In this paper we treat the problem of determining optimally (in the least-squares sense) the 3D coordinates of a point, given its noisy images formed by any number of cameras of known geometry. The optimality criterion is determined by the covariance matrices associated with the images of the point. The covariance matrices are not restricted to be positive definite but are allowed to be singular. Thus, image points constrained to lie along straight lines can be handled as well. Estimation of the covariance of the reconstructed point is provided. The often appearing two-camera stereo case is treated in detail. It is shown in this case that, under reasonable conditions, the main step of the reconstruction reduces to finding the unique zero of a sixth degree polynomial in the interval (0, 1).