Collinearity equation

The collinearity equation is used in photogrammetry and remote sensing to relate coordinates in a sensor plane (in two dimensions) to object coordinates (in three dimensions).

The most obvious use of these equations is for images recorded by a camera. In this case the equation describes transformations from object space (X, Y, Z) to image coordinates (x, y). It forms the basis for the equations used in bundle adjustment. They indicate that the image point (on the sensor plate of the camera), the observed point (on the object) and the projection center of the camera were aligned when the picture was taken.