Circle Extraction via Least Squares and the Kalman Filter

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 parameter estimation. The Kalman filter algorithm is an extended version arranged to estimate the circle's parameters.