Tracking 3D coplanar points in the invariant perspective coordinates plane

This paper shows how to estimate the 3D planar motion of point coordinates from uncalibrated sequence images, irrespective of the camera motion. Assuming that four stationary reference points with known scene coordinates are seen, the reconstruction problem is solved through recursive coordinates estimations in the 3D reference plane while tracking is done in a space of invariant projective parameters instead of affine or Euclidean parameters. The invariant perspective coordinates plane-axis correspond to cross-ratios defining the relative position of a point with respect to four reference points-supplies a matching space invariant for any homography or camera motion. According to the extended Kalman filter formalism, we discuss the discriminatory power of the invariant perspective coordinates and describe geometrical constraints in order to reduce false matches. Experiments are done with a reference rectangle of known Euclidean coordinates. Results show the interest of this method yielding to a high reconstruction accuracy