Graphics Reference
In-Depth Information
parameters and the extrinsic parameters. Intrinsic parameters relate to the internal parameters
of the camera, such as the image coordinates of the principal point, the focal length, pixel
shape (its aspect ratio), and the skew. They are represented by the 3
3 upper triangular
matrix
K
. Extrinsic (or external) parameters relate to the pose of the camera, defined by the
3
×
3 rotation matrix
R
and its position
t
with respect to a global coordinate system.
Camera
calibration
is the process of estimating the intrinsic and extrinsic parameters of the cameras.
3D reconstruction can be roughly defined as the inverse of the imaging process; given a
pixel
p
on one image, 3D reconstruction seeks to find the 3D coordinates of the point
P
that
is imaged onto
p
. This is an ill-posed problem because with the inverse imaging process a
pixel
p
maps into a ray
v
that starts from the camera center and passes through the pixel
p
.
The ray direction
×
v
can be computed from the camera pose
R
and its intrinsic parameters
K
as follows;
R
−
1
K
−
1
p
=
v
(1.2)
R
−
1
K
−
1
p
1.2.1 Depth from Triangulation
If
q
is the image of the same 3D point
P
taken by another camera from a different viewing
angle, then the 3D coordinates of
P
can be recovered by estimating the intersection of the two
rays,
v
1
and
v
2
, that start from the camera centers passing, respectively, through
p
and
q
. This
is known as the
optical triangulation
principle.
p
and
q
are called
corresponding
or
matching
pixels because they are the images of the same 3D point
P
.
A 3D point
P
is the intersection of
n
(
n
>
1) rays
v
i
passing through the optical centers
c
i
of cameras
n
. This can also be referred to
passive optical triangulation
.
As illustrated in Figure 1.2, all points on
v
i
project to
p
i
, given a set of corresponding pixels
p
i
captured by the cameras
C
i
, and their corresponding rays
v
i
, the 3D location of
P
can
be found by intersecting the rays
v
i
. In practice, however, these rays will often not intersect.
{
C
i
}
where
i
=
1
,...,
P
v
i
v
i
p
i
C
i
Figure 1.2
Multiview stereo determines the position of a point in space by finding the intersection of
the rays
v
i
passing through the center of projection
c
i
of the
i
th camera and the projection of the point
P
in each image,
p
i
