Covariance Propagation for Guided Matching

We present a general approach and analytical method for determining a search region for use in guided matching under projective mappings. Our approach is based on the propagation of covariance through a first-order approximation of the error model to define the boundary of the search region for a specified probability and we provide an analytical expression for the Jacobian matrix used in the covariance propagation calculation. The resulting closed-form expression is easy to implement and generalizes to n dimensions. We apply our method to point-to-point mapping under a planar homography, point-to-line mapping under a fundamental matrix, and mosaic construction from video in the case of the video looping back on itself.

[1]  金谷 健一.  Statistical optimization for geometric computation : theory and practice , 2005 .

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

[3]  Carlo Tomasi,et al.  Good features to track , 1994, 1994 Proceedings of IEEE Conference on Computer Vision and Pattern Recognition.

[4]  Richard I. Hartley,et al.  Euclidean Reconstruction from Uncalibrated Views , 1993, Applications of Invariance in Computer Vision.

[5]  Olivier D. Faugeras,et al.  Characterizing the Uncertainty of the Fundamental Matrix , 1997, Comput. Vis. Image Underst..

[6]  Zhengyou Zhang,et al.  Determining the Epipolar Geometry and its Uncertainty: A Review , 1998, International Journal of Computer Vision.

[7]  Alexander Graham,et al.  Kronecker Products and Matrix Calculus: With Applications , 1981 .

[8]  P. Anandan,et al.  Implicit representation and scene reconstruction from probability density functions , 1999, Proceedings. 1999 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (Cat. No PR00149).

[9]  Ian D. Reid,et al.  A plane measuring device , 1999, Image Vis. Comput..

[10]  Bill Triggs,et al.  Joint feature distributions for image correspondence , 2001, Proceedings Eighth IEEE International Conference on Computer Vision. ICCV 2001.

[11]  Andrew W. Fitzgibbon,et al.  Bundle Adjustment - A Modern Synthesis , 1999, Workshop on Vision Algorithms.

[12]  Andrew Zisserman,et al.  Automated mosaicing with super-resolution zoom , 1998, Proceedings. 1998 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (Cat. No.98CB36231).

[13]  Wolfgang Förstner,et al.  Uncertainty and Projective Geometry , 2005 .

[14]  Takeo Kanade,et al.  An Iterative Image Registration Technique with an Application to Stereo Vision , 1981, IJCAI.

[15]  Bernhard P. Wrobel,et al.  Multiple View Geometry in Computer Vision , 2001 .

[16]  Robert C. Bolles,et al.  Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography , 1981, CACM.