Camera Self-Calibration Using the Singular Value Decomposition of the Fundamental Matrix: From Point Correspondences to 3D Measurements

This paper deals with a fundamental problem in motion and stereo analysis, namely that of determining the camera intrinsic calibration parameters. A novel method is proposed that follows the autocalibration paradigm, according to which calibration is achieved not with the aid of a calibration pattern but by observing a number of image features in a set of successive images. The proposed method relies upon the Singular Value Decomposition of the fundamental matrix, which leads to a particularly simple form of the Kruppa equations. In contrast to the classical formulation that yields an over-determined system of constraints, the derivation proposed here provides a straightforward answer to the problem of determining which constraints to employ among the set of available ones. Moreover, the derivatio- n is a purely algebraic one, without a need for resorting to the somewhat non-intuitive geometric concept of the \em absolute conic. Apart from the fundamental matrix itself, no other quantities that can be extracted from it (e.g. the epipoles) are needed for the derivation. Experimental results from extensive simulations and several image sequences demonstrate the effectiveness of the proposed method in accurately estimating the intrinsic calibration matrices. It is also shown that the computed intrinsic calibration matrices are sufficient for recovering 3D motion and performing metric measurements from uncalibrated images.