Robust detection of degenerate configurations while estimating the fundamental matrix

Journal article

We present a new method for the detection of multiple solutions or degeneracy when estimating thefundamental matrix, with specific emphasis on robustness to data contamination (mismatches). The fundamental matrix encapsulates all the information on camera motion and internal parameters available from image feature correspondences between two views. It is often used as a first step in structure from motion algorithms. If the set of correspondences is degenerate, then this structure cannot be accurately recovered and many solutions explain the data equally well. It is essential that we are alerted to such eventualities. As current feature matchers are very prone to mismatching the degeneracy detection method must also be robust to outliers.

In this paper a definition of degeneracy is given and all two-view nondegenerate and degenerate cases are catalogued in a logical way by introducing the language of varieties from algebraic geometry. It is then shown how each of the cases can be robustly determined from image correspondences via a scoring function we develop. These ideas define a methodology which allows the simultaneous detection of degeneracy and outliers. The method is called PLUNDER-DL and is a generalization of the robust estimator RANSAC.

The method is evaluated on many differing pairs of real images. In particular it is demonstrated that proper modeling of degeneracy in the presence of outliers enables the detection of mismatches which would otherwise be missed. All processing including point matching, degeneracy detection, and outlier detection is automatic.

Authors: Torr, PHS; Zisserman, A; Maybank, SJ

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Elsevier
• Journal: Computer Vision and Image Understanding
• Volume: 71
• Issue: 3
• Pages: 312-333
• Publication date: 1998-09-01
• Acceptance date: 1996-11-01
• DOI: 10.1006/cviu.1997.0559
• EISSN: 1090-235X
• ISSN: 1049-9660
• Language: English
• Keywords: SBTMR; robust methods; model selection; degeneracy; motion analysis; fundamental matrix; MDL; epipolar geometry