We present an original multiple views method to perform a robust and detailed 3D reconstruction of a static scene from several images taken by one or more uncalibrated cameras. Making use only of fundamental matrices we are able to combine even heterogeneous video and/or photo sequences. In particular we give a characterization of camera matrices space consistent with a given fundamental matrix...

Human action recognition from videos draws tremendous interest in the past many years. In this work, we first find that the trifocal tensor resides in a twelve dimensional subspace of the original space if the first two views are already matched and the fundamental matrix between them is known, which we refer to as subtensor. Then we use the subtensor to perform the task of action recognition u...

Consider two views of a multi-body scene consisting of k planar bodies moving in pure translation one relative to the other. We show that the fundamental matrices, one per body, live in a 3-dimensional subspace, which when represented as a step-3 extensor is the common transversal on the collection of extensors defined by the homography matrices H1; :::; Hk of the moving planes. We show that as...

We propose a method for the recovery of projective shape and motion from multiple images of a scene by the factorization of a matrix containing the images of all points in all views. This factorization is only possible when the image points are correctly scaled. The major technical contribution of this paper is a practical method for the recovery of these scalings, using only fundamental matric...

This paper describes initial work on a family of projective reconstruction techniques that extract projection matrices directly and linearly from matching tensors estimated from image data. The simplest methods use fundamental matrices and epipoles, alternative ones use trilinear tensors. All of the data is treated uniformly, and there is no reliance on ‘privileged’ images or tokens. The approa...

The fundamental matrix solution of the quantum Knizhnik-Zamolodchikov equation associated with Uq(ŝl2) is constructed for |q| = 1. The formula for its determinant is given in terms of the double sine function.

We consider the fundamental matrix solution associated to piecewise smooth differential systems of Filippov type, in which the vector field varies discontinuously as solution trajectories reach one or more surfaces. We review the cases of transversal intersection and of sliding motion on one surface. We also consider the case when sliding motion takes place on the intersection of two or more su...

This work presents an automatic hybrid matching of central catadioptric and perspective images. It is based on the hybrid epipolar geometry. The goal is to obtain correspondences between an omnidirectional image and a conventional perspective image taken from different points of view. Mixing both kind of images has multiple applications, since an omnidirectional image captures many information ...

Two methods are given for the calculus of the fundamental matrix for the generalized linear differential equations on the Banach space of functions of bounded variation. The main result extends the Peano-Baker formula in this framework.

We discuss the geometry of rational maps from a projective space of an arbitrary dimension to the product of projective spaces of lower dimensions induced by linear projections. In particular, we give a purely algebro-geometric proof of the projective reconstruction theorem by Hartley and Schaffalitzky [HS09].