ROBUST-DETECTION OF DEGENERATE CONFIGURATIONS WHILE ESTIMATING THE FUNDAMENTAL MATRIX

We present a new method for the detection of multiple solutions or deg eneracy when estimating the fundamental matrix, with specific emphasis on robustness to data contamination (mismatches), The fundamental mat rix encapsulates all the information on camera motion and internal par ameters 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 can not be accurately recovered and many solutions explain the data equall y 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 defi nition of degeneracy is given and all two-view nondegenerate and degen erate cases are catalogued in a logical way by introducing the languag e of varieties from algebraic geometry. It is then shown how each of t he cases can be robustly determined from image correspondences via a s coring function we develop, These ideas define a methodology which all ows the simultaneous detection of degeneracy and outliers. The method is called PLUNDER-DL and is a generalization of the robust estimator R ANSAC, The method is evaluated on many differing pairs of real images, In particular it is demonstrated that proper modeling of degeneracy i n the presence of outliers enables the detection of mismatches which w ould otherwise be missed. All processing including point matching, deg eneracy detection, and outlier detection is automatic. (C) 1998 Academ ic Press.