Motion Analysis Methods. Gerald Smith

Transcription

1 Motion Analysis Methods Gerald Smith Measurement Activity: How accurately can the diameter of a golf ball and a koosh ball be measured? Diameter? 1

2 What is the diameter of a golf ball? What errors are involved in making such a measurement? What is the diameter of a koosh ball? What errors are involved in making such a measurement? 2

3 Making measurements requires considerable care in setting up the data collection and calibration, but is also affected by what is being measured... diameter = 4.26 cm or 42.6 mm diameter = 9 cm Report numbers from measurements in a way that allows the reader to understand the uncertainty involved in the measurement. Accuracy and Precision Phidgets Wordpress.com 3

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5 Use number of Significant Figures in your recorded number to reflect the "quality" of the measurement. The last digit recorded is somewhat uncertain. For example, hand timing with a stopwatch: 9.87 seconds. The last digit is uncertain. (3 significant figures, 0.01 second precision) Y Quantifying Images--Requires finding positions in 2 or 3-dimensional space X 5

6 What are the errors that affect a position measurement from an image? Lens and Sensor Distortions Camera Motion and Vibration Perspective Error Random and Systematic Digitizing Errors 6

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8 Precision of Mechanical Measurements: How many decimal places are appropriate? Temporal (having to do with timing of events) Kinematic (position, velocity, acceleration) Kinetic (force, torque, energy, power) Instrumentation for capturing motion at high speed: Still Images plus Video Casio Exilim EX-F1 Video recording at 300 fps with resolution of 512 x 384 pixels Vicon Motion Analysis System with T-20 cameras Motion capture at 500 fps using a sensor with resolution 1600 x 1200 pixels. Infrared not visible light. Computer calculation of 3-Dimensional Positions of Reflective Markers 8

9 (Standard Video) High Speed Video allows visualization of events at much higher resolution in time 9

10 High Speed Video: 30,000 fps Video as a Timing Device: Assume the Time between Pictures is Constant What is the time for one revolution of the pedals? Video Frame Rate: 60 fps Count 40 frames for a full revolution or 1.5 revolutions per second 10

11 30 frames per second How much time is a snap of the fingers? 300 frames per second Playback 1 / 10 th of normal speed 600 frames per second Playback 1 / 20 th of normal speed How much time for a water balloon to collapse? 11

12 How much time for an air balloon to pop? How to determine real life dimensions on an image? 12

13 1 meter 1 meter 1 meter 1 meter If the camera is perpendicular to the plane of motion, the image will be undistorted. Dimensions in horizontal and vertical directions anywhere on the image will be consistent. 1 meter 1 meter 1 meter 1 meter If the camera is not perpendicular to the plane of motion, the image will be distorted. Dimensions in horizontal and vertical directions will not be consistent. 13

14 How to determine real life dimensions on an image? Look at the image pixels and use them like a grid. 40 Pixels ~ 1 meter 13.6 Pixels or about 0.34 meter Find a Scaling Factor from pixels to meters. 1 meter Simple 2-Dimensional Analysis Camera optical axis perpendicular to plane of motion Conversion Factor for converting from image coordinates to real coordinates camera 14

15 Running at 8 mph 3.58 m/s Video Playback at 10% of Real Timing How to perform such video analysis? o r P r e g g o L 15

16 Direct Linear Transformation (DLT) 2-Dimensional DLT: Image Space (u, v) Object Space (x, y) Looking for a solution like this: x = f(u, v) y = g(u, v) 2-Dimensional DLT: Based on Camera Characteristics and Position there must be equations of this form: We want equations that are the inverse of what is available: u = Ax + B v = Ay + C A, B and C are called "camera constants" x = (u - B) A y = (v A- C) 16

17 x = (u - B) A y = (v A- C) Not enough information to solve this system of equations. Add "Control Points" of known position to gain more information. Two Control Points: (x 1, y 1 ) and (x 2, y 2 ) Image coordinates of control points: (u 1, v 1 ) and (u 2, v 2 ) Gives 4 equations and 3 unknowns (A, B and C). Solve using least squares statistical methods. Calibration Phase involves finding camera constants A, B and C. Computation Phase involves using equations with A, B and C along with image measurements to determine Object Space (real) coordinates. x = (u - B) A y = (v A- C) 17

18 Some Human Motion occurs Primarily in the Sagittal Plane and can be analyzed using 2-D Methods Other activities involve considerable rotation and require 3-D analysis methods 18

19 Direct Linear Transformation (DLT) 3-Dimensional DLT: Image Space (u, v) Looking for a solution like this: Object Space (x, y, z) x = f(u, v) y = g(u, v) z = h(u, v) 3-Dimensional DLT: Based on Camera Characteristics and Position there must be equations of this form: u = v = Ax + By + Cz + D Ex + Fy + Gz + 1 Hx + Jy + Kz + L Ex + Fy + Gz + 1 A, B, C, D, E, F, G, H, J, K, L are called "camera constants" 11 camera constants. Must have more information, so introduce control points. How many? 6 control points will give 12 equations. Solve using least squares statistics techniques. 19

20 With Camera Constants known, have two equations but three unknowns (x, y, z). How to solve? u = v = Ax + By + Cz + D Ex + Fy + Gz + 1 Hx + Jy + Kz + L Ex + Fy + Gz + 1 Get more information by introducing a second camera. u 2 = v 2 = A 2 x + B 2 y + C 2 z + D 2 E 2 x + F 2 y + G 2 z + 1 H 2 x + J 2 y + K 2 z + L 2 E 2 x + F 2 y + G 2 z + 1 To find (x, y, z) we have (u, v) coordinates from two camera views. This gives four equations and three unknowns. Solve using least squares techniques. u 1 = v 1 = u 2 = v 2 = A 1 x + B 1 y + C 1 z + D 1 E 1 x + F 1 y + G 1 z + 1 H 1 x + J 1 y + K 1 z + L 1 E 1 x + F 1 y + G 1 z + 1 A 2 x + B 2 y + C 2 z + D 2 E 2 x + F 2 y + G 2 z + 1 H 2 x + J 2 y + K 2 z + L 2 E 2 x + F 2 y + G 2 z

21 Requirements for 3-Dimensional DLT: Calibration Phase involves placing 6 or more control points into field of motion Two or more cameras placed around field of motion Camera images taken synchronously (at the same time) Questions for 3-dimensional DLT: Where should control points be placed for best results? Where should cameras be placed for best results? How large are the errors in such 3-D calculations? Where do the errors come from? 21

22 Engr325 Winter, 2018 Obtaining 3D Position Coordinates DUE: Wednesday, February 14, Start of class. In Monday's lecture and in this week's lab activity you are dealing with two-dimensional motion analysis - obtaining 2D position-time data. Some measurement error sources were discussed in the lecture. You will encounter some of these in carrying out the lab analysis. However, motion rarely involves pure planar, 2D displacements. Three-dimensional motion is more typical of the real world. Your challenge is to devise a methodology for obtaining 3D position coordinates (X, Y, Z) for a single point in space such as illustrated below. Answer the following questions: 1) How could you obtain the position coordinates of a point in the classroom? Be detailed about how you would in fact do the measurements. 2) What instrumentation would you use? 3) How accurate do you think your measurement would be? 4) What systematic errors might be involved? 5) How precise would your measurement be? 6) How much variability would you likely observe with repeated measurements of the same point? To Turn In This page stapled to your solutions which are all to be done in accordance with the School of Engineering guidelines found on the course web page. 22