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We propose an approach to solving the Kruppa equations for camera self-calibration. Traditionally, the unknown scale factors in the Kruppa equations are eliminated first, leading to a set of nonlinear constraints. Instead, we determine the scale factors by a Levenberg-Marquardt optimization or genetic optimization technique first. Then, the camera's intrinsic parameters are derived from the resulting linear constraints. Extensive simulations as well as experiments with real images verify that the above technique is both accurate and robust.