A Computer Algorithm for Reconstructing a Scene from Two Satellite Images

A new camera model for transforming object space coordinates into image coordinates as affected by a push-broom sensor traveling in a straight line is described. It is shown that this transformation can be encoded in a 3 × 4 matrix M representing a non-linear Cremona transformation of object space into image space. Significantly, unlike other known models for satellite cameras, M can be estimated without recourse to iterative techniques. Experimental results demonstrate that the proposed model is quite accurate even for push-broom cameras in low-earth orbits (e.g. SPOT and LANDSAT). A 4 × 4 matrix Q, christened hyperbolic essential matrix, that contains the relative camera models in a stereo setting, is derived. The matrix Q is similar in spirit to that derived by Longuet-Higgins [?]. However, unlike the latter, it represents the non-linear transformation of a point [u1, v1] in the first image to its corresponding hyperbolic epipolar curve in the second image. A linear method for computing Q from image correspondences is described. It is shown that from two images, the camera models and the corresponding 3-D points can be determined only up to an affine transformatin of 3-D object space and this is the best that can be done in the absence of any ground-truth. If 6 or more ground control points, visible in both images, are provided the stereo problem can be solved using only linear techniques.