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3
2.5
2
1.5
1
0.5
0
0
20
40
60
80
100
120
Feature index
3
2.5
2
1.5
1
0.5
0
0
20
40
60
80
100
120
140
Feature index
(a)
(b)
(c)
Fig. 2 Estimation of epipolar geometry: (a) and (b) matching results and epipolar geometry
recovered, and (c) the Euclidean distances (pixels) versus feature index.
intrinsic camera matrix M int . The camera transformation between the two images
and the scene geometry is recovered by assuming a pinhole camera model [36].
It is known that walking is an internally periodic process that becomes mature at
around 12 months [30]. Let d
be the periodic component of the generic displace-
ment function in terms of time t during motion. The “oscillating property" of the
motion pattern is expressed as a truncated Fourier series
(
t
)
N
k = 1 d k sin ( ω k t + φ k ) ,
d
(
t
)=
d 0 +
(7)
2
T p
( T p is a time period).
where the frequencies are
ω k =
ω k indicate the k -th har-
monics of the function d
,i.e.thefirst k components of the Fourier series after the
fundamental frequency. d 0 is the mean value, and d k and
(
t
)
φ k are the amplitude and
phase of the k -th harmonic in one stride period respectively [4]. As demonstrated
in the experimental results presented here, and more extensively in [40], a value
of N
3 allows normal gait patterns to be properly represented. Examples can be
found in Fig. 3. A model of lower complexity leads to large fitting errors and of
higher complexity to fitting of random and aperiodic fluctuations. Hence, for six
degrees of freedom, each represented by ten parameters in a truncated series, the
motion model has a total of 60 parameters. The camera transformations obtained
from successive frame-to-frame correspondences are used to form the gait model,
established over the sequence. As discussed in Section 2, a change in
=
ω k requires
updating of the gait model. This deterministic gait model is used to achieve bet-
ter prediction of the movement of features within the camera field of view over a
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