Homography Estimation from the Common Self-Polar Triangle of Separate Ellipses

How to avoid ambiguity is a challenging problem for conic-based homography estimation. In this paper, we address the problem of homography estimation from two separate ellipses. We find that any two ellipses have a unique common self-polar triangle, which can provide three line correspondences. Furthermore, by investigating the location features of the common self-polar triangle, we show that one vertex of the triangle lies outside of both ellipses, while the other two vertices lies inside the ellipses separately. Accordingly, one more line correspondence can be obtained from the intersections of the conics and the common self-polar triangle. Therefore, four line correspondences can be obtained based on the common self-polar triangle, which can provide enough constraints for the homography estimation. The main contributions in this paper include: (1) A new discovery on the location features of the common self-polar triangle of separate ellipses. (2) A novel approach for homography estimation. Simulate experiments and real experiments are conducted to demonstrate the feasibility and accuracy of our approach.

[1]  Jun-Sik Kim,et al.  Geometric and algebraic constraints of projected concentric circles and their applications to camera calibration , 2005, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[2]  Jiri Matas,et al.  Homography estimation from correspondences of local elliptical features , 2012, Proceedings of the 21st International Conference on Pattern Recognition (ICPR2012).

[3]  John F. Canny,et al.  A Computational Approach to Edge Detection , 1986, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[4]  Christos Conomis.  Conics-Based Homography Estimation from Invariant Points and Pole-Polar Relationships , 2006, Third International Symposium on 3D Data Processing, Visualization, and Transmission (3DPVT'06).

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

[6]  Long Quan,et al.  Conic Reconstruction and Correspondence From Two Views , 1996, IEEE Trans. Pattern Anal. Mach. Intell..

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

[8]  Juho Kannala,et al.  Algorithms for Computing a Planar Homography from Conics in Correspondence , 2006, BMVC.

[9]  Akihiro Sugimoto.  A Linear Algorithm for Computing the Homography from Conics in Correspondence , 2004, Journal of Mathematical Imaging and Vision.

[10]  John Wright,et al.  Homography from Coplanar Ellipses with Application to Forensic Blood Splatter Reconstruction , 2006, 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'06).

[11]  Charles T. Loop,et al.  Computing rectifying homographies for stereo vision , 1999, Proceedings. 1999 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (Cat. No PR00149).

[12]  F. P. W.,et al.  Higher Geometry , 2022 .

[13]  Pierre Gurdjos,et al.  Euclidean Structure from N geq 2 Parallel Circles: Theory and Algorithms , 2006, ECCV.

[14]  Christin Wirth.  The Essential Physics of Medical Imaging , 2003, European Journal of Nuclear Medicine and Molecular Imaging.

[15]  James J. Little,et al.  AUTOMATIC RECTIFICATION OF LONG IMAGE SEQUENCES , 2003 .

[16]  Zhanyi Hu,et al.  Camera Calibration from the Quasi-affine Invariance of Two Parallel Circles , 2004, ECCV.

[17]  David A. Forsyth,et al.  Relative motion and pose from arbitrary plane curves , 1992, Image Vis. Comput..

[18]  Hui Zhang,et al.  Camera Calibration Based on the Common Self-polar Triangle of Sphere Images , 2014, ACCV.

[19]  A. Z..  An Introduction to Projective Geometry , 1938, Nature.

[20]  Zhengyou Zhang,et al.  A Flexible New Technique for Camera Calibration , 2000, IEEE Trans. Pattern Anal. Mach. Intell..

[21]  Andrew P. Paplinski,et al.  Tangency of conics and quadrics , 2006 .

[22]  Matthew A. Brown,et al.  Recognising panoramas , 2003, Proceedings Ninth IEEE International Conference on Computer Vision.

[23]  Jonathan Nissanov,et al.  Symmetry-based 3D brain reconstruction , 2004, 2004 2nd IEEE International Symposium on Biomedical Imaging: Nano to Macro (IEEE Cat No. 04EX821).

[24]  Zezhi Chen,et al.  Uncalibrated two-view metrology , 2004, Proceedings of the 17th International Conference on Pattern Recognition, 2004. ICPR 2004..

[25]  Louis Napoleon George Filon.  An Introduction to Projective Geometry , 2007 .

[26]  Hui Zhang,et al.  The common self-polar triangle of concentric circles and its application to camera calibration , 2015, 2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR).