Recently, a number of new and interesting image acquisition techniques appeared, e.g. pushbroom cameras, stereo panoramas, omnivergent mosaics, and spherical mosaics. These image acquisition techniques often acquire large number of images from a moving camera and then choose some pixels from each image to form a mosaic. Since the cameras move, the rays corresponding to individual pixels of the mosaics do not pass through one center of projection. Instead, they may be incident to, e.g., a line, a circle, or a sphere. Such mosaic can be so viewed as images taken by a non-central camera, a camera that does not have a center of projection.

The mosaics can be, and actually are, used to reconstruct scenes because they posses the important advantage compared to classical pinhole cameras that almost complete surrounding is seen from each viewpoint. However, the mosaic stereo geometry can be rather complicated, depending on the way the mosaic was acquired.

We study stereo geometries of non-central cameras that allow to reconstruct scenes from multiple mosaics. We show that in order to reduce the correspondence search to one-dimensional search along curves in mosaics (which are analogous to epipolar lines) the rays of the cameras have to lie in double ruled surfaces (which are analogous to epipolar planes).

The double ruled surfaces can intersect themselves in complicated ways. We make a classification of possible stereo geometries w.r.t. the size of the intersection set, starting from the classical epipolar geometry (all rays from one camera intersect in a projection center), going over the epilinear geometries (rays from one camera intersect on curves, e.g. lines, circles, conics), and ending, maybe surprisingly, at the oblique geometry (rays from one camera do not intersect at all).

We further analyze the extreme situation of the oblique geometry where the rays from one non-classical camera do not intersect. We show that oblique cameras exist, give an example of a physically realizable oblique camera, and characterize those oblique cameras, which are given by collineations in three-dimensional real projective space. We also show that the oblique cameras generated by collineations can be understood as a generalization of central cameras.