An important task of the industrial image processing, like accuracy applications of the car manufacturing industry, is the 3-dimensional pose estimation of rigid bodies in relation to a determined world coordinate system. Therefore, the object targeted pose estimation uses the so-called bundle adjustment method, which for more than three points leads to the formulation of a least squares problem.

For each camera the solution of this problem leads to small errors, i.e. the actual reproductions of the single features in each image do not correspond to the theoretical reproductions dependent on the camera calibration, object and position data. These deformations lead to distortions of the complete system which - with the cancellation of an object feature by non-recognition or camera failure - result in more or less heavy deviations from the physical position.

In technical applications using CCD cameras the most common camera model is the pinhole model. The parameters are the focal distance, lens distortion 1st order, chip main point and scale factors.
In practice there are several, by this model not registered, influences like sub-scanning of the image, geometrical errors of the CCD-chip and temperature dependence of the scale factors. These effects result in a non-linear behaviour for each camera and lead to deviations for the image processing system.

In general there are two algorithms to force stability for the camera-based pose estimation system.

The first one is to move the physical object data onto the theoretical reproductions of the image data after defining the object zero position by a reference measurement. The implemented additional con-straint for obtaining an explicit solution is to move the object data onto the direct line to the theoretical reproductions.

The second way to force stability is an "In Process Calibration" of the cameras while considering the object in zero position. A non-iterative quarternion method for generating a supplementary rotation matrix is presented.

At least the paper presents results based on this new bundle adjustment method. They are calculated from simulated data including specific disturbances and they demonstrate that both methods are work-ing equally good. A combination of both methods will improve the results in real applications.

Werner.Neddermeyer@informatik.fh-ge.de