Reconstruction of Linearly Parameterized Models from Single Images with a Camera of Unknown Focal Length

Thumbnail Image
Penn collection
Departmental Papers (CIS)
Degree type
3D reconstruction
uncalibrated imagery
numerical optimization
Grant number
Copyright date
Related resources
Jelinek, David

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. 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.

Date Range for Data Collection (Start Date)
Date Range for Data Collection (End Date)
Digital Object Identifier
Series name and number
Publication date
Journal title
Volume number
Issue number
Publisher DOI
Journal Issue
Copyright 2001 IEEE. Reprinted from IEEE Transactions on Pattern Analysis and Machine Intelligence, Volume 23, Issue 7, July 2001, pages 767-773. Publisher URL: sNumber=20256&puNumber=34 This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of the University of Pennsylvania's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to By choosing to view this document, you agree to all provisions of the copyright laws protecting it.
Recommended citation