next up previous
Next: The Fundamental Matrix Up: No Title Previous: Homogeneous Notation Interlude

The Essential Matrix

There are two camera coordinate systems, related by a rotation and a translation :

Taking the vector product with , followed by the scalar product with

which expresses that the vectors , and are coplanar. Using

gives a relation between image points in the camera coordinate systems, . This can be written , where

is the Essential matrix. This is the algebraic representation of epipolar geometry for known calibration.

Then using the calibration matrices to relate the image point in pixels to the point in the camera coordinate system:

which defines the Fundamental matrix, by


Bob Fisher
Wed Apr 16 00:58:54 BST 1997