A Linear Mapping for Stereo Triangulation

A novel and computationally simple method is presented for triangulation of 3D points corresponding to the image coordinates in a pair of stereo images. The image points are described in terms of homogeneous coordinates which are jointly represented as the outer products of these homogeneous coordinates. This paper derives a linear transformation which maps the joint representation directly to the homogeneous representation of the corresponding 3D point in the scene. Compared to the other triangulation methods this approach gives similar reconstruction error but is numerically faster, since it only requires linear operations. The proposed method is projective invariant in the same way as the optimal method of Hartley and Sturm. The methods has a ”blind plane”; a plane through the camera focal points which cannot be reconstructed by this method. For ”forward-looking” camera configurations, however, the blind plane can be placed outside the visible scene and does not constitute a problem.