcome the pixel limits. Figure 4.24(a) visualizes the results of the cross-correlation of an image ROI around the right boundary of a transparent tube with the template that yields maximum score. The maximum is located at position Mmax =(19, 5). These coordinates refer directly to the edge position in the image, since the template function is known and therefore the exact location of the template ridge. The real maximum that describes the tube edge location most accurate may lie in between of two grid positions. With respect to the measuring task, the edge has to be detected as accurate as possible. Interpolation methods have been introduced in Section 2.3.4 to overcome the pixel grid limits in edge detection. The same can be applied at this stage to the template matching results. Cubic spline interpolation is used to compute the subpixel maximum within a certain neighborhood around the discrete maximum. Cubic splines approximate a function based on a set of sample points using piecewise third-order polynomials. They have the advantage of being smooth in the first-derivative and continuous in the second derivative, both within an interval and its boundaries [53]. The interpolation is performed only with respect to the x direction, since this is the measuring direction. A subpixel location with respect to y has only a marginal effect on themeasurements.Ideally,themeasuringpointsontheleftandrightsidehavethesame y value. Assuming the real maximum location is displaced by maximal 0.5 pixels at each
88 CHAPTER 4. LENGTH MEASUREMENT APPROACH 0.8 0.6 0.4 0.2 0 -0.2 -0.4 0.8 0.6 0.4 0.2 0 -0.2 -0.4 -0.6 5 4 3 2 1 0 30 -0.6 0 5 10 15 20 25 30 (b) 25 samples cubic spline interpolation maximum 20 (a) 1 0.8 0.6 0.4 0.2 0 -0.2 15 10 5 -0.4 10 10.5 11 11.5 12 12.5 13 13.5 14 14.5 15 (c) 0 samples cubic spline interpolation maximum Figure 4.24: (a) Cross-correlation results of an image patch around the right boundary of a transparent tube and the best scoring template. The maximum is located at position (19, 5). (b) Cubic spline interpolation in a local neighborhood around the maximum. In this case, the interpolated maximum is equal to the discrete position. (c) Matching results of a different image. Here, the interpolated subpixel maximum differs from the discrete maximum and can be found at x =12.2.
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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
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2.1. VISUAL MEASUREMENTS 11 (a) Fig
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2.1. VISUAL MEASUREMENTS 13 Figure
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2.1. VISUAL MEASUREMENTS 15 � xd
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2.2. ILLUMINATION 17 tubes alternat
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2.2. ILLUMINATION 19 effect of comp
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2.3. EDGE DETECTION 21 i 2 i 1 0 (a
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2.3. EDGE DETECTION 23 N × 1 kerne
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2.3. EDGE DETECTION 25 These operat
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2.3. EDGE DETECTION 27 (a) 0 ◦ (b
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2.4. TEMPLATE MATCHING 29 accuracy
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3. Hardware Configuration This chap
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3.2. CAMERA SETUP 33 3.2. Camera se
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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 76 and 77: 4.3. CAMERA CALIBRATION 61 Figure 4
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 -
Page 96 and 97: 4.5. MEASURING POINT DETECTION 81 0
Page 98 and 99: 4.5. MEASURING POINT DETECTION 83 o
Page 100 and 101: 4.5. MEASURING POINT DETECTION 85 (
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
Page 126 and 127: 5.3. EXPERIMENTAL RESULTS 111 Lengt
Page 128 and 129: 5.3. EXPERIMENTAL RESULTS 113 GTD [
Page 130 and 131: 5.3. EXPERIMENTAL RESULTS 115 gray
Page 134 and 135: 5.3. EXPERIMENTAL RESULTS 119 (a) (
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Page 140 and 141: 5.3. EXPERIMENTAL RESULTS 125 Total
Page 142 and 143: 5.3. EXPERIMENTAL RESULTS 127 Color
Page 144 and 145: 5.3. EXPERIMENTAL RESULTS 129 Task
Page 146 and 147: 5.4. DISCUSSION AND FUTURE WORK 131
Page 148 and 149: 6. Conclusion In this thesis a func
Page 150: 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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