225
P, = 09° -1 with oy 2 100 mm, R, - (S,-0,)^ -/ with o, - 05 pixel, Q, =0,2-1 with o, - 0.
image acquisition, edge detection, polygon approximation 40 ms (video real time)
preprocessing 100 ms
subpixel interpolation 90 ms
feature tracking 30 ms
3-D structure estimation:
initial state vector computation 6 ms
Kalman filtering 9 ms
Table 1. Computing times for a VMEbus system with Motorola 68040 processor.
5. CONCLUSION
A passive method for the 3-D measurement of workpieces has been presented, which relies on the evaluation of image
sequences supplied by a standard CCD camera. The approach is based on a recursive extension of conventional stereo
triangulation in terms of an Extended Kalman filter algorithm, which allows for the on-line processing of image
sequences of arbitrary length. Objects are described in terms of their polygonal contour lines. Each of the moving
polygon vertices is separately considered a dynamic system, which is represented in discrete time using state-space
notation. The state vector to be estimated is defined as the spatial position of the vertex with reference to the camera
coordinate frame. This formulation yields a lower-dimensional system matrix compared with approaches using more
complex geometric features and results in main advantages as to computational load and processing times. The known
relative motion between camera and scene allows for the computation of the system matrix, while the measurement
equations are obtained from the nonlinear mathematical modelling of the optical projection. The 3-D structure of the
workpiece can be reconstructed from the estimated vertex positions. The resulting accuracy as well as the attained
computing times show that the technique is applicable for a wide variety of industrial real time applications. The method
has already been employed and tested as part of a system for the recognition and localisation of 3-D objects.
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IAPRS, Vol. 30, Part 5W1, ISPRS Intercommission Workshop “From Pixels to Sequences”, Zurich, March 22-24 1995
