Master Thesis - Fachbereich Informatik

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2.1. VISUAL MEASUREMENTS 15 � xd yd � � ˜x = L(˜r) ˜y � (2.9) where (˜x, ˜y) T is the undistorted and (xd,yd) the corresponding distorted image position. The function L(˜r) determines the amount of distortion depending on the radial distance ˜r = � ˜x 2 +˜y 2 from the center for radial distortion. The correction of the distortion at a measured position p =(x, y) can be computed as: ˆx = xc + L(r)(x − xc) (2.10) ˆy = yc + L(r)(y − yc) (2.11) where (ˆx, ˆy) T is the undistorted (corrected) position, (xc,yc) T the center of the radial distortion, and r = � (x − xc) 2 +(y − yc) 2 theradialdistancebetweenp and the center of distortion. An arbitrary distortion factor L(r) can be approximated by the following equation [30]: L(r) =1+ m� κir i i (2.12) whichisdefinedforr > 0andL(0) = 1. The distortion coefficients κi as well as the center of radial distortion (xc,yc) T can be seen as additional intrinsic parameters of the camera model. The number of coefficients m depends on the required accuracy and the available computation time. Usually less than the first three or four coefficients are considered. In common calibration procedures such as the calibration method proposed by Tsai [67], only the even coefficients (i.e. κ2, κ4,...) are taken into account while odd coefficients are set to zero. In this case, one or two coefficients are sufficient to compensate for the distortion in most cases [31]. Beside the radial distortion model, there are several other models including tangential, linear, and thin prism distortion [31]. Usually a radial distortion model is combined with a tangential model as proposed in [11, 12]. There are several approaches to compute the unknown intrinsic and extrinsic parameters of a camera. The most common methods are based on known correspondences between real world points and image coordinates. A chessboard-like calibration grid has become quite common as a calibration pattern. The corners of the grid provide a set of coplanar points. The world coordinates can be easily determined if one defines a coordinate system with the X- andY axis lying orthogonal in the chessboard plane and Z = 0 for all points. A corner not to close to the center represents the world origin. Based on these definitions, each corner of the calibration pattern can be described in the form (X, Y, Z) T . Threedimensional calibration rigs composed of orthogonal chessboard-planes are also used quite often. In a captured image of the calibration pattern, the corners can be extracted at pixel (or subpixel) level, and mapped to world coordinates. If there is a sufficient number of correspondences, one can try to solve a homogeneous linear system of equations based on
16 CHAPTER 2. TECHNICAL BACKGROUND the projection matrix M. The solution is also denoted as implicit camera calibration, since the resulting parameters do not have any physical meaning [31]. In the next stage, the intrinsic and extrinsic camera parameters can be extracted from the computed solution of M [21]. There are linear and nonlinear methods to solve for the projection matrix. Linear methods assume an ideal pinhole camera and ignore distortion effects. Thus, these methods can be solved in closed-form. Abdel-Aziz and Karara [1] introduced a direct linear transform (DLT) to compute the parameters in a noniterative algorithm. If higher accuracy is needed, nonlinear optimization techniques have been investigated to accomplish for distortion models. Usually, the parameters are estimated by minimizing the pixel error between a measured point correspondence and the reprojected position of the world point using the projection matrix in least-square sense. This is an iterative process that may end up with a bad solution unless a good initial guess is available [70]. Therefore, linear and nonlinear methods are combined as the DLT can be used for initialization of the nonlinear optimization. One well-known two-step calibration method was proposed by Tsai [67, 39] 2.2. Illumination In machine vision applications, the right choice of illumination can simplify the further image processing considerably [16]. It can preprocess the input signal (e.g. enhance contrast or object boundaries, eliminate background, diminish unwanted features etc.) without consuming any computational power. On the other hand, even the best imaging sensor can not compensate for the loss in image quality induced by poor illumination. There are several different approaches of illumination in MV. Depending on the application one has to consider what has to be inspected (e.g. boundaries, surface patterns or color), what are the material properties of the objects to be inspected (e.g. lighting reflection characteristics or translucency) and what are the environmental conditions (e.g. background characteristics, object dimension, camera position or the available space to install light sources). In the following, different types of light sources and lighting setups used in MV are introduced. 2.2.1. Light Sources The light sources commonly used in machine vision include high-frequency fluorescent tubes, halogen lamps, xenon light bulbs, laser diodes and light emitting diodes (LED) [18]. High-frequency fluorescent lights High-frequency fluorescent light sources are widely used in machine vision applications, since they produce a homogeneous, uniform, and very bright illumination. They feature white or ultraviolet light at low development of heat, thus, there is no need for fan cooling. Standard fluorescent light tubes are not suitable for vision applications since they flicker cyclically with the power supply frequency. This yields unwanted changes in intensity or color in the video image, whereas the effect increases, if the capturing rate of the camera is close to the power supply frequency (e.g. 50Hz in Germany). High-frequency fluorescent
Page 1 and 2: Fachbereich Informatik Department o
Page 4: Acknowledgments First of all, I wou
Page 8 and 9: Contents Acknowledgments iii Abstra
Page 10 and 11: Contents ix 5.3.7. TubeLength .....
Page 12 and 13: List of Tables 1.1. Rangeoftubetype
Page 14 and 15: List of Figures 2.1. AccuracyandPre
Page 16 and 17: 1. Introduction Heat shrinkable tub
Page 18 and 19: 1.2. PROBLEM STATEMENT 3 hazards, r
Page 20 and 21: 1.4. RELATED WORK 5 Length [mm] Tol
Page 22 and 23: 1.5. THESIS OUTLINE 7 The vision pa
Page 24 and 25: 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 32 and 33: 2.2. ILLUMINATION 17 tubes alternat
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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
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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
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Page 52 and 53: 3.2. CAMERA SETUP 37 Figure 3.4: Co
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Page 58 and 59: 3.3. ILLUMINATION 43 f V 12mm 129mm
Page 60 and 61: 3.3. ILLUMINATION 45 (a) (b) (c) Fi
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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
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4.4. TUBE LOCALIZATION 65 (a) (b) F
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4.4. TUBE LOCALIZATION 67 � 1 Psm
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4.4. TUBE LOCALIZATION 69 Global Th
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4.4. TUBE LOCALIZATION 71 but also
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4.4. TUBE LOCALIZATION 73 Global Re
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4.5. MEASURING POINT DETECTION 75 f
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4.5. MEASURING POINT DETECTION 77 T
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4.5. MEASURING POINT DETECTION 79 -
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4.5. MEASURING POINT DETECTION 81 0
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4.5. MEASURING POINT DETECTION 83 o
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4.5. MEASURING POINT DETECTION 85 (
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4.5. MEASURING POINT DETECTION 87 w
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4.6. MEASURING 89 side of the tube,
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4.6. MEASURING 91 fcor(x) =−(c1x
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4.7. TEACH-IN 93 inthemeasuringplan
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4.7. TEACH-IN 95 The pair of a pixe
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5. Results and Evaluation 5.1. Expe
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5.1. EXPERIMENTAL DESIGN 99 between
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5.1. EXPERIMENTAL DESIGN 101 where
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5.1. EXPERIMENTAL DESIGN 103 Ground
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5.2. TEST SCENARIOS 105 enough, the
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5.3. EXPERIMENTAL RESULTS 107 The t
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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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