Algebraic and Geometric Tools to Compute Projective and Permutation Invariants

Studies the computation of projective invariants in pairs of images from uncalibrated cameras and presents a detailed study of the projective and permutation invariants for configurations of points and/or lines. Two basic computational approaches are given, one algebraic and one geometric. In each case, invariants are computed in projective space or directly from image measurements. Finally, we develop combinations of those projective invariants which are insensitive to permutations of the geometric primitives of each of the basic configurations.

[1]  Olivier D. Faugeras,et al.  Algebraic and Geometric Tools to Compute Projective and Permutation Invariants , 1997, AFPAC.

[2]  Olivier D. Faugeras,et al.  From projective to Euclidean reconstruction , 1996, Proceedings CVPR IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[3]  Gian-Carlo Rota,et al.  On the Foundations of Combinatorial Theory: IX Combinatorial Methods in Invariant Theory , 1974 .

[4]  K. Åström,et al.  Random Cross Ratios , 1995 .

[5]  D. Hestenes,et al.  Projective geometry with Clifford algebra , 1991 .

[6]  Gabriela Csurka,et al.  Modelisation projective des objets tridimensionnels en vision par ordinateur , 1996 .

[7]  Patrick Gros,et al.  3D projective invariants from two images , 1993, Optics & Photonics.

[8]  O. Faugeras,et al.  Applications of non-metric vision to some visual guided tasks , 1994, Proceedings of the Intelligent Vehicles '94 Symposium.

[9]  Fadi Dornaika,et al.  Visually guided object grasping , 1998, IEEE Trans. Robotics Autom..

[10]  Radu Horaud,et al.  Self-calibration and Euclidean reconstruction using motions of a stereo rig , 1998, Sixth International Conference on Computer Vision (IEEE Cat. No.98CH36271).

[11]  Stefan Carlsson,et al.  The Dou8ble Algebra: An Effective Tool for Computing Invariants in Computer Vision , 1993, Applications of Invariance in Computer Vision.

[12]  Olivier D. Faugeras,et al.  Computing three dimensional project invariants from a pair of images using the Grassmann-Cayley algebra , 1998, Image Vis. Comput..

[13]  I. Reid,et al.  Metric calibration of a stereo rig , 1995, Proceedings IEEE Workshop on Representation of Visual Scenes (In Conjunction with ICCV'95).

[14]  R. Hartley.  Invariants of Lines in Space , 1993 .

[15]  Luce Morin,et al.  Quelques contributions des invariants projectifs à la vision par ordinateur , 1993 .

[16]  J. G. Semple,et al.  Algebraic Projective Geometry , 1953 .

[17]  U. Uenohara,et al.  Geometric invariants for verification in 3-D object tracking , 1996, Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems. IROS '96.

[18]  Eduardo Bayro-Corrochano,et al.  A new methodology for computing invariants in computer vision , 1996, Proceedings of 13th International Conference on Pattern Recognition.

[19]  Reiner Lenz,et al.  Correspondence of Coplanar Features Through p-Invariant Representations , 1993, Applications of Invariance in Computer Vision.