Reconstruction of linearly parameterized models from single images with a camera of unknown focal length

This paper deals with the problem of recovering the dimensions of an object and its pose from a single image acquired with a camera of unknown focal length. It is assumed that the object in question can be modeled as a polyhedron where the coordinates of the vertices can be expressed as a linear function of a dimension vector, λ. The reconstruction program takes as input a set of correspondences between features in the model and features in the image. From this information the program determines an appropriate projection model for the camera (scaled orthographic or perspective), the dimensions of the object, its pose relative to the camera and, in the case of perspective projection, the focal length of the camera. We demonstrate that this reconstruction task can be framed as an unconstrained optimization problem involving a small number of variables, no more than four, regardless of the number of parameters in the dimension vector