Abstract for cipolla_RoySoc

Royal Society

THE VISUAL MOTION OF CURVES AND SURFACES.

Roberto Cipolla

1998

For smooth curved surfaces the dominant image feature is the apparent contour or outline. This is the projection of the contour generator - the locus of points on the surface which separate visible and occluded parts. The contour generator is dependent of the local surface geometry and the viewpoint. Each viewpoint will generate a different contour generator. This paper addresses the problem of recovering the 3D shape and motion of curves and surfaces from image sequences of apparent contours.

For known viewer motion the visible surfaces can then be reconstructed by exploiting a spatio-temporal parametrization of the apparent contours and contour generators under viewer motion. A natural parametrization exploits the contour generators and the epipolar geometry between successive viewpoints. The epipolar parametrization (Cipolla & Blake 1992) leads to simplified expressions for the recovery of depth and surface curvatures from image velocities and accelerations and known viewer motion.

The parametrization is, however, degenerate when the apparent contour is singular since the ray is tangent to the contour generator (Koenderink & Van Doorn 1976) and at frontier points (Giblin & Weiss 1994) when the epipolar plane is a tangent plane to the surface. At these isolated points the epipolar parametrization can no longer be used to recover the local surface geometry. This paper reviews the epipolar parametrization and shows how the degenerate cases can be used to recover surface geometry and unknown viewer motion from apparent contours of curved surfaces. Practical implementations are outlined.


(ftp:) cipolla_RoySoc.ps.Z (http:) cipolla_RoySoc.ps.Z
PDF (automatically generated from original PostScript document - may be badly aliased on screen):
  (ftp:) cipolla_RoySoc.pdf | (http:) cipolla_RoySoc.pdf

If you have difficulty viewing files that end '.gz', which are gzip compressed, then you may be able to find tools to uncompress them at the gzip web site.

If you have difficulty viewing files that are in PostScript, (ending '.ps' or '.ps.gz'), then you may be able to find tools to view them at the gsview web site.

We have attempted to provide automatically generated PDF copies of documents for which only PostScript versions have previously been available. These are clearly marked in the database - due to the nature of the automatic conversion process, they are likely to be badly aliased when viewed at default resolution on screen by acroread.