Master Thesis - Fachbereich Informatik

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2.3. EDGE DETECTION 23 N × 1 kernel. This increases the performance significantly for large images and N. More information about convolution and filter separation can be found for example in [64]. The general procedure of edge enhancement in common derivative-based edge detectors can be summarized into two steps: 1. Smoothing of the image by convolving with a smoothing function 2. Differentiation of the smoothed image Mathematically, this can be expressed as follows (here with respect to x): Iedge(x, y) = K∂/∂x ∗ (S ∗ I(x, y)) (2.18) = (K∂/∂x ∗ S) ∗ I(x, y) = ∂S ∗ I(x, y) ∂x where K∂/∂x indicates the filter kernel approximating the partial derivative with respect to x. S represents the kernel of the smoothing function. Again, the associativity of the convolution can be used to optimize processing. Thus, instead of first smoothing the image with kernel S and then calculating the partial derivative, it is possible to reduce the problem to a single convolution with the partial derivative of the smoothing kernel ∂S ∂x . Hence, the first-order derivative of a Gaussian is suited as an edge detector which is less sensitive to noise compared to finite difference filters [24]. The response of the edge detector can be parametrized by the standard deviation of the Gaussian to control the scale of detected edges, i.e. the level of detail. A larger σ suppresses high-frequency edges for example. 2.3.3. Common Edge Detectors Due to the large number of approaches in this section only a selection of common edge detectors can be presented. Figure 2.7 visualizes the edge responses of different edge detectors that will be introduced in the following in more detail. Sobel Edge Detector A very early edge detector that is still used quite often in the present is the Sobel operator. It was first described in [51] and attributed to Sobel. It is the smallest difference filter with odd number of coefficients that averages the image in the direction perpendicular to the differentiation [36]. The corresponding filter kernel for x and y are: ⎡ SOBELX = ⎣ ⎡ SOBELY = ⎣ 1 0 −1 2 0 −2 1 0 −1 ⎤ 1 2 1 0 0 0 −1 −2 −1 ⎦ (2.19) ⎤ ⎦ (2.20)
24 CHAPTER 2. TECHNICAL BACKGROUND (a) (b) (c) (d) Figure 2.7: Comparison of different edge detectors. (a) Common LENA test image. (b) Gradient magnitude based on Sobel operator. (c) Edges enhanced via the discrete Laplace operator. (d) Result of Canny edge detector (Hyteresis thresholds: 150, 100).
Page 1 and 2: Fachbereich Informatik Department o
Page 4: Acknowledgments First of all, I wou
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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
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Page 44 and 45: 2.4. TEMPLATE MATCHING 29 accuracy
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Page 68 and 69: 4.2. MODEL KNOWLEDGE AND ASSUMPTION
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Page 76 and 77: 4.3. CAMERA CALIBRATION 61 Figure 4
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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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