Single Axis Geometry by Fitting Conics

In this paper, we describe a new approach for recovering 3D geometry from an uncalibrated image sequence of a single axis (turntable) motion. Unlike previous methods, the computation of multiple views encoded by the fundamental matrix or trifocal tensor is not required. Instead, the new approach is based on fitting a conic locus to corresponding image points over multiple views. It is then shown that the geometry of single axis motion can be recovered given at least two such conics. In the case of two conics the reconstruction may have a two fold ambiguity, but this ambiguity is removed if three conics are used. The approach enables the geometry of the single axis motion (the 3D rotation axis and Euclidean geometry in planes perpendicular to this axis) to be estimated using the minimal number of parameters. It is demonstrated that a Maximum Likelihood Estimation results in measurements that are as good as or superior to those obtained by previous methods, and with a far simpler algorithm. Examples are given on various real sequences, which show the accuracy and robustness of the new algorithm.