In the two-view case, point matching constraints are represented by the fundamental matrix. In the three-view case, the point matching constraints are indirectly represented by three trifocal tensors corresponding to the three camera matrices. A direct representation of the point matching constraints can be obtained by applying suitable transformations on the trifocal tensors. This paper discus...

The Crossed-Slits (X-Slits) camera is defined by two nonintersecting slits, which replace the pinhole in the common perspective camera. Each point in space is projected to the image plane by a ray which passes through the point and the two slits. The X-Slits projection model includes the pushbroom camera as a special case. In addition, it describes a certain class of panoramic images, which are...

In this paper we develop a theory of linear differential systems analogous to the classical one for ODEs, including the obtaining of fundamental matrices, the development of a variation of parameters formula and the expression of the Green’s functions. We also derive interesting results in the case of differential equations with reflection and generalize the Hyperbolic Phasor Addition Formula t...

This paper presents an optimal linear algorithm for computing the fundamental matrix from corresponding points over two images under an assumed model, which admits independent Gaussian noise that is not necessarily isotropic or homogeneous. We derive a theoretical bound and demonstrate by experiments that our algorithm delivers results in the vicinity of the bound. Simulated and real-image exam...

Since for recognition tasks it is known that planar invariants are more easily obtained than others, decomposing a scene in terms of planar parts becomes very interresting. This paper presents a new approach to find the projections of planar surfaces in a pair of images. For this task we introduce the facet concept defined by linked edges (chains) and corners. We use collineations as projective...

In this paper, the geometric relationship between mosaic images for concentric panorama acquired by slit cameras along circular paths is considered. A concentric epipolar constraint is derived for mosaic images. It is shown how the concentric epipolar constraint can be used to calibrate the slit camera using point correspondences in two mosaic images. The concentric epipolar constraint is furth...

We propose a new constructive procedure to factorize the fundamental real matrix of a linear system of differential equations as the product of the exponentials of a symmetric and a skew-symmetric matrix. Both matrices are explicitly constructed as series whose terms are computed recursively. The procedure is shown to converge for sufficiently small times. In this way, explicit exponential repr...

The existence and uniqueness of a periodic solution of the system of differential equations d dt x(t) = A(t)x(t − ) are proved. In particular the Krasnoselskii’s fixed point theorem and the contraction mapping principle are used in the analysis. In addition, the notion of fundamental matrix solution coupled with Floquet theory is also employed.  

I Transformations and Projections 5 2 Camera Models 5 3 Plane to plane transformations 9 3.1 Plane projectivities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 3.2 Homogeneous line representation . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.3 Duality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.4 Projective tra...