相关论文: Equivalence of Two Expressions of Principal Line

The objective of this paper is to rectify any monocular image by computing a homography matrix that transforms it to a bird's eye (overhead) view. We make the following contributions: (i) we show that the homography matrix can be…

We present a complete classification of all minimal problems for generic arrangements of points and lines completely observed by calibrated perspective cameras. We show that there are only 30 minimal problems in total, no problems exist for…

It is well known that a purely inseparable field extension $L/F$ with some extra property and degree $[L:F]=4$ determines a Clifford parallelism on the set of lines of the three-dimensional projective space over $F$. By extending the ground…

The goal of the proposed method is to directly obtain a pose matrix of a known rectangular target, without estimation, using geometric techniques. This method is specifically tailored for real-time, extreme imaging setups exceeding…

We study algebraic varieties associated with the camera resectioning problem. We characterize these resectioning varieties' multigraded vanishing ideals using Gr\"obner basis techniques. As an application, we derive and re-interpret…

A recent paper showed how to find sets of finite affine or projective planes constructed on a common set of points, so that lines of one plane meet lines of a different plane in at most two points. In this paper, those results are…

Five equivalence classes had been found for systems of two second-order ordinary differential equations, transformable to linear equations (linearizable systems) by a change of variables. An "optimal (or simplest) canonical form" of linear…

In topological data analysis, two-parameter persistence can be studied using the representation theory of the 2d commutative grid, the tensor product of two Dynkin quivers of type A. In a previous work, we defined interval approximations…

We present a derivation for estimating the roll and pitch orientation of a partially calibrated camera mounted above a planar surface, using minimal scene information. Specifically, we assume known intrinsic parameters and a fixed height…

Lie's linearizability criteria for scalar second-order ordinary differential equations had been extended to systems of second-order ordinary differential equations by using geometric methods. These methods not only yield the linearizing…

The structured light projection technique is a representative active method for 3-D reconstruction, but many researchers face challenges with the intricate projector calibration process. To address this complexity, we employs an additional…

Generalized eigenvalue problems involving a singular pencil may be very challenging to solve, both with respect to accuracy and efficiency. While Part I presented a rank-completing addition to a singular pencil, we now develop two…

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…

We study the challenging problem of estimating the relative pose of three calibrated cameras from four point correspondences. We propose novel efficient solutions to this problem that are based on the simple idea of using four…

Accurate calibration of camera intrinsic parameters is crucial to various computer vision-based applications in the fields of intelligent systems, autonomous vehicles, etc. However, existing calibration schemes are incompetent for finding…

The present paper is devoted to studying of minimal parametric fillings of finite metric spaces (a version of optimal connection problem) by methods of Linear Programming. The estimate on the multiplicity of multi-tours appearing in the…

We construct two combinatorially equivalent line arrangements in the complex projective plane such that the fundamental groups of their complements are not isomorphic. The proof uses a new invariant of the fundamental group of the…

Absolute parallelism (AP) geometry is frequently used for physical applications. Although it is wider than Riemannian geometry, it has two main defects. The first is that its path equation does not represent physical trajectories of any…

A challenge in image based metrology and forensics is intrinsic camera calibration when the used camera is unavailable. The unavailability raises two questions. The first question is how to find the projection model that describes the…

The exact computation of the matching distance for multi-parameter persistence modules is an active area of research in computational topology. Achieving an easily obtainable exact computation of this distance would permit multi-parameter…