The goal of augmented reality is to insert virtual objects into real video sequences. This paper shows that by incorporating image-based geometric constraints over mul-tiple views, we improve on traditional techniques which use purely 3D information. The constraints imposed are chosen to directly target perceptual cues, important to the human visual system, by which errors in AR are most readily perceived. Imposi-tion of the constraints is achieved by constrained maximum-likelihood estimation, and blends projective, affine and Euclidean geometry as appropriate in different cases. We introduce a number of examples of augmented reality tasks, show how image-based constraints can be incorporated into current 3D-based systems, and demonstrate the improvements conferred.

Cantor, Estrin and Turn have described a special-purpose structure to implement sequential table look-up (STL) algorithms for the evaluation of ln x and exp x.1 Tables of precomputed constants are used to transform the argument into a range where the function may be approximated by a simple polynomial. The transformation for ln x, originally proposed by Bemer,2 is where the set of constants ai are precomputed. A power series expansion for ln x is