A canonical framework for sequences of images

This paper deals with the problem of analysing sequences of images of rigid point objects taken by uncalibrated cameras. It is assumed that the correspondences between the points in the different images are known. The paper introduces a new framework for this problem. Corresponding points in a sequence of n images are related to each other by a fixed n-linear form. This form is an object invariant property, closely linked to the motion of the camera relative to the fixed world. We first describe a reduced setting in which these multilinear forms are easier to understand and analyse. This new formulation of the multilinear forms is then extended to the calibrated case. This formulation makes apparent the connection between camera motion, camera matrices and multilinear forms and the similarities between the calibrated and uncalibrated cases. These new ideas are then used to derive simple linear methods for extracting camera motion from sequences of images.

[1]  Olivier D. Faugeras,et al.  What can be seen in three dimensions with an uncalibrated stereo rig , 1992, ECCV.

[2]  K Strm.  Automatic Mapmaking , 1993 .

[3]  Long Quan,et al.  Invariants of 6 Points from 3 Uncalibrated Images , 1994, ECCV.

[4]  Gunnar Sparr,et al.  A Common Framework for Kinetic Depth, Reconstruction and Motion for Deformable Objects , 1994, ECCV.

[5]  A. Heyden.  Reconstruction from Three Images of Six Point Objects , 1994 .

[6]  Nassir Navab,et al.  Relative affine structure: theory and application to 3D reconstruction from perspective views , 1994, 1994 Proceedings of IEEE Conference on Computer Vision and Pattern Recognition.

[7]  Thierry Viéville,et al.  Canonic Representations for the Geometries of Multiple Projective Views , 1994, ECCV.

[8]  Amnon Shashua,et al.  Trilinearity in Visual Recognition by Alignment , 1994, ECCV.

[9]  David W. Murray,et al.  A unifying framework for structure and motion recovery from image sequences , 1995, Proceedings of IEEE International Conference on Computer Vision.

[10]  Bill Triggs,et al.  Matching constraints and the joint image , 1995, Proceedings of IEEE International Conference on Computer Vision.

[11]  Karl Johan Åström,et al.  A Canonic Framework for Sequences of Images: Similarities between the Calibrated and the Uncalibrated Case , 1995 .

[12]  Roberto Cipolla,et al.  Motion from the frontier of curved surfaces , 1995, Proceedings of IEEE International Conference on Computer Vision.

[13]  Anders Heyden,et al.  Reconstruction from image sequences by means of relative depths , 1995, Proceedings of IEEE International Conference on Computer Vision.

[14]  Olivier D. Faugeras,et al.  On the geometry and algebra of the point and line correspondences between N images , 1995, Proceedings of IEEE International Conference on Computer Vision.

[15]  Henrik I. Christensen,et al.  Using the Relation Between a Plane Projectivity and the Fundamental Matrix , 1996 .