as: to obtain a record that will enable the accurate measurement of the position of the centre of rotation of each of the moving body segments and of the time lapse between successive pictures. The following problems and sources of error can be identified in two-dimensional recording of sports movements.
• The three-dimensionality of the position of centres of rotation requires the analysis of movements recorded from one camera to be done with care.
• Any non-coincidence of the plane of motion (the plane of performance) and the plane perpendicular to the optical axis of the camera (the photo-graphic plane) is a source of error if calibration is performed with a simple scaling object in the plane of motion.
• Perspective and parallax errors need attention. Perspective error is the apparent discrepancy in length between two objects of equal length, such as left and right limbs, when one of the limbs is closer to the camera than the other. It occurs for movements away from the photographic plane. The term is also sometimes used to refer to the error in recorded length for a limb or body segment which is at an angle to the photographic plane and therefore appears to be shorter than it really is. Associated with this error is that caused by viewing away from the optical axis, such that, across the plane of motion, the view is not always side-on, as at the positions marked (*) in Figure 5.8(b). This is sometimes referred to as parallax error.
The combined result of these optical errors is that limbs nearer to the camera appear bigger and appear to travel further than those further away. This causes errors in the digitized coordinates.
Figure 5.7 Hip axis to shoulder axis angle (reconstructed view from above).
Recording the movement 177
• Lens distortions, and film distortions such as stretching and imperfect reg-istration, may be a source of error.
• Locations of joint axes of rotation are only estimates, based on the posi-tions of superficial skin markers or identification of anatomical landmarks.
Use of skin markers can both help and hinder the biomechanist, as they move with respect to the underlying bone and to one another. The digitiz-ing of such markers, or estimatdigitiz-ing the positions of axes of rotation with-out their use, is probably the major source of random error (or noise) in recorded joint coordinates. Locating joint axes of rotation is especially difficult when the joint is obscured by other body parts or by clothing.
• The accuracy of the sampling rate is no problem for video, but needs calibrating for cine cameras. Much biomechanical software will require a constant value of the frame rate.
• Other possible sources of error include: the sharpness of the projected image; locating cine film in the camera and projector gates; camera vibra-tion; digitizing errors, related to coordinate digitizer resolution and hu-man digitizer errors; computer round-off errors.
Figure 5.8 Errors from viewing movements away from the photographic plane and optical axis of the camera: (a) side view; (b) as seen from above.
178 Cinematography and video analysis
For three-dimensional analysis, there are other potential error sources, although several of those above are partly or wholly overcome.
• Relating the two-dimensional video or film image coordinates to the three-dimensional movement space (‘real world’ or object) coordinates may be a source of error. Several methods of doing this will be considered below, but they all present problems. Use of an array of calibration points, such as a ‘calibration frame’ (e.g. Figure 5.9), is probably the most common method. Errors within the frame volume can be accurately assessed, while those outside the frame will be greater and more difficult to assess (see Wood and Marshall, 1986). Errors will increase with the ratio of the size of the movement space to that of the image.
• All the calibration points must be clearly visible on the images from both cameras; they must also have three-dimensional coordinates that are known to a good accuracy.
• Placements of cameras must relate to the algorithm chosen for reconstruc-tion of the movement space coordinates. Errors will be caused by devia-tions from these requirements.
In summary, digitized coordinate data will be contaminated with measurement inaccuracies or errors. These will be random (noise), systematic, or both. All obvious systematic errors (such as those caused by Figure 5.9 A typical calibration frame.
Experimental procedures 179 lens distortion and errors in calibration objects) should be identified and
removed, for example by calibration or software corrections. Any remaining sources of systematic error will then be very small or of low frequency and will, therefore, have little effect on velocities and accelerations. The remaining random noise in the displacement data, expressed as relative errors, has been estimated as within 1% for a point in the photographic plane for two-dimensional cinematography and within 2% for a point in the calibration volume for three-dimensional cinematography (Dainty et al., 1987). Random errors must be minimized at source by good experimental procedures. Any remaining noise should be removed, as far as possible, from the digitized data before further data processing. These two aspects will be covered in the next two sections. Also, more consideration needs to be given to the estimation of errors in digitized coordinate data and their effects on derived values (e.g. Payton and Bartlett, 1995).