Estimation of stereo and motion parameters using a variational principle

摘要

The problems of extracting 3D structure from stereo or motion parameters from optic flow are now analytically tractable but numerically ill-conditioned. A variational principle is proposed which alleviates ill-conditioning and saturates rapidly with data so that even a small excess (over a minimal number) of data points yields accurate results. It involves no adjustable parameters (unlike many applications of the regularization theory) and no assumptions about measurement errors, which, in fact, it seeks to estimate and minimize. The technique is illustrated with image resolutions varying from 1024 to 128 pixels square, using between 6 and 30 data points (5 data points define a unique solution) perturbed by at most 0.2 pixels. The error in the computed direction of translation was 2.7 deg in the worst case (128 × 128 pixels, 15 data points). It was 1.2 deg with only six data points for an image 1024 square.