Circle Extraction via Least Squares and the Kalman Filter

Abstr~tct. Two new techniques have been developed to extract circles in computer images and this paper clarifies their implementation. One technique uses nonlinear least squares, the other an extended Kalman filter. Parameter estimation is based on analysing the residual gradient direction where the locus of an approximation to a circle intersects the target circle. This approach allows powerful estimation techniques to be used for feature extraction in computer vision. The least squares technique is based on adapting an earlier method developed for ellipse extraction which has been modified not only for circle estimation but also to reduce sensitivity in par~a~aeter estimation. The Kalman filter algorithm is an extended version arranged to estimate the circle's parameters. Simulation results show that both techniques can extract circles in application but the Kalman filter implementation took more iterations and a number of factors limit its use The least squares technique only is shown applied to grey level images. Both techniques serve to extract circles when an initial approximation to the circle is known and hence are most suited to tracking circles in computer images. The techniques are at present being extended to include data weighting accordfaag to edge magnitude and direction.