The Surface Model

Using digital cameras for measurement purposes requires the knowledge of the mapping between 3D world points and 2D positions on the image plane. There are many different mathematical models that provide this mapping for a specific imaging system. Grossberg and Nayar proposed a discrete generic camera model, which does not make any assumptions about the structure of this system. The model describes a digital camera by assigning an arbitrary viewing ray to each pixel of the camera image. This makes the model applicable to any kind of camera, especially also to non-central ones like onmidirectional catadioptrics. However, this model is difficult to use in practice, as there is no direct method for mapping a 3D point to the image or determining rays for subpixel image positions.
In this work, the Surface Model, an uncertain continuous representation of the generic camera model, will be introduced. It uses a spline surface in 6D Plücker space to describe the camera. The interpolation abilities of the spline surface allow the viewing ray and its uncertainty for any (subpixel) position to be easily determined. Furthermore, the description facilitates the mapping from 3D world points to the image.
The calibration of the generic model has to be performed pixel-wise and is technically involved and time-consuming. In this work, hand-held sparse planar chessboard patterns are used for calibration. The uncertainties of the corresponding image point measurements are taken into account and propagated during the complete calibration procedure to obtain an uncertain model. Simulations prove the validity of each step and the practical applicability of the procedure is shown by calibrating several real cameras of different types.