Multiperspective Modeling and Rendering Using General Linear Cameras

Abstract

We present a General Linear Camera (GLC) model that unifies many previous camera models into a single representation. The GLC model is capable of describing all perspective (pinhole), orthographic, and many multiperspective (including pushbroom and two-slit) cameras, as well as epipolar plane images. It also includes three new and previously unexplored multiperspective linear cameras. The GLC model is both general and linear in the sense that, given any vector space where rays are represented as points, it describes all 2D affine subspaces (planes) that can be formed by affine combinations of 3 rays. The incident radiance seen along the rays found on subregions of these 2D linear subspaces are a precise definition of a projected image of a 3D scene. We model the GLC imaging process in terms of two separate stages: the mapping of 3D geometry to rays and the sampling of these rays over an image plane. We derive a closed-form solution to projecting 3D points in a scene to rays in a GLC and a notion of GLC collineation analogous to pinhole cameras. Finally, we develop a GLC ray-tracer for the direct rendering of GLC images. The GLC ray-tracer is able to create a broad class of multiperspective effects and it provides flexible collineation controls to reduce multiperspective distortions.