Integrated self-calibration of single axis motion for three-dimensional reconstruction of roots

In this study, the authors present an integrated approach for recovering both the intrinsic and extrinsic parameters of a camera from the silhouettes and feature point tracking of an object in a turntable image sequence. Their motivation in taking the integrated approach is to solve the problem of obtaining the Euclidean three-dimensional (3D) reconstruction of cereal roots growing in gellan gum or objects immersed in water and imaged under turntable motion. The problem of self-calibration by previous approaches is especially difficult in this case as the initialisation of the rotation axis from the bi-tangent lines to the surface of revolution is not feasible. The conics projected from the circular trajectories of root tips are highly eccentric. Their approach is to initialise the axis of rotation l_s from the centre of the conics fitted to feature point trajectory. An estimate of l_s is then iteratively estimated by minimising an error function in estimating the harmonic homology introduced by the surface of symmetry. They compare the results of their approach to those of the maximum-likelihood estimation-based approach to conic fitting of point feature trajectories. They show results of real 3D reconstruction of roots, which are detailed enough for phenotypic analysis and are better both quantitatively and qualitatively than those using just feature point tracking.