In perspective cameras, images of a frontal-parallel 3D object preserve its aspect ratio invariant to its depth. Such an invariance is useful in photography but is unique to perspective projection. In this paper, we show that alternative non-perspective cameras such as the crossed-slit or XSlit cameras exhibit a different depth-dependent aspect ratio (DDAR) property that can be used to 3D recovery. We first conduct a comprehensive analysis to characterize DDAR, infer object depth from its AR, and model recoverable depth range, sensitivity, and error. We show that repeated shape patterns in real Manhattan World scenes can be used for 3D reconstruction using a single XSlit image. We also extend our analysis to model slopes of lines. Specifically, parallel 3D lines exhibit depth-dependent slopes (DDS) on their images which can also be used to infer their depths. We validate our analyses using real XSlit cameras, XSlit panoramas, and catadioptric mirrors. Experiments show that DDAR and DDS provide important depth cues and enable effective single-image scene reconstruction.
We analyze the geometry of the two-slit camera and come to two conclusions. First, we show that the definition given [9] makes sense only if the two slits are not intersecting. Secondly, we prove that the complete image from a two-slit camera cannot be obtained as an intersection of the rays of the two-slit camera with a plane in space. Motivated by the quest for a unified representation of various cameras by simple geometrical objects, we give a new definition of linear oblique cameras as those which comprise all real lines incident with some non-real line and show that it is equivalent with the definition we gave earlier. We also show that no single line neither in the real projective space nor in its coplexification, can be used to define analogously a two-slit camera. We introduce anew kind of mosaicing, where the position of the sampling strip varies as a function of the input camera location. The new images that are generated this way correspond to a new projection model defined by two slits, termed here the Crossed-Slits (X-Slits) projection. In this projection model, every 3D point is projected by a ray defined as the line that passes through that point and intersects the two slits. The intersection of the projection rays with the imaging surface defines the image. X-Slits mosaicing provides two benefits. First, the generated mosaics are closer to perspective images than traditional pushbroom mosaics. Second, by simple manipulations of the strip sampling function, we can change the location of one of the virtual slits, providing a virtual walkthrough of a X-Slits camera; all this can be done without recovering any 3D geometry and without calibration. A number of examples where we translate the virtual camera and change its orientation are given; the examples demonstrate realistic changes in parallax, reflections, and occlusions. A theory of stereo image formation is presented that enables a complete classification of all possible stereo views, including non-perspective varieties. Towards this end, the notion of epipolar geometry is generalized to apply to multiperspective images. It is shown that any stereo pair must consist of rays lying on one of three varieties of quadric surfaces. A unified representation is developed to model all classes of stereo views, based on the concept of a quadric view. The benefits include a unified treatment of projection and triangulation operations for all stereo views. The framework is applied to derive new types of stereo image representations with unusual and useful properties. Traditional stereo matching assumes perspective viewing cameras under a translational motion: the second camera is translated away from the first one to create parallax. In this paper, we investigate a different, rotational stereo model on a special multi-perspective camera, the XSlit camera [9, 24]. We show that rotational XSlit (R-XSlit) stereo can be effectively created by fixing the sensor and slit locations but switching the two slits' directions. We first derive the epipolar geometry of R-XSlit in the 4D light field ray space. Our derivation leads to a simple but effective scheme for locating corresponding epipolar "curves". To conduct stereo matching, we further derive a new disparity term in our model and develop a patch-based graph-cut solution. To validate our theory, we assemble an XSlit lens by using a pair of cylindrical lenses coupled with slit-shaped apertures. The XSlit lens can be mounted on commodity cameras where the slit directions are adjustable to form desirable R-XSlit pairs. We show through experiments that R-XSlit provides a potentially advantageous imaging system for conducting fixed-location, dynamic baseline stereo.  This paper addresses the problem of characterizing a general class of cameras under reasonable, “linear” assumptions. Concretely, we use the formalism and terminology of classical projective geometry to model cameras by two-parameter linear families of straight lines-that is, degenerate reguli (rank-3 families) and non-degenerate linear congruences (rank-4 families). This model captures both the general linear cameras of Yu and McMillan and the linear oblique cameras of Pajdla. From a geometric perspective, it affords a simple classification of all possible camera configurations. From an analytical viewpoint, it also provides a simple and unified methodology for deriving general formulas for projection and inverse projection, triangulation, and binocular and trinocular geometry. 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. Our 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 affine subspaces are a precise definition of a projected image of a 3D scene. The GLC model also provides an intuitive physical interpretation, which can be used to characterize real imaging systems. Finally, since the GLC model provides a complete description of all 2D affine subspaces, it can be used as a tool for first-order differential analysis of arbitrary (higher-order) multiperspective imaging systems.