Trifocal Relative Pose from Lines at Points and its Efficient Solution

We present a new minimal problem for relative pose estimation mixing point features with lines incident at points observed in three views and its efficient homotopy continuation solver. We demonstrate the generality of the approach by analyzing and solving an additional problem with mixed point and line correspondences in three views. The minimal problems include correspondences of (i) three points and one line and (ii) three points and two lines through two of the points which is reported and analyzed here for the first time. These are difficult to solve, as they have 216 and - as shown here - 312 solutions, but cover important practical situations when line and point features appear together, e.g., in urban scenes or when observing curves. We demonstrate that even such difficult problems can be solved robustly using a suitable homotopy continuation technique and we provide an implementation optimized for minimal problems that can be integrated into engineering applications. Our simulated and real experiments demonstrate our solvers in the camera geometry computation task in structure from motion. We show that new solvers allow for reconstructing challenging scenes where the standard two-view initialization of structure from motion fails.Comment: This material is based upon work supported by the National Science Foundation under Grant No. DMS-1439786 while most authors were in residence at Brown University's Institute for Computational and Experimental Research in Mathematics -- ICERM, in Providence, R

Structure and motion estimation from complex features in three views

In this paper we introduce the notion of a quiver, which is a feature based on a point and a number of directions. We investigate the constraints different kinds of quivers pose on the camera geometry. In particular we study three types of quivers, having one, two and three directions respectively. For these quivers we investigate structure and motion estimation for two minimal cases. For 1-quivers, three such features seen in three affine views yields a (unique) linear solution. For three 3-quivers in three uncalibrated projective views we get up to twelve solutions, but simulations show that in most cases we get a unique solution. We also study two-quivers seen in three views, where simulations show that such features give more stable estimation of the trifocal tensor, as opposed to only using line or point information