Carter, John
Fully Corrected Human Walks
5 A POSE INVARIANT MEASURE
Further consideration of Equation (9) suggests that if tan(£), rather
than the angle £ itself is used as a measure (and D.C. and scaling
terms are ignored) then a personal biometric signature can be
directly calculated from a measured signature without knowledge
of the trajectory (a) or leg (a) angles. The coefficients of the gait
curves for the five different trajectory angles are tabulated in
0 1 Table 1. The coefficients 4, and 4, vary as expected from
Walk Phase in radians Equation (9), but the remaining coefficients are constant within a
few percent of each other.
Measured gait angle in degrees
Figure 9 Hip rotation curves corrected for
trajectory angle and leg angle using Eqn. 9.
Angle Ap A1 qi A» œ A3 Œ
0 -0.083 0.411 -0.985 0.232 1.64 0.197 -2.56
10 -0.144 0.383 -1.017 0.204 1.67 0.228 -2.48
20 -0.184 0.356 -1.065 0.230 1.68 0.192 -2.47
30 -0.211 0.331 -1.106 0.215 1.68 0.199 -2.62
40 -0.247 0.272 -1.069 0.205 1.73 0.178 -2.61
N
Fit Function: tan(y) — A, + A, [sino *0)4 = 4, sin(n.œ+6, ) where N=3 and we [0.27]
n=2
Table 1: Coefficients resulting from fitting a modified Fourier series to the average human walks at various angles.
This is consistent with the model presented in this paper, and indicates that phase and high order amplitude
measurements of gait signatures are independent of pose. However this result must be conditional on the assumption
that the variation seen is due primarily to measurement error and not to natural fluctuations in the subject's gait. A
detailed study of the variation is beyond the scope of this paper.
6 FURTHER WORK
There is still considerable work required to bring the gait biometric to maturity. The effects of clothing, mood,
footwear, speed of walking must all be studied and their effect quantified. In addition the geometrical corrections
presented here must be developed to include cases where the subject does not walk in a straight line or where the
camera tracks the subject, possibly using a zoom lens to achieve maximum resolution. Furthermore, following the
surprising discovery of the effects of leg angle, the conclusions of Section 3.1 must be revisited experimentally.
Furthermore, detailed studies of the effects of experimental error, repeatability and subject variability must be carried
out before the efficacy of gait as a biometric for large populations is known.
7 CONCLUSIONS
We have shown that the effects of gait trajectory can be discounted when deriving experimental gait signatures.
Analytic measures have been developed to correct an angular measurement currently used as a basis for automatic gait
recognition. Experimentation has shown that a cosine correction rule and its extended form can normalise hip rotation
angle signatures with respect to the gait trajectory. Although the analysis presented here assumes that the camera and
gait trajectories are coplanar it is easily extensible to other arrangements.
120 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B5. Amsterdam 2000.
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