Related papers: The photography method: solving pentagon equation
Details for known solutions of some geometric and algebraic problems with the help of origami are presented: two theorems of Haga, the general cubic equation, especially the heptagon equation, doubling the cube as well as the trisection of…
The structure of the reconstruction algorithm OPED permits a natural way to generate additional data, while still preserving the essential feature of the algorithm. This provides a method for image reconstruction for limited angel problems.…
It was shown recently that the constraints on the initial data for Einstein's equations may be posed as an evolutionary problem [9]. In one of the proposed two methods the constraints can be replaced by a first order symmetrizable…
This paper describes the passage of light through a system of waveplates mathematically in terms of quaternions, an extension of the complex numbers, instead of the more usual Jones vectors and Jones matrices. Both the light beam and the…
We show that the transformation equation for the tardyon velocity involves two generic functions which in turn depend on the relative velocity of the involved reference frames, on the tardyon velocity u and on the polar angle which define…
The tridiagonal representation approach is an algebraic method for solving second order differential wave equations. Using this approach in the solution of quantum mechanical problems, we encounter two new classes of orthogonal polynomials…
In this paper, we study closed-form optimal solutions to two-view triangulation with known internal calibration and pose. By formulating the triangulation problem as $L_1$ and $L_\infty$ minimization of angular reprojection errors, we…
Finding, counting and/or listing triangles (three vertices with three edges) in large graphs are natural fundamental problems, which received recently much attention because of their importance in complex network analysis. We provide here a…
We consider the Standard Model with an extended scalar sector, and study the possible effects of the physics underlying such a model using an effective lagrangian parametrization. It is found that certain two photon processes offer windows…
Images are an important source of information for spacecraft navigation and for three-dimensional reconstruction of observed space objects. Both of these applications take the form of a triangulation problem when the camera has a known…
This survey aims to collect the main results of the theory of the set-theoretical solutions to the pentagon equation obtained up to now in the literature. In particular, we present some classes of solutions and raise some questions.
Flip graphs are a ubiquitous class of graphs, which encode relations induced on a set of combinatorial objects by elementary, local changes. Skeletons of associahedra, for instance, are the graphs induced by quadrilateral flips in…
Normals with unknown parameters (NUP) can be used to convert nontrivial model-based estimation problems into iterations of linear least-squares or Gaussian estimation problems. In this paper, we extend this approach by augmenting factor…
In this paper we present an efficient computational and symbolic algorithms for solving a backward pentadiagonal linear systems. The implementation of the algorithms using Computer Algebra Systems (CAS) such as MAPLE, MACSYMA, MATHEMATICA,…
First, we review existing attenuation models and discuss their causality properties, which we believe to be essential for algorithms for inversion with attenuated data. Then, we survey causality properties of common attenuation models. We…
We construct a function of the edge-lengths of a triangulated surface whose variation under a rescaling of all the edges that meet at a vertex is the defect angle at that vertex. We interpret this function as a gravitational effective…
In this paper we obtain cyclic pentagons and hexagons with rational sides, diagonals and area all of which are expressed in terms of rational functions of several arbitrary rational parameters. On suitable scaling, we obtain cyclic…
Given a surface $\Sigma$ equipped with a set $P$ of marked points, we consider the triangulations of $\Sigma$ with vertex set $P$. The flip-graph of $\Sigma$ whose vertices are these triangulations, and whose edges correspond to flipping…
Functional lifting methods provide a tool for approximating solutions of difficult non-convex problems by embedding them into a larger space. In this work, we investigate a mathematically rigorous formulation based on embedding into the…
Convexity prior is one of the main cue for human vision and shape completion with important applications in image processing, computer vision. This paper focuses on characterization methods for convex objects and applications in image…