Master Thesis - Fachbereich Informatik

4.3. CAMERA CALIBRATION 63
is computed, each point in the image is transformed by H. Obviously, this is an expensive
operation for larger images. Furthermore, in practice the question is where to place the
calibration points. One possibility is to place them on top of the guide bars. The system
could automatically detect the calibration points and check whether these points lie on a
rectangle in the affine image space. This requires a very accurate positioning of the guide
bars, and all marker points should be coplanar, i.e. lie in one plane. Assuming one can
solve this mechanical problem there is still another problem, since - depending on how the
destination rectangle is defined - the warped image may be scaled. In any case, warping
discrete image points requires interpolation since transformed points may fall in between
the discrete grid. Obviously, this can reduce the image quality.
Online Grid Calibration Although the previous described approach does not require an
accurate positioning of the camera, there are several drawbacks especially with respect to
performance and image reliability. If there is a way to adjust the camera perfectly one
does not need warping and perspective correction. However, a human operator must be
able to perform this positioning task in an appropriate time.
Therefore, an interactive camera positioning method has been developed denoted as
Online Grid Calibration.
First, the distance of the parallel guide bars has to be adjusted to the current tube size.
Then, a planar chessboard pattern of known size is placed between the guide bars on the
conveyor within the visual field of the camera. The horizontal lines on the chessboard must
be parallel to the guide bars (see Figure 4.11). To simplify the adjustments, a mechanical
device may be developed that can be placed in between the guide bars combining the
function of a spacer bringing the guide bars into the right distance, and the calibration grid
that perfectly fits into the space between the guide bars with the designated orientation.
The underlying idea is as follows: If the chessboard is imaged in a way that vertical lines
in the world are vertical in the image and horizontal lines appear horizontal respectively,
while each grid cell of the chessboard results in the same size in the image, the camera is
adjusted accurate enough to yield a fronto-orthogonal view.
The process of camera adjustment can be simplified if the operator gets a feedback in
real-time of how close the current viewing position is to the optimal position. Therefore,
the live images of the camera are overlaid with an optimal visual grid of squares. This grid
can be parametrized by two points, i.e. the upper left corner and the lower right corner
respectively as well as the vertical and horizontal size of each grid cell. The operator can
move the grid in horizontal and vertical direction and adjust the size. This is a good
feature to initialize the grid or to perform the fine adjustments.
For each image, the correspondence between the overlaid virtual grid and the underlying
image data is computed. A two step method has been developed. At first the image
gradient both in vertical and horizontal direction is extracted using the SOBELX and
SOBELY operator. This information can be used to approximate the gradient magnitude
and orientation (see Equation 2.21 and 2.24). Since there is a strong contrast between
the black and white chessboard cells, the gradient magnitude at the edges is strong as
well. If the virtual grid matches the current image data, the gradient orientation φ(p)
on horizontal grid lines must be ideally π/2 or3π/2 respectively depending on whether
an edge is a black-white or white-black transition. Remind that the gradient direction is
always perpendicular to the edge. Correspondingly, vertical grid lines have orientations of