Extracting projective structure from single perspective views of 3D point sets

A number of recent papers have argued that invariants do not exist for three-dimensional point sets in general position, which has often been misinterpreted to mean that invariants cannot be computed for any three-dimensional structure. It is proved by example that although the general statement is true, invariants do exist for structured three-dimensional point sets. Projective invariants are derived for two object classes: the first is for points that lie on the vertices of polyhedra, and the second for objects that are projectively equivalent to ones possessing a bilateral symmetry. The motivations for computing such invariants are twofold: they can be used for recognition, and they can be used to compute projective structure. Examples of invariants computed from real images are given.<<ETX>>

[1]  Edward M. Riseman,et al.  The non-existence of general-case view-invariants , 1992 .

[2]  Isaac Weiss,et al.  Projective invariants of shapes , 1988, Proceedings CVPR '88: The Computer Society Conference on Computer Vision and Pattern Recognition.

[3]  Rajiv Gupta,et al.  Stereo from uncalibrated cameras , 1992, Proceedings 1992 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[4]  Shimon Ullman,et al.  Limitations of Non Model-Based Recognition Schemes , 1992, ECCV.

[5]  Roger Mohr,et al.  Projective Geometry and Computer Vision , 1993, Handbook of Pattern Recognition and Computer Vision.

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

[7]  David A. Forsyth,et al.  Invariant Descriptors for 3D Object Recognition and Pose , 1991, IEEE Trans. Pattern Anal. Mach. Intell..

[8]  David W. Jacobs,et al.  Model group indexing for recognition , 1991, Proceedings. 1991 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[9]  D. Forsyth,et al.  Extracting Projective Information from Single Views of 3D Point Sets , 1993 .

[10]  David A. Forsyth,et al.  Efficient model library access by projectively invariant indexing functions , 1992, Proceedings 1992 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[11]  P. Beardsley,et al.  Affine and Projective Structure from Motion , 1992 .

[12]  Peter C. Wayner,et al.  Efficiently using invariant theory for model-based matching , 1991, Proceedings. 1991 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[13]  K. Sugihara.  Machine interpretation of line drawings , 1986, MIT Press series in artificial intelligence.

[14]  Luce Morin,et al.  Relative positioning from geometric invariants , 1991, Proceedings. 1991 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[15]  C. H. Chen,et al.  Handbook of Pattern Recognition and Computer Vision , 1993 .

[16]  Luc Van Gool,et al.  Recognition and semi-differential invariants , 1991, Proceedings. 1991 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[17]  Yehezkel Lamdan,et al.  Object recognition by affine invariant matching , 2011, Proceedings CVPR '88: The Computer Society Conference on Computer Vision and Pattern Recognition.