Camera Self-Calibration Using the Kruppa Equations and the SVD of the Fundamental Matrix: The Case of Varying Intrinsic Parameters

Estimation of the camera intrinsic calibration parameters is a prerequisite to a wide variety of vision tasks related to motion and stereo analysis. A major breakthrough related to the intrinsic calibration problem was the introduction in the early nineties of 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. Until recently, however, most research efforts have been focused on applying the autocalibration paradigm to estimating constant intrinsic calibration parameters. Therefore, such approaches are inapplicable to cases where the intrinsic parameters undergo continuous changes due to focusing and/or zooming. In this paper, our previous work for autocalibration in the case of constant camera intrinsic parameters is extended and a novel autocalibration method capable of handling variable intrinsic parameters is proposed. The 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, a purely algebraic derivation is proposed here which provides a straightforward answer to the problem of determining which constraints to employ among the set of available ones. Additionally, the new formulation does not employ the epipoles, which are known to be difficult to estimate accurately. The intrinsic calibration parameters are recovered from the This work was funded in part under the VIRGO research network (EC Contract No ERBFMRX-CT96-0049) of the TMR Programme. 2 Manolis I.A. LOURAKIS and Rachid DERICHE developed constraints through a nonlinear minimization scheme that explicitly takes into consideration the uncertainty associated with the estimates of the employed fundamental matrices. Detailed experimental results using both simulated and real image sequences demonstrate the feasibility of the approach. Key-words: Self-Calibration, Varying Intrinsic Parameters, Kruppa Equations, 3D Reconstruction, Motion Analysis, Stereo, Structure from Motion.