This paper proposes a new scheme for multi-image projective reconstruction based on a projective grid space. The projective grid space is defined by two basis views and the fundamental matrix relating these views. Given fundamental matrices relating other views to each of the two basis views, this projective grid space can be related to any view. In the projective grid space as a general space ...

In this paper, we are going to answer the following question: assuming that we have estimates for the epipolar geometry and its uncertainty between two views, how probable it is that a new, independent point pair will satisfy the true epipolar geometry and be, in this sense, a feasible candidate correspondence pair? If we knew the true fundamental matrix, the answer would be trivial but in real...

The problem we study is; Given N views and a subset of the N2 interview fundamental matrices, which of the other fundamental matrices can we compute using only the precomputed fundamental matrices. This has applications in 3D reconstruction and when we want to reproject an area of one view on another, or to compute epipolar lines when the correspondence problem is too difficult to compute betwe...

As is well known, the fundamental matrix (I − P + eπ) plays an important role in the performance analysis of Markov systems, where P is the transition probability matrix, e is the column vector of ones, and π is the row vector of the steady state distribution. It is used to compute the performance potential (relative value function) of Markov decision processes under the average criterion, such...

Given an aperiodic random walk on a finite graph, an expression will be derived for the hitting times in terms of the eigenvalues of the transition matrix. The process of diagonalizing the transition matrix and its associated fundamental matrix will be discussed. These results will then be applied to a random walk on a rook graph. Lastly, a cover time bound depending on the hitting times will b...

A computer vision method is proposed to determine all the visible 3D planar surfaces in a scene from uncalibrated images and locate them in a single 3D projective space. Most of the existing methods for reconstructing planar objects use point correspondences to estimate the fundamental matrix and derive the compatible projection equations, before they apply the standard triangulation technique ...

—The aim of this work is twofold : a) it uses the fundamental matrix of the resolvent of a regular pencil in order to provide an algorithm for the computation of the fundamental matrix of the resolvent of a polynomial matrix, and b) it proposes a closed formula for the forward, backward and symmetric solution of an AutoRegressive Moving Average (ARMA). This closed formula is represented in term...

Those groups r which act properly discontinuously and aillnely on II?’ with compact fundamental domain are classified. First it is shown that such a group f contains a solvable subgroup of finite index, thus establishing a conjecture of Auslander in dimension three. Then unimodular simply transitive alTine actions on IR’ are classified; this leads to a classification of atTine crystallographic ...

Consider a system evolving according to an absorbing discretetime Markov chain with known transition matrix. The state of the system is observed at two points in time, separated by an unknown number of generations. We are interested in calculating the expected elapsed time and its variance. We provide a novel, exact solution, which is computable from the fundamental matrix of a related absorbin...

The Viewing Graph [1] represents several views linked by the corresponding fundamental matrices, estimated pairwise. Given a Viewing Graph, the tuples of consistent camera matrices form a family that we call the Solution Set. This paper provides a theoretical framework that formalizes different properties of the topology, linear solvability and number of solutions of multi-camera systems. We sy...