Degeneracy of the Linear Seventeen-Point Algorithm for Generalized Essential Matrix

Abstract

In estimating motions of multi-centered optical systems using the generalized camera model, one can use the linear seventeen-point algorithm for obtaining a generalized essential matrix, the counterpart of the eight-point algorithm for the essential matrix of a pair of cameras. Like the eight-point algorithm, the seventeen-point algorithm has degenerate cases. However, mechanisms of the degeneracy of this algorithm have not been investigated. We propose a method to find degenerate cases of the algorithm by decomposing a measurement matrix that is used in the algorithm into two matrices about ray directions and centers of projections. This decomposition method allows us not only to prove degeneracy of the previously known degenerate cases, but also to find a new degenerate configuration.