Related papers: On Some Properties of Calibrated Trifocal Tensors

Global methods to Structure from Motion have gained popularity in recent years. A significant drawback of global methods is their sensitivity to collinear camera settings. In this paper, we introduce an analysis and algorithms for averaging…

This paper proposes the geometric relationship of epipolar geometry and orientation- and scale-covariant, e.g., SIFT, features. We derive a new linear constraint relating the unknown elements of the fundamental matrix and the orientation…

The intersection matrix of a simplicial complex has entries equal to the rank of the intersection of its facets. In [1] the authors prove the intersection matrix is enough to determine a triangulation of a surface up to isomorphism. In this…

The goal of this paper is to generalize the theory of triangularizing matrices to linear transformations of an arbitrary vector space, without placing any restrictions on the dimension of the space or on the base field. We define a…

Correspondences between k-tuples of points are key in multiple view geometry and motion analysis. Regular transformations are posed by homographies between two projective planes that serves as structural models for images. Such…

In this article, we formulate necessary and sufficient polynomial equations for the existence of a symmetry plane or an order-two axial symmetry for a totally symmetric tensor of order n $\ge$ 1. These conditions are effective and of degree…

In this paper, we give a necessary and sufficient condition for an even order three dimensional strongly symmetric circulant tensor to be positive semi-definite. In some cases, we show that this condition is also sufficient for this tensor…

The process of camera calibration involves estimating the intrinsic and extrinsic parameters, which are essential for accurately performing tasks such as 3D reconstruction, object tracking and augmented reality. In this work, we propose a…

This paper is devoted to an intrinsic geometrical classification of three-mirror telescopes. The problem is formulated as the study of the connected components of a semi-algebraic set. Under first order approximation, we give the general…

Tightness of a triangulated manifold is a topological condition, roughly meaning that any simplexwise linear embedding of the triangulation into euclidean space is "as convex as possible". It can thus be understood as a generalization of…

Multi-view Geometry is reviewed from an Algebraic Geometry perspective and multi-focal tensors are constructed as equivariant projections of the Grassmannian. A connection to the principal minor assignment problem is made by considering…

(shortened) We determine the transformation matrix T that maps multiple images with resolved features onto one another and that is based on a Taylor-expanded lensing potential close to a point on the critical curve within our…

This paper considers the foundational question of the existence of a fundamental (resp. essential) matrix given $m$ point correspondences in two views. We present a complete answer for the existence of fundamental matrices for any value of…

In recent work, algebraic computational software was used to provide the exact algebraic conditions under which a sixtuple $\{F^{ij}\}$ of fundamental matrices, corresponding to $4$ images, will be compatible, i.e. there will exist cameras…

For a symmetric system, we want to study the problem of crossing an hypersurface in the neighborhood of a given point, when we suppose that all of the available vector fields are tangent to the hypersurface at the point. Classically one…

One of the apparent advantages of quantum computers over their classical counterparts is their ability to efficiently contract tensor networks. In this article, we study some implications of this fact in the case of topological tensor…

In this paper we give the new sufficient conditions of entanglement for multipartite qubit density matrixes. We discuss in detail the case for tripartite qubit density matrixes. As a criterion in concrete application, its steps are quite…

Recovering 3D human pose from multi-view imagery typically relies on precise camera calibration, which is often unavailable in real-world scenarios, thereby severely limiting the applicability of existing methods. To overcome this…

For a 4th order 3-dimensional symmetric tensor with its some entries $1$ or $-1$, we show the analytic sufficient and necessary conditions of its positive definiteness. By applying these conclusions, several strict inequalities is bulit for…

For a 4th order 3-dimensional cyclic symmetric tensor, a sufficient and necessary condition is bulit for its positive semi-definiteness. A sufficient and necessary condition of positive definiteness is showed for a 4th order $n$-dimensional…