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Chapter 3: Data Collection and Modeling 31and θ are the skew and tilt compensation factors. The s ii matrix takes care of therotation in the three rectangular axes while (x 0 , y 0 , z 0 ) compensates for the translation.wpu1 =wpv0 w p 0010 sinθu ku0 v 001 0cosθku1kv00 f0 0 0 0of00s0 s1s112131sss122232sss132333 0 0 0000000X− x0 Y− y 0 Z− z 0 1(3.5)Equation 3.5 can be simplified into Equation 3.6 with 12 unknown parameters that canbe determined with at least 6 points positioned in the world coordinate systemprojected into the sensor coordinates.wpua =wpva w p a112131aaa122232aaa132333aaa142434X Y Z 1(3.6)After calibration we know the equation for all rays hitting the sensor plane. However,we still do not know from which point along the ray that it started. To find out whereour sheet-of-light rays start we introduce a simple calibration step (Figure 3.3 (b))using the sheet-of-light to calibrate a single profile. By finding the sensor positionswhere the light sheet hits the calibration target we can compute the world coordinatesfor the laser plane. Thus, calibration gives us the rays for each sensor coordinate, andthe laser plane equation, using which we can find the world coordinates for each point.This process of calibration can be better understood with the help of Figure 3.3. Figure3.3(a) is the status of the CCD when it is viewing the laser line (white line on CCDshown in Figure 3.3(b)). The sensor position is detected with sub pixel accuracy(based on the intensity on the CCD because of the laser line) for the rangemeasurement. We solve for the 12 unknown parameters as a system of linearequations. Theoretically, for the system described in Equation 3.6 we need sixequations to compute the parameters. We increase the reliability and reduce possibleerror by using 40 points on the calibration target. With the 40 real-world coordinatesas in Figure 3.3(c) known we compute a transformation matrix that maps the sensorcoordinates to the real world in 3D. We use this transformation matrix for our futurescans without disturbing the geometry of the scanning mechanism.
Chapter 3: Data Collection and Modeling 32(a)(b)SensorProjectionReal World(c)Figure 3.3: The process of calibration. (a) Single profile calibration. (b) Thephysical calibration target designed to compute the 12 unknown parameters using 40points. (c) The transformation from the sensor projection coordinates to the realworld.
Page 1 and 2: To the Graduate Council:I am submit
Page 3 and 4: Acknowledgementsii“Experience is
Page 5 and 6: Contents1 INTRODUCTION.............
Page 7 and 8: List of TablesviTable 2.1:Qualitati
Page 9 and 10: viiiFigure 5.2: Curvature analysis
Page 11 and 12: Chapter 1: Introduction 21.1 Motiva
Page 13 and 14: Chapter 1: Introduction 41.2 Propos
Page 15 and 16: Chapter 1: Introduction 6We then pe
Page 17 and 18: Chapter 2: Literature Review 8Shape
Page 19 and 20: Chapter 2: Literature Review 102.2.
Page 21 and 22: Chapter 2: Literature Review 12Bimb
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Page 25 and 26: Chapter 2: Literature Review 16foun
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Page 31 and 32: Chapter 2: Literature Review 22Gots
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Page 49 and 50: Chapter 4: Algorithm Overview 404.1
Page 51 and 52: Chapter 4: Algorithm Overview 42Tri
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Page 55 and 56: Chapter 4: Algorithm Overview 46The
Page 57 and 58: Chapter 4: Algorithm Overview 48of
Page 59 and 60: Chapter 4: Algorithm Overview 50∞
Page 61 and 62: Chapter 4: Algorithm Overview 52The
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Chapter 6: Conclusions 82complexity
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Bibliography 84BIBLIOGRAPHY
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Bibliography 86[Biermann, 2001][Bel
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Bibliography 88[Cyr and Kimia, 2001
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Bibliography 90[Gourley, 1998][Gosh
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Bibliography 92[Joshi and Chang, 19
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Bibliography 94[Meyer, 2002][Morse,
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Bibliography 96[Safar et al., 2000]
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Bibliography 98parts,” IEEE Trans
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Vita 100VITASreenivas Rangan Sukuma
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