Camera Self-Calibration and the Fundamental Matrix

Dr. Stephen Dow

Department of Mathematics
University of Alabama in Huntsville

April 7, 2000

Abstract

A central focus of photogrammetry is the extraction of 3D locations of points from their imaged 2D positions on a stereo pair of photographs. Given two corresponding 2D positions, the 3D location is easily computed as a ray intersection, provided certain parameters describing the internal geometry of the camera and specifying the relative position and orientation of the two camera locations are known. These two sets of parameters are traditionally called interior orientation and relative orientation. The process of determining the interior orientation is called camera calibration. Traditionally it is done as a separate setup step by photographing a calibration object having a set of control points with known coordinates. However, methods have recently been developed for performing self-calibration, in which the camera parameters are determined directly from a series of images not containing a calibration object. The recent methods depend on equations involving the fundamental matrix, a 3 × 3 matrix which neatly encapsulates the parameters of a stereo pair. In this talk we will present the basic equations involving the fundamental matrix and survey work on how it may be used for self calibration.