Autocalibration and the absolute quadric

We describe a new method for camera autocalibration and scaled Euclidean structure and motion, from three or more views taken by a moving camera with fixed but unknown intrinsic parameters. The motion constancy of these is used to rectify an initial projective reconstruction. Euclidean scene structure is formulated in terms of the absolute quadric - the singular dual 3D quadric (4 x 4 rank 3 matrix) giving the Euclidean dot-product between plane normals. This is equivalent to the traditional absolute conic but simpler to use. It encodes both affine and Euclidean structure, and projects very simply to the dual absolute image conic which encodes camera calibration. Requiring the projection to be constant gives a bilinear constraint between the absolute quadric and image conic, from which both can be recovered nonlinearly from m greater than or equal to 3 images, or quasi-linearly from m greater than or equal to 4. Calibration and Euclidean structure follow easily. The nonlinear method is stabler, faster, more accurate and more general than the quasi-linear one. It is based on a general constrained optimization technique - sequential quadratic programming - that may well be useful in other vision problems.