We present theories of multiperspective projection and collineation. Given an arbitrary multiperspective imaging system that captures smoothly varying set of rays, we show how to map the rays onto a 2D ray manifold embedded in a 4D linear vector space. The characteristics of this imaging system, such as its projection, collineation, and image distortions can be analyzed by studying the 2-D tangent planes of this ray manifold. These tangent planes correspond to the recently proposed General Linear Camera (GLC) model.

In this paper, we study the imaging process of the GLCs. We show the GLC imaging process can be broken down into two separate stages: the mapping of 3D geometry to rays and the sampling of those rays over an image plane. We derive a closed-form solution to projecting 3D points in a scene to rays in a GLC. A GLC image is created by sampling these rays over an image plane. We develop a notion of GLC collineation analogous to pinhole cameras. GLC collineation describes the transformation between the images of a single GLC due to changes in sampling and image plane selection. We show that general GLC collineations can be characterized by a quartic (4th order) rational function. GLC projection and collineation provides a basis for developing new computer vision algorithms suitable for analyzing a wider range of imaging systems than current methods, based on simple pinhole projection models, permit.