Over the past decade there has been a rapid development in the understanding and modelling of the geometry of multiple views in computer vision. The theory and practice have now reached a level of maturity where excellent results can be achieved for problems that were certainly unsolved a decade ago, and often thought unsolvable. These tasks and algorithms include:

• Given two images, and no other information, compute matches between the images, and the 3D position of the points that generate these matches and the cameras that generate the images.

• Given three images, and no other information, similarly compute the matches between images of points and lines, and the position in 3D of these points and lines and the cameras.

• Compute the epipolar geometry of a stereo rig, and trifocal geometry of a trinocular rig, without requiring a calibration object.

• Compute the internal calibration of a camera from a sequence of images of natural scenes (i.e. calibration “on the fly”).

The distinctive flavour of these algorithms is that they are uncalibrated – it is not necessary to know or first need to compute the camera internal parameters (such as the focal length).

Underpinning these algorithms is a new and more complete theoretical understanding of the geometry of multiple uncalibrated views: the number of parameters involved, the constraints between points and lines imaged in the views; and the retrieval of cameras and 3-space points from image correspondences.