Randomness and geometric features in computer vision

It is often necessary to handle randomness and geometry in computer vision, for instance to match and fuse together noisy geometric features such as points, lines or 3D frames, or to estimate a geometric transformation from a set of matched features. However, the proper handling of these geometric features is far more difficult than for points, and a number of paradoxes can arise. We analyse in this article three basic problems: (1) what is a uniform random distribution of features, (2) how to define a distance between features, and (3) what is the "mean feature" of a number of feature measurements, and we propose generic methods to solve them.

[1]  Paul J. Besl,et al.  A Method for Registration of 3-D Shapes , 1992, IEEE Trans. Pattern Anal. Mach. Intell..

[2]  M. Fréchet.  Les éléments aléatoires de nature quelconque dans un espace distancié , 1948 .

[3]  Olivier Faugeras,et al.  3D Dynamic Scene Analysis: A Stereo Based Approach , 1992 .

[4]  Hugh Durrant-Whyte,et al.  Integration, coordination, and control of multi-sensor robot systems , 1987 .

[5]  M. Émery,et al.  Sur le barycentre d'une probabilité dans une variété , 1991 .

[6]  Olivier D. Faugeras,et al.  HYPER: A New Approach for the Recognition and Positioning of Two-Dimensional Objects , 1986, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[7]  L. Santaló.  Integral geometry and geometric probability , 1976 .

[8]  W. Eric L. Grimson,et al.  On the sensitivity of geometric hashing , 1990, [1990] Proceedings Third International Conference on Computer Vision.

[9]  Olivier Faugeras,et al.  Uncertainty Manipulation and Parameter Estimation , 1992 .

[10]  William Grimson,et al.  Object recognition by computer - the role of geometric constraints , 1991 .

[11]  Yehezkel Lamdan,et al.  Geometric Hashing: A General And Efficient Model-based Recognition Scheme , 1988, [1988 Proceedings] Second International Conference on Computer Vision.

[12]  Xavier Pennec,et al.  Correctness and robustness of 3D rigid matching with bounded sensor error , 1993 .

[13]  G. Hochschild,et al.  The Structure of Lie Groups. , 1967 .

[14]  Nicholas Ayache,et al.  An 0(n2) algorithm for 3D substructure matching of proteins , 1994 .

[15]  Yehezkel Lamdan,et al.  On the error analysis of 'geometric hashing' , 1991, Proceedings. 1991 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[16]  S. Altmann.  Rotations, Quaternions, and Double Groups , 1986 .

[17]  Robert A. Hummel,et al.  Distributed Bayesian object recognition , 1993, Proceedings of IEEE Conference on Computer Vision and Pattern Recognition.

[18]  Nicholas Ayache,et al.  Artificial vision for mobile robots - stereo vision and multisensory perception , 1991 .

[19]  Xavier Pennec,et al.  A Framework for Uncertainty and Validation of 3-D Registration Methods Based on Points and Frames , 1995, Proceedings of IEEE International Conference on Computer Vision.