Ray geometry in non-pinhole cameras: a survey

Abstract

A pinhole camera collects rays passing through a common 3D point and its image resembles what would be seen by human eyes. In contrast, a non-pinhole (multiperspective) camera combines rays collected by different viewpoints. Despite their incongruity of view, their images are able to preserve spatial coherence and can depict, within a single context, details of a scene that are simultaneously inaccessible from a single view, yet easily interpretable by a viewer. In this paper, we thoroughly discuss the design, modeling, and implementation of a broad class of nonpinhole cameras and their applications in computer graphics and vision. These include mathematical (conceptual) camera models such as the General Linear Cameras and real non-pinhole cameras such as catadioptric cameras and projectors. A unique component of this paper is a ray geometry analysis that uniformly models these non-pinhole cameras as manifolds of rays and ray constraints. We also model the thin lens as a ray transform and study how ray geometry is changed by the thin lens for studying distortions and defocusing. We hope to provide mathematical fundamentals to satisfy computer vision researchers as well as tools and algorithms to aid computer graphics and optical engineering researchers.

A Camera Model for Line-Scan Cameras with Telecentric Lenses

“…Thus, with respect to the taxonomy by Sturm et al (2010), line-scan cameras with telecentric lenses are central cameras (Sturm et al 2010, Section 3), unlike line-scan cameras with entocentric lenses, which are axial cameras (Ramalingam et al 2006;Sturm et al 2010, Section 3.1.4). Furthermore, with respect to the taxonomy by Ye and Yu (2014), line-scan cameras with telecentric lenses are orthographic cameras and not pushbroom cameras.…”

Saliency Detection on Light Field

“…Using the focal stack, we can fuse an all-focus image, e.g., through photomontage [2]. We refer the readers to the comprehensive survey on light field imaging [19,36] for more details about the refocusing algorithm.…”

General Models for Rational Cameras and the Case of Two-Slit Projections

“…Our study of canonical forms and calibration matrices in Section 3 also leads to a natural definition of essential tensors: for example, an essential tensor could be defined by (22) where (A 1 , A 2 ), (B 1 , B 2 ) are all of the form (16) with K 1 , K 2 being the identity. Proposition 1 then guarantees that for any pair of "parallel" two-slit cameras as in (14), we can uniquely write the epipolar tensor as 25) where E ijkl is an essential tensor. This closely resembles the analogous decomposition of fundamental matrices.…”

“…1 All retinas are projectively equivalent, and thus the essential part of the imaging process is the map λ Lc : P 3 \ c → L c associating a point with the corresponding visual ray in the bundle L c of all lines through the pinhole c [17]. Similarly, many non-central cameras can be imagined (and actually constructed [21,22,25]) by replacing the line bundle L c with a more general family of lines. For example, Pajdla [14] and Batog et al [2] have considered cameras that are associated with linear congruences, i.e., twodimensional families of lines that obey linear constraints.…”