Extraction of 3D shape from optic flow: a geometric approach

Abstract

Several 3D shape measures are derived directly from the velocity field generated by a rigid curved surface patch under perspective projection. We use invariance under rotation of the image plane to decompose the velocity field into differential invariants. From a combination of these invariants, we construct an approximation to the absolute value of the shape index, to the curvature, and to the principal direction. We show the effect of these approximations to be small for a 6/spl deg/ field-of-view.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>