Information Technology Reference
In-Depth Information
search window, or allows a longer gap between frames, each resulting in greater
efficiency. Further, there is less chance of an incorrect match as the probability of
similarity between detected features is reduced. The nature of the gait model de-
scribed by Eq. (7) determines the use of a nonlinear optimization process. This is
a
dependent
multivariate process, and the stability of the possible solution is not
guaranteed since too many unknown parameters reside in the optimization [15].
We register the projection of a 3-D “template", yielded by the gait model, with the
2-D feature points in the latest frame. This is an incomplete data problem because
the correspondences are not known accurately
apriori
as there are incorrect corre-
spondences and errors in position. We expect that a number of
outliers
may occur in
the corresponding matches. Hence, we derive a
global
rather than a
local
similarity
between the actual correspondences and the image projections of the scene structure.
In the presence of incorrect feature correspondence, robust registration and recov-
ery of the camera transformation between frames is explored using a maximum a
posteriori (MAP) strategy, instantiated by the expectation-maximization (EM) algo-
rithm [11]. Hence, we iterate the
expectation and maximization
until convergence
is reached at the
global minimum
. The expectation step indicates
a posteriori
prob-
abilities of the incomplete data using Gaussian mixture models, given the image
observations and belief in motion provided by the gait model. The maximization
step involves a
maximum a posteriori estimate
to refine the predicted motion pa-
rameters in order to obtain a minimum sum of Euclidean distances between image
points. Our approach is inspired by that used by Cross and Hancock [7], Choi
et al.
[5] and Zhou
et al.
[41]. However, the key difference is the use of the gait model
to predict frame-to-frame camera transformations, thus improving the efficiency of
the approach. In comparison with [41], we have extended our evaluation to include
synthetic and real pedestrian sequences in which walking velocity changes. Further-
more, we have added an experiment investigating the effect of moving obstacles
(other pedestrians) in real image sequences.
4.1
Estimating Motion Parameters by a MAP Strategy
˜
˜
Consider a
dynamic
representation for the registration,
f
(
α
t
,
˜
β
t
,
φ
t
)
,where ˜
α
t
refers
˜
to the 3-D points recovered from corresponding image points,
β
t
is the image obser-
vation, and
˜
φ
t
is the current prediction of the camera transformation, based on the
longer term gait model, at time
t
. Given a good
˜
φ
t
, the posterior probability (or the
˜
˜
likelihood of the hypothesis,
˜
˜
β
t
.
Assuming individual image points are conditionally
independent
[5], the joint
probability is therefore
φ
t
),
p
(
β
t
|
φ
t
)
, is maximized to find an optimal
˜
˜
φ
t
)=
∏
i
˜
˜
p
(
β
t
|
p
(
β
t
i
|
φ
t
)
,
(8)
where
i
is the index of an image point. Using Bayes' rule,
˜
˜
φ
t
)=
∑
j
˜
˜
˜
˜
p
(
β
t
i
|
p
(
β
t
i
|
α
t j
,
φ
t
)
p
(
α
t j
)
,
(9)
Search WWH ::
Custom Search