A unified approach is presented for instantiating model and camera parameters in the verification process of visual recognition. Recognition implies the generation of a hypothesis, a map between projected model data and image data. An important part of the problem remaining is the instantiation of model and camera parameters to verify the hypothesis. We present this camera pose determination as a non-linear least squares problem, with functions minimizing distance between the projected model and image data. This approach treats both camera and model parameters as the same, simplifying the camera/sensor calibration problem. Coordinate trees with null components, an original data structure, models the objects in the image. This allows the calculation of analytical partial derivatives (with respect to the parameters of model and camera). We discuss objective model functions that best suit general applications. The incorporation of various numeric techniques is analyzed, with tables displaying convergence results for various models and parameters. Good convergence results are obtained and this method can be integrated into general vision applications. No depth information is required, and the algorithms also hold in noisy images, adding much robustness to our techniques. A natural extension of these techniques is to instantiate the parameters of generally constrained models.