Trifocal Relative Pose from Lines at Points and its Efficient Solution

Abstract

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.

PL$$_1$$P - Point-Line Minimal Problems Under Partial Visibility in Three Views

“…Our implementation in Macaulay2 [54,55] is similar to that used in prior work [32]. The next result shows that there are many interesting problems with small degrees that are solvable with existing solving technology [56,38].…”

“…These restrictions make the task of enumerating problems tractable while making it still possible to account for very practical incidence cases where several existing feature detectors are applicable. For instance, SIFT [36] and LAF [37] provide quivers (points with one direction attached), which can be interpreted as lines through the points and used to compute relative camera poses [38].…”

PLMP - Point-Line Minimal Problems in Complete Multi-View Visibility

“…We characterized a new class of minimal problems and discovered problems with small numbers of solutions that call for constructing their efficient solvers [12].…”