Related papers: Line Multiview Varieties
Multinets are certain configurations of lines and points with multiplicities in the complex projective plane P2. They are used in the studies of resonance and characteristic varieties of complex hyperplane arrangement complements and…
Discriminantal arrangements are hyperplane arrangements, which are generalized braid ones. They are constructed from given hyperplane arrangements, but their combinatorics are not invariant under combinatorial equivalence. However, it is…
Metric learning seeks to embed images of objects suchthat class-defined relations are captured by the embeddingspace. However, variability in images is not just due to different depicted object classes, but also depends on other latent…
We study the set of image tuples arising from fixed cameras observing varying planar 3-dimensional point configurations. We derive a formula for the number of complex critical points of the triangulation problem, which seeks to reconstruct…
In some scenarios, a single input image may not be enough to allow the object classification. In those cases, it is crucial to explore the complementary information extracted from images presenting the same object from multiple perspectives…
We introduce a new topological invariant of complex line arrangements in the complex projective plane, derived from the interaction between their complement and the boundary of a regular neighbourhood. The motivation is to identify Zariski…
A variety $X$ is covered by lines if there exist a finite number of lines contained in $X$ passing through each general point. I prove two theorems. Theorem 1:Let $X^n\subset P^M$ be a variety covered by lines. Then there are at most $n!$…
Vanishing points and vanishing lines are classical geometrical concepts in perspective cameras that have a lineage dating back to 3 centuries. A vanishing point is a point on the image plane where parallel lines in 3D space appear to…
In this work we show that the classical subject of general valuation theory and Zariski-Riemann varieties has a much wider scope than commutative algebra and desingularization theory. We construct and investigate birational projective limit…
Line spectral estimation (LSE) from multi snapshot samples is studied utilizing the variational Bayesian methods. Motivated by the recently proposed variational line spectral estimation (VALSE) method for a single snapshot, we develop the…
A finite unit norm tight frame is a collection of $r$ vectors in $\mathbb{R}^n$ that generalizes the notion of orthonormal bases. The affine finite unit norm tight frame variety is the Zariski closure of the set of finite unit norm tight…
Correspondences between 3D lines and their 2D images captured by a camera are often used to determine position and orientation of the camera in space. In this work, we propose a novel algebraic algorithm to estimate the camera pose. We…
For the problem of 3D object recognition, researchers using deep learning methods have developed several very different input representations, including "multi-view" snapshots taken from discrete viewpoints around an object, as well as…
We propose a scene-level inverse rendering framework that uses multi-view images to decompose the scene into geometry, a SVBRDF, and 3D spatially-varying lighting. Because multi-view images provide a variety of information about the scene,…
We introduce cosurfaces with values in the group \(\PC_n(H)\) of \(H\)-valued reciprocal pairwise comparison matrices. The composition law is covariant on upper triangular coefficients and contravariant on lower triangular coefficients,…
Object triangulation, 3-D object tracking, feature correspondence, and camera calibration are key problems for estimation from camera networks. This paper addresses these problems within a unified Bayesian framework for joint multi-object…
We propose a multi-camera LiDAR-visual-inertial odometry framework, Multi-LVI-SAM, which fuses data from multiple fisheye cameras, LiDAR and inertial sensors for highly accurate and robust state estimation. To enable efficient and…
We define a topological invariant of complex projective plane curves. As an application, we present new examples of arithmetic Zariski pairs.
We classify representations of the mapping class group of a surface of genus $g$ (with at most one puncture or boundary component) up to dimension $3g-3$. Any such representation is the direct sum of a representation in dimension $2g$ or…
This paper proposes a global approach for the multi-view registration of unordered range scans. As the basis of multi-view registration, pair-wise registration is very pivotal. Therefore, we first select a good descriptor and accelerate its…