Biomedical Engineering Reference
In-Depth Information
- the extrinsic parameters, which can vary according to
the position of the camera in the workspace:
R
3X3
the
rotation matrix transforming the coordinate system linked to
the workspace to the coordinate system linked to the camera,
tx, ty
and
t
z
the components of the translation vector
between these two coordinate systems.
In total, there are 12 parameters to calculate (the rotation
matrix contains nine elements, but with only three
independent elements corresponding to three angles). Some
systems also take into account eventual distortions induced
by the camera optics, especially the radial and tangential
distortions.
Calibrating the camera involves determining the
numerical value of the parameters of this model.
If
older
systems relied on static calibration
via
the direct linear
transform (DLT) method developed by Abdel-Aziz and
Karara [ABD 71] or one of their variants [HAT 88], requiring
a reference object on which coordinates with a minimum of
six control points to be placed in the center of the study
volume, the current systems use a two-step calibration.
First, a static calibration uses a fairly simple reference object
(square) on which the coordinates in the center of the four
markers are known, placed in the center of the study
volume. Acquiring an image of this object using the cameras
allows an initial estimate of the intrinsic and extrinsic
parameters, by setting a predefined value to the focal
lengths. This static calibration is followed by dynamic
calibration, which exploits the properties of epipolar
geometry (see Figure 2.8), during which an operator will
move a rod with two or three markers, whose distances are
known, through the entire study volume [CER 98]. This
stage requires that sufficient data are acquired in order to
optimize the calculation of all parameters in all the cameras.
In these two calibration steps, the average error on the
marker position is relatively homogeneous through the
