EPIPOLAR GEOMETRY FROM PROFILES UNDER CIRCULAR MOTION

P.R.D.S. Mendonça, K-Y. K. Wong and R. Cipolla

2001

This paper addresses the problem of motion estimation from profiles (also known as apparent contours) of an object rotating on a turntable in front of a single camera. Its main contribution is the development of a practical and accurate technique for solving this problem from profiles alone, which is precise enough to allow the reconstruction of the shape of the object. No correspondences between points or lines are necessary, although the method proposed can be used equally when these features are available, without any further adaptation. Symmetry properties of the surface of revolution swept out by the rotating object are exploited to obtain the image of the rotation axis and the homography relating epipolar lines in 2 views, in a robust and elegant way. These, together with geometric constraints for images of rotating objects, are then used to obtain first the image of the horizon, which is the projection of the plane that contains the camera centers, and then the epipoles, thus fully determining the epipolar geometry of the image sequence. The estimation of the epipolar geometry by this sequential approach (image of rotation axis --- homography --- image of the horizon --- epipoles) avoids many of the problems usually found in other algorithms for motion recovery from profiles. In particular, the search for the epipoles, by far the most critical step, is carried out as a simple one-dimensional optimization problem. The initialization of the parameters is trivial and completely automatic for all stages of the algorithm. After the estimation of the epipolar geometry, the Euclidean motion is recovered using the fixed intrinsic parameters of the camera, obtained either from a calibration grid or from self-calibration techniques. Finally, the spinning object is reconstructed from its profiles, using the motion estimated in the previous stage. Results from real data are presented, demonstrating the efficiency and usefulness of the proposed methods.

(ftp:) mendonca_PAMI.ps.gz (http:) mendonca_PAMI.ps.gz

PDF (automatically generated from original PostScript document - may be badly aliased on screen):

(ftp:) mendonca_PAMI.pdf | (http:) mendonca_PAMI.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.