The collinearity equation is used in photogrammetry

Photogrammetry

Photogrammetry is the practice of determining the geometric properties of objects from photographic images. Photogrammetry is as old as modern photography and can be dated to the mid-nineteenth century....

 and remote sensing

Remote sensing

Remote sensing is the acquisition of information about an object or phenomenon, without making physical contact with the object. In modern usage, the term generally refers to the use of aerial sensor technologies to detect and classify objects on Earth by means of propagated signals 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

Bundle adjustment

Given a set of images depicting a number of 3D points from different viewpoints, bundle adjustment can be defined as the problem of simultaneously refining the 3D coordinates describing the scene geometry as well as the parameters of the relative motion and the optical characteristics of the camera...

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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.