Integrated Frameworks for Three-Dimensional Scene Reconstruction - 3D Computer Vision: Efficient Methods and Applications - page 238

Ta b l e 5 . 5 Influence of small
changes of the pose
parameters on the observed
edge, photopolarimetric, and
depth cues

Intensity,
polarisation

Edges Depth

Rotation angles Strong Weak Weak

Lateral translation ( x,y ) Weak Strong Weak

Translation in z Weak Weak Strong

For minimisation of the overall error e T we use an iterative gradient descent ap-
proach. We have chosen this algorithm because of its stable convergence behaviour,
but other optimisation methods are possible. It is impossible to calculate analyti-
cally the derivatives of the total error term with respect to the pose parameters, as
the error term is computed based on rendered images; thus the gradient is evaluated
numerically. If a certain cue does not provide useful information (which may e.g.
be the case for polarisation data when the surface material only weakly polarises
the reflected light, or for edges in the presence of a cluttered background), this cue
can be neglected in the optimisation procedure by setting the corresponding weight
factor in ( 5.46 ) to zero. It is shown experimentally in this section and in Sect. 6.1
that pose estimation remains possible when relying on merely two or three different
cues.
Our framework requires a priori information about the object pose for initialisa-
tion of the nonlinear optimisation routine, and thus it is especially useful for pose
refinement. In comparison, the template matching-based approach of von Bank et
al. ( 2003 ) yields five pose parameters without a priori knowledge about them, while
the sixth parameter, the distance to the object, is assumed to be exactly known. In the
addressed application domain of industrial quality inspection, a priori information
about the pose is available from the CAD data of the part itself and the workpiece to
which it is attached. Here it is not necessary to detect the part in an arbitrary pose,
but rather to measure small differences between the reference pose parameters and
those desired according to the CAD data. Hence, when applied in the context of in-
dustrial quality inspection, our method should be initialised with the pose given by
the CAD data, and depending on the tolerances stored in the CAD data, a production
fault is indicated when the deviation of one or several pose parameters exceeds the
tolerance value. The experimental evaluation presented in the next section shows
that our framework is able to detect small differences between the true and desired
object poses.

5.6.5 Experimental Evaluation Based on a Simple Real-World
Object

For a first evaluation of the performance of the presented approach we estimated
the pose of a simple cuboid-shaped real-world object (a rubber) and compared the
results to the independently derived ground truth. The images were taken with a