Three-dimensional curve reconstruction from multiple images

In this study, the authors propose a new approach for reconstructing three-dimensional (3D) curves from multiple 2D images taken by uncalibrated cameras. The method is point based and does not require parameterisation of 2D or 3D curves. 2D curves are detected on multiple views as sequences of sampled points along the curves. A curve in 3D space is reconstructed as a sequence of 3D points sampled along the curve that minimise the geometric distances from their projections to the measured 2D curves on different images (i.e. 2D reprojection error). The minimisation problem is solved by an iterative algorithm which is guaranteed to converge to a (local) minimum of the 2D reprojection error. Without requiring calibrated cameras or additional point features, their method can reconstruct multiple 3D curves simultaneously from multiple images and it readily handles images with missing and/or partially occluded curves.