Closed-Form Expression for Focal Lengths from the Fundamental Matrix

We describe an algorithm for decomposing a fundamental matrix computed from point correspondences over two images into the focal lengths of the two images and the camera motion parameters in a closed-form expression. Our algorithm is based on the decomposability condition of the essential matrix expressed in terms of its scalar invariants. We give a complete analysis for degenerate camera con gurations. We also describe an algorithm for computing a single focal length in the degenerate case and analyze the indeterminacy condition.