Iterative algorithm for offsets, rotation and scale estimation for contour superposition

The article presents an iterative algorithm for contour superposition. The contours to be superposed are linked by a transformation that includes offsets, angle of rotation, and scale. The points of the contours to be machined do not have a one-to-one correspondence. We have developed the procedure to estimate superposition parameters. This procedure includes the offsets estimation in the Cartesian coordinate system, the rotate and scale estimation in the log-polar coordinate system. The low error in evaluation of parameters is provided by the iteration procedure. The offset rating is used for correction of the angle of rotation and scale, and vice versa. Numerical modeling was used to estimate the error of the superposition parameters depending on the noise power. The error of the developed algorithm is similar to the brute force algorithm but speed processing is faster. The algorithm can be used in real-time measuring systems.