Carter, John 
  
3.4 Human Walking 
Uncorrected Human Walks Corrected Human Walks 
  
  
I 
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T 
1 
  
  
  
  
  
  
Measured gait angle in degrees 
Measured gait angle in degrees 
  
0. 1.2 3 4 5.6 7 
Walk Phase in radians Walk Phase in radians 
Figure 7 Hip rotation angle, plotted Figure 8 Hip rotation angles, corrected using 
against walking phase. The trajectory Eqn. 2. 
angle is varied from 0 to 40 , in 
descending order on the graph. 
In the second experiment a female subject was videoed walking at different angles to the camera. The average distance 
between the subject and the camera was 4 metres, and the gait trajectory varied from 0° to 40° in 10-degree steps. The 
subject was constrained to walk along an 80cm track, laid out at a specified angle to the camera direction. The camera 
system described above was used, and the walking sequences were recorded on a Panasonic AG-73330-B SVHS video 
recorder. The sequences were digitised with a high-resolution direct-to-disk colour frame grabbing system. These 
experiments took place out-of-doors under bright but diffuse sunlight, against a natural backdrop. Placing two marks on 
each of the subject's legs, one just below the hip and the other just above the knee, facilitated image processing and 
angle determination. The contrasting colour used was easily recognisable in the digitised video data and was manually 
marked in each frame. Again the hip rotation angle was derived and recorded as a function of video frame. In each 
sequence the reference frame was chosen where the subject's leading foot was flat on the ground, and a complete cycle 
was measured. Other work has used the heel strike as reference®’. Heel strike occurs Just before our chosen reference 
point and was not used here, as it was difficult to determine in the range of poses used in this study. Figure 1, shows an 
example frame for a 20° walk. Repeated experiments were performed and, following Cunado’, a 4" order Fourier series 
was fitted to the ensemble data to generate a gait curve. Figure 6 shows gait curves for the different trajectory angles 
studied. Equation (2) was used to correct the gait curve, with result in figure 7. It is clear that in this case the simple 
rotated pendulum model does not correct the gait angle. Close inspection of the uncorrected gait curves, and the raw 
data, indicates that not only must the gait signature be scaled but there is also an offset apparently proportional to the 
trajectory angle. The simple model developed in this section actually assumes that the leg swings in a plane 
perpendicular to the ground. Measurements made on the subject's legs indicate that the lower (knee) and upper (hip) 
marks lie on a plane approximately 18° from the vertical. This has the effect that even when the gait angle is zero, a 
non-zero trajectory angle will cause the apparent gait angle to be non-zero. This is the cause of the D.C. offsets apparent 
in Figure 7. Clearly, if the gait curves are to be invariant then a better correction model must be developed. 
4 A MODEL FOR GAIT ANGLE CORRECTION 
Consider a swinging pendulum, see Figure 2, representing the leg, which is characterised by an angle £, the angle the 
leg makes to the vertical, and an angle q which is the angle the plane defined by the swinging leg makes with the 
direction to the camera, here after known as the trajectory angle. The hip position is at a point H = [x y z[lina3- 
dimensional co-ordinate system also defined in Figure 1. The position of the knee KX is 
K -|Isin(9)*x 1cos(9)*y z[, (3) 
where / is the length of the thigh. The effect of the trajectory angle is analogous to rotation about the vertical. This has 
no effect on the hip position, as this can be assumed to lie on the rotation axis, while the effect on the knee position can 
  
118 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B5. Amsterdam 2000. 
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