Abstract—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, $\lambda$. 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. This paper describes how the reconstruction problem can be framed as an optimization over a compact set with low dimension—no more than four. This optimization problem can be solved efficiently by coupling standard nonlinear optimization techniques with a multistart method which generates multiple starting points for the optimizer by sampling the parameter space uniformly. The result is an efficient, reliable solution system that does not require initial estimates for any of the parameters being estimated.