Calculation of the geometric parameters of an ellipse in space by its edges in the images

Abstract

A method for the calculation of the geometric parameters of an ellipse in space from stereo images is derived. Provided the orientation of the cameras is known, a residual for any ray, starting on the ellipse boundaries in the images, to the ellipse in space can be derived, if suitable initial values of the parameters are determined in a first step. Minimizing the residuals by a least squares method yields the required parameters. The ellipses need not be totally visible in the images, no homologous points are required by this procedure; thus the method is well suited for automatic image processing.