Triangulation

Richard Hartley (1) , Peter Sturm (2)

1 Austalian National University
2 MOVI - Modeling, localization, recognition and interpretation in computer vision

In this paper, we consider the problem of finding the position of a point in space given its position in two images taken with cameras with known calibration and pose. This process requires the intersection of two known rays in space, and is commonly known as triangulation. In the absence of noise, this problem is trivial. When noise is present, the two rays will not generally meet, in which case it is necessary to find the best point of intersection. This problem is especially critical in affine and projective reconstruction in which there is no meaningful metric information about the object space. It is desirable to find a triangulation method that is invariant to projective transformations of space. This paper solves that problem by assuming a Gaussian noise model for perturbation of the image coordinates. A non-iterative solution is given that finds a global minimum. Extensive comparisons of the new method with several other methods show that it consistently gives superior results.

Richard Hartley, Peter Sturm. Triangulation. 6th International Conference on Computer Analysis of Images and Patterns (CAIP '95), Sep 1995, Prague, Czech Republic. pp.190-197, ⟨10.1007/3-540-60268-2_296⟩. ⟨inria-00525713⟩