The developments in optical metrology and computer vision require more and more advanced camera models. Their geometric calibration is of essential importance. Usually, low-dimensional models are used, which however often have insufficient accuracy for the respective applications. A more sophisticated approach uses the generalized camera model. Here, each pixel is described individually by its geometric ray properties. Our efforts in this article strive to improve this model. Hence, we propose a new approach for calibration. Moreover, we show how the immense number of parameters can be efficiently calculated and how the measurement uncertainties of reference features can be effectively utilized. We demonstrate the benefits of our method through an extensive evaluation of different cameras, namely a standard webcam and a microlens-based light field camera.