Fast multiple-view L2 triangulation with occlusion handling

Multiple-view L2 triangulation is a key problem in computer vision. This paper addresses the standard case where all image points are available, and the case where some image points are not available. In the latter case, it is supposed that the unknown image point belongs to a known region such as a line segment or an ellipse, as it happens for instance due to occlusions. For this problem we propose two methods based on linear matrix inequalities (LMIs). The first method, named TFML, exploits the fundamental matrix and is fast (the average computational time with two and three-views is 0.01 and 0.05 s on Matlab) at the expense of possible conservatism, which however it is shown to occur rarely in practice, and which can be immediately detected. The second method, named TPML, exploits the projection matrix, is slower, but allows one to reduce the conservatism by using techniques for optimization over polynomials. Various examples with synthetic and real data illustrate the proposed strategy.

Research highlights
► Image points allowed to be uncertain on line segments and ellipses.
► Fast computation of a candidate solution via convex optimization.
► Optimality can be immediately established.
► Non-optimal cases are rare with real data.
► When non-optimal, conservatism can be reduced by increasing the numerical complexity.