Graphics Reference
In-Depth Information
2.2.3.3 The Multiocular Extension of the CCD Algorithm
The multiocular extension of the CCD algorithm relies on the projection of the
boundary of a three-dimensional contour model into each image. The intrinsic and
extrinsic parameters of the camera model (Bouguet,
2007
) are obtained by multi-
ocular camera calibration (Krüger et al.,
2004
). An arbitrary number of images
N
c
can be used for this projection. The input values of the MOCCD algorithm are
N
c
images and the Gaussian a priori distribution
p(
T
)
m
T
, Σ
T
)
of the model
parameters
T
, which define the three-dimensional object model. To achieve a more
robust segmentation, the input image
I
c,t
of the MOCCD algorithm is computed
using (
2.11
) and the original camera images
I
c,t
with
c
≈
p(
T
|
∈{
1
,...,N
c
}
at the time
steps
t
and
(t
1
)
. Before the first iteration, the MOCCD algorithm is initialised
by setting the mean vector and covariance matrix
(
m
T
,Σ
T
)
to be optimised to the
given a priori density parameters
(
−
m
T
, Σ
T
)
. The MOCCD algorithm then consists
of three steps.
Step 1: Extraction and Projection of the Three-Dimensional Model
The in-
trinsic and extrinsic camera parameters are used to project the extracted outline of
the three-dimensional model to each camera image
I
c
. The MOCCD algorithm ex-
tends the CCD algorithm to multiple calibrated cameras by projecting the boundary
of a three-dimensional model into each camera image
I
c
. Therefore, the MOCCD
algorithm requires the extraction and projection of the outline of the used three-
dimensional model.
A three-dimensional hand-forearm model (cf. Sect.
2.2.3.1
) is fitted to the im-
ages of a trinocular camera. The outline of our three-dimensional model in each
camera coordinate system is extracted by computing a vector from the origin of
each camera coordinate system to th
e poin
t in the wrist, e.g.
C
1
p
2
for camera 1.
This vector and the direction vector
p
1
p
2
of the forearm span a plane. The nor-
mal vector of this plane is intersected with the three-dimensional model to yield
the three-dimensional outline observed from the camera viewpoint. The extracted
three-dimensional contour model for the given camera, which consists of 13 points,
is projected into the pixel coordinate system of the camera. The corresponding two-
dimensional contour model is computed by an Akima interpolation (Akima,
1970
)
along the curve with the 13 projected points as control points. Figure
2.10
depicts
the extraction and projection of the three-dimensional contour model for camera 1.
Step 2: Learning Local Probability Distributions from all
N
c
Images
For all
N
c
camera images
I
c
compute the local probability distributions
S
c
(
m
T
,Σ
T
)
on
both sides of the curve. This step is similar to step 1 of the CCD algorithm; the only
difference is that the probability distributions
S
c
(
m
T
,Σ
T
)
on both sides of the curve
are learned for all
N
c
camera images
I
c
.
Step 3: Refinement of the Estimate (MAP Estimation)
The curve density pa-
rameters
(
m
T
,Σ
T
)
are refined towards the maximum of (
2.30
) by performing a
Search WWH ::
Custom Search