Homogeneous Coordinates
The mapping from 3D coordinates of points in space to 2D image coordinates can also be represented in homogeneous coordinates. Let be a representation of a 3D point in homogeneous coordinates (a 4-dimensional vector), and let be a representation of the image of this point in the pinhole camera (a 3-dimensional vector). Then the following relation holds
where is the camera matrix and the means equality between elements of projective spaces. This implies that the left and right hand sides are equal up to a non-zero scalar multiplication. A consequence of this relation is that also can be seen as an element of a projective space; two camera matrices are equivalent if they are equal up to a scalar multiplication. This description of the pinhole camera mapping, as a linear transformation instead of as a fraction of two linear expressions, makes it possible to simplify many derivations of relations between 3D and 2D coordinates.
Read more about this topic: Pinhole Camera Model
Famous quotes containing the word homogeneous:
“O my Brothers! love your Country. Our Country is our home, the home which God has given us, placing therein a numerous family which we love and are loved by, and with which we have a more intimate and quicker communion of feeling and thought than with others; a family which by its concentration upon a given spot, and by the homogeneous nature of its elements, is destined for a special kind of activity.”
—Giuseppe Mazzini (1805–1872)