Gait Analysis and Human Motion Tracking - Intelligent Video Event Analysis and Understanding - page 51

(refer to [6]). The vector v satisfies the following equations:
|

| = θ deg ,
cos

v

θ deg )= 1

(28)

( 0 . 5 − ζ ,

where θ deg is an intermediate parameter used in the process.

The derivation of the transformation parameters using the EM scheme is based
on the prediction of the gait model. Therefore, the final variation of the motion be-
tween frames is the arithmetic summation of the prediction and the changes due
to the optimisation. The EM platform should efficiently converge to a unique so-
lution, φ ∗ , rather than several solutions due to under-estimation or over-estimation,

where a large inaccuracy arises. It is difficult to prove this in theory. In practice,
Meilijson [18] claims that Newton-type or other gradient methods provide the so-
lution required quickly but tend to be unstable. Therefore we apply the Levenberg-
Marquardt method [23], using the prediction based on the history of the recovered
motion parameters.

5 Experimental Results

To demonstrate improved performance, we compare the proposed gait-based ego-
motion tracking with the benchmark STK algorithm, which uses a short-term dis-
placement model. We employ synthetic test data, from a checked test pattern and a
computer game simulation for comparison of the algorithms with known periodic
gait parameters of the form of Eq. (7). We also employ real data from a camera
mounted on a pedestrian. As we do not have independent extraction of gait in this
case, we compare texture mapped images using extracted parameters with the real
image data, which gives a strong subjective comparison. The experimental results
are augmented considerably in [40].

5.1 Synthetic Checked Target: Accuracy Tests

The algorithm was tested using five synthetic sequences of a checked pattern, il-
lustrated in Fig. 4 (frame size: 630 630 pixels 2 ), including translational and ro-

tational motions of varying velocity. A right-handed Cartesian coordinate system
wasusedinwhichthe Z axis is normal to the image plane. Although the target was
simple, we added progressively increasing levels of Gaussian noise of mean zero
and variance 0.0 to 12.0 on an intensity scale from 0.0 to 255.0. 150 features were
extracted in the first frame but this number was reduced as features were lost as
tracking continued. In the sequence of Fig. 4, the pattern translates along the X and
Z axes and rotates about the Z -axis. In phase 1, the gait model is established in the
first 50 frames using the STK algorithm, Fig. 5 shows that the recovery of the t x
parameter is degraded with increased noise; for a variance of 12.0, the estimated
translation along the X axis has an absolute error of 0.1 - 0.5 units (1 unit: 19cm).
Similar results are observed for the t z and

×

θ z components [40]. The key comparison