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3x4 Projection Matrix

There are three coordinate systems involved --- camera, image and world.

  1. Camera: perspective projection.

    This can be written as a linear mapping between homogeneous coordinates (the equation is only up to a scale factor):

    where a projection matrix represents a map from 3D to 2D.

  2. Image: (intrinsic/internal camera parameters)

    is a upper triangular matrix, called the camera calibration matrix:

    where , .

  3. World: (extrinsic/external camera parameters)
    The Euclidean transformation between the camera and world coordinates is :

Finally, concatenating the three matrices,

which defines the projection matrix from Euclidean 3-space to an image:

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