1 Imaging Techniques for Flow and Motion Measurement Lecture 20 Lichuan Gui University of Mississippi 2011 Stereo High-speed Motion Tracking

2 –Stereo high-speed imaging system in wind tunnel test Stereo High-speed Motion Tracking Test model - length: 7 inches (178 mm) - diameter: 0.7 inches (0.18 mm) High-speed cameras - lenses: 60mm Nikon Micro-Nikkor - 30  view angle difference - frame rate: up to 4000 fps - resolution: 1024X512 pixels Measurement volume - width: 305 mm - height: 152 mm - maximal depth: 104 mm Strobe light - Synchronized with camera

–Stereo system coordinates 3 Physical coordinates: (x, y, z) Image coordinates: (x*, y*) Camera coordinates: (x’, y’, H) Camera view angles: ( ,  ) Stereo High-speed Motion Tracking

–Calibrate stereo system with target shift 1. Image calibration target at z=0 4 Stereo High-speed Motion Tracking

2. Forward shifted target at z s /2 –Calibrate stereo system with target shift 5 Stereo High-speed Motion Tracking

3. Backward shifted target at -z s /2 –Calibrate stereo system with target shift 6 Stereo High-speed Motion Tracking

–Calibrate stereo system with target shift 7 Geometrical relations: Reduced equations for calibration points k=1,2,3, , N : Sum square difference function: Stereo High-speed Motion Tracking

–Calibrate stereo system with target shift 8 Linear equation system to determine H and x’ : Equation to determine y’ : Conditions for achieve a minimal sum square difference: Stereo High-speed Motion Tracking

–Stereo coordinate reconstruction 9 Camera coordinates: (x’ a, y’ a, H a ) for left camera, (x’ b, y’ b, H b ) for right camera Image coordinates: (x a, y a ) for left camera, (x b, y b ) for right camera Reconstructed physical coordinates: (x, y, z) Camera view angle at image frame center (x 0, y 0, z 0 ): Stereo High-speed Motion Tracking

10 –3D motion tracking Tracking variables - model center: (xc, yc, zc) - roll angle:  - pitch angle:  - yaw angle:  Surface marker local coordinates - L: axial coordinate - R: radius coordinate -  : angular coordinate Surface marker coordinates (x, y, z) - image pattern tracking results Geometrical relations - three equations - known variables: (x, y, c, L, R,  ) - unknown variables: (xc, yc, zc, , ,  ) - multiple surface markers required Stereo High-speed Motion Tracking

11 Available data - surface markers (L n, R n,  n ) - tracked position (x n, y n, z n ) - n=1, 2, 3, …,M First step - determine ,  at minimum of D 1 ( ,  ) - y c determined accordingly Second step - determine  at the minimum of D 2 (  ) - x c determined accordingly Third step - determine z c with known variables –Least square approach Stereo High-speed Motion Tracking

12 –Simulated 3D motion (300mmx150mm,  =0-45 ,  =0-20 ,  =0-10  ) - 7-inch revolving surface model, 120 frames - red image from left camera with view angle  =15 ,  =3  - green image for right camera with view angle  =-22.5 ,  =-2  Stereo High-speed Motion Tracking

13 –Tracked surface makers - spherical dots & cross-sections of grid lines - combination of 18 surface markers for 9 test cases Stereo High-speed Motion Tracking

14 –Simulation results - 4-point results agree well with given values - coordinate biases < 0.5 mm - angular biases < 1  Stereo High-speed Motion Tracking

15 –Simulation results - minimum of 3 surface marker required - 4 surface markers sufficient to achieve high accuracy - more markers not help because of add-in noises - discussion limited in high image quality cases Stereo High-speed Motion Tracking

16 –4-point tracking method 1. Distribution of markers “1”, “2”, “3” and “4” - Line “1-3” parallel to model axis - Plane “2-4-c” perpendicular to model axis (“c” on axis, may not be at center) - Point “2” and “4” at the same radius R - Sufficient angular difference between line “c-2” and “c-4” - When line “1-3” not parallel to model axis, plane “1-c-3”  line “2-4” 4-point method less sensitive to image noises than multi-point least square approach Stereo High-speed Motion Tracking

17 –4-point tracking method 2. Pitch and yaw angle determined with line “1-3” that parallel to model axis Stereo High-speed Motion Tracking

18 –4-point tracking method 3. Roll angle and “c” position determined in “2-4-c” plane Define midpoint “m” on line “2-4”: Line “c-m” determined with “c-m”  “1-3” & “c-m”  “2-4”: Length of “m-c”: Model position: Roll angle: Stereo High-speed Motion Tracking

19 –Experimental results - 80mm cylindrical model, 20mm diameter, 2000 fps, 1024x512 pixels - left image from left camera with view angle  =16.0 ,  =-0.3  - right image from right camera with view angle  =-15.3 ,  =-.1  Stereo High-speed Motion Tracking

20 –Experimental results - x-motion: linear, dx/dt = m/s - y-motion: parabolic, dy/dt 2 = m/s 2 - z-motion: linear, dz/dt = 0.16 m/s - roll angle: linear, d  /dt = r/s - pitch angle: linear, d  /dt = r/s - yaw angle: linear, d  /dt = 0.05 r/s Stereo High-speed Motion Tracking

21 –References Lichuan Gui, Nathan E. Murray and John M. Seiner (2010) Tracking an aerodynamic model in a wind tunnel with a stereo high-speed imaging system. The 3rd International Congress on Image and Signal Processing (CISP’10), October 16-18, Yantai, China –Practice with EDPIV Application example #a Homework