A(t) is an hX« matrix with complex-valued elements which are measurable and bounded for ¿^0, and p is an «-vector with measurable, complex-valued elements. The norm of a vector (matrix) will be denoted by || -|| and is defined as the sum of the magnitudes of the elements. A vector (matrix) will be called bounded if its norm is bounded on i^O and convergent if its elements tend to finite limits ...

In this paper, we will introduce a common framework for the deenition and operations on the diierent multiple view tensors. The novelty of the proposed formulation is to not x any parameters of the camera matrices, but instead letting a group act on them and look at the diierent orbits. In this setting the multiple view geometry can be viewed as a four-dimensional linear manifold in IR 3m , whe...

In this paper, a generalization of the level dependent Quasi-Birth-and-Death (QBD) chains is presented. We analyze nested level dependent QBD chains and provide the complete characterization of their fundamental matrices in terms of minimal non-negative solutions of a number of matrix quadratic equations. Our results provide mixed matrix-geometric solution for the stationary distribution of nes...

Thas paper addresses the problem of computing the fundamental matrix which describes a geometric relationshzp between a pair of stereo images: the epipo1ar geometry. W e propose here a novel method based on virtual parallax. Instead of computing directely the 3 x 3 fundamental matrix, we compute a homography with one epipole position, and show that this is equivalent to compute the fundamental ...

A single-view matching constraint is described which represents a necessary condition which 6 points in an image must satisfy if they are the images of 6 known 3D points under an arbitrary projective transformation. Similar to the well-known matching constrains for two or more view, represented by fundamental matrices or trifocal tensors, single-view matching constrains are represented by tenso...

Various computer vision applications involve recovery and estimation of multiple motions from images of dynamic scenes. The exact nature of objects’ motions and the camera parameters are often not known a priori and therefore, the most general motion model (the fundamental matrix) is applied. Although the estimation of a fundamental matrix and its use for motion segmentation are well understood...

Abstract. We consider half–infinite triangular Toeplitz matrices with slow decay of the elements and prove under a monotonicity condition that the elements of the inverse matrix, as well as the elements of the fundamental matrix, decay to zero. We provide a quantitative description of the decay of the fundamental matrix in terms of p–norms. The results add to the classical results of Jaffard an...

For linear di erential algebraic equations of tractability index 1 the notion of the adjoint equation is analysed in full detail. Its solvability is shown at the lowest possible smoothness. The fundamental matrices of both equations are de ned and their relationships are characterized.

Epipolar geometry is the geometry situation of two cameras depicting the same scene. For un-calibrated cameras epipolar geometry is compactly described by the fundamental matrix. Estimation of the fundamental matrix is trivial if we have a set of corresponding points in the two images. Corresponding points are often found using e.g. the Harris interest point detector, but there are several adva...

This paper describes how the fundamental matrix, F , the trifocal tensor T jk i and the quadrilinear relationship existing between corresponding points in four uncalibrated projective images may be derived in a common framework involving matrix determinants. Part of the paper contains a derivation of previous results, and is intended as a summary and reformulation. The derivations are based on ...