Perturbation Analysis of the 8-Point Algorithm: A Case Study for Wide FoV Cameras

Thiago L. T. da Silveira, Claudio R. Jung; Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2019, pp. 11757-11766

This paper presents a perturbation analysis for the estimate of epipolar matrices using the 8-Point Algorithm (8-PA). Our approach explores existing bounds for singular subspaces and relates them to the 8-PA, without assuming any kind of error distribution for the matched features. In particular, if we use unit vectors as homogeneous image coordinates, we show that having a wide spatial distribution of matched features in both views tends to generate lower error bounds for the epipolar matrix error. Our experimental validation indicates that the bounds and the effective errors tend to decrease as the camera Field of View (FoV) increases, and that using the 8-PA for spherical images (that present 360degx180deg FoV) leads to accurate essential matrices. As an additional contribution, we present bounds for the direction of the translation vector extracted from the essential matrix based on singular subspace analysis.