Related papers: Triangulation of Points Constrained to a Plane
Chirotopes are a common combinatorial abstraction of (planar) point sets. In this paper we investigate decomposition methods for chirotopes, and their application to the problem of counting the number of triangulations supported by a given…
This paper uses mathematics to analyze the challenges of geometrically noisy environments on triangulation. Given widely accepted algorithmic triangulation methods, such as O (n ln n) or a simpler O (n^3) method, we can mathematically prove…
3D Gaussian Splatting (3DGS) is a powerful reconstruction technique, but it needs to be initialized from accurate camera poses and high-fidelity point clouds. Typically, the initialization is taken from Structure-from-Motion (SfM)…
Calibration in a multi camera network has widely been studied for over several years starting from the earlier days of photogrammetry. Many authors have presented several calibration algorithms with their relative advantages and…
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…
Supervised approaches to 3D pose estimation from single images are remarkably effective when labeled data is abundant. However, as the acquisition of ground-truth 3D labels is labor intensive and time consuming, recent attention has shifted…
In this paper, we present a new framework for reducing the computational complexity of geometric vision problems through targeted reweighting of the cost functions used to minimize reprojection errors. Triangulation - the task of estimating…
In the point set embeddability problem, we are given a plane graph $G$ with $n$ vertices and a point set $S$ with $n$ points. Now the goal is to answer the question whether there exists a straight-line drawing of $G$ such that each vertex…
Estimating 3D human poses from video is a challenging problem. The lack of 3D human pose annotations is a major obstacle for supervised training and for generalization to unseen datasets. In this work, we address this problem by proposing a…
We present two novel solutions for multi-view 3D human pose estimation based on new learnable triangulation methods that combine 3D information from multiple 2D views. The first (baseline) solution is a basic differentiable algebraic…
We present a fast and accurate solution to the perspective $n$-points problem, by way of a new approach to the n=4 case. Our solution hinges on a novel separation of variables: given four 3D points and four corresponding 2D points on the…
This paper presents PlanarSplatting, an ultra-fast and accurate surface reconstruction approach for multiview indoor images. We take the 3D planes as the main objective due to their compactness and structural expressiveness in indoor…
Triangulation refers to the problem of finding a 3D point from its 2D projections on multiple camera images. For solving this problem, it is the common practice to use so-called optimal triangulation method, which we call the L2 method in…
The paper studies planar surface reconstruction of indoor scenes from two views with unknown camera poses. While prior approaches have successfully created object-centric reconstructions of many scenes, they fail to exploit other…
3D Gaussian Splatting is crucial for real-time novel view synthesis due to its efficiency and ability to render photorealistic images. However, building a 3D Gaussian is guided solely by photometric loss, which can result in inconsistencies…
To enumerate 3-manifold triangulations with a given property, one typically begins with a set of potential face pairing graphs (also known as dual 1-skeletons), and then attempts to flesh each graph out into full triangulations using an…
We have developed a general Bayesian algorithm for determining the coordinates of points in a three-dimensional space. The algorithm takes as input a set of probabilistic constraints on the coordinates of the points, and an a priori…
We present a new and simple randomized algorithm for constructing the Delaunay triangulation using nearest neighbor graphs for point location. Under suitable assumptions, it runs in linear expected time for points in the plane with…
We introduce a new family of minimal problems for reconstruction from multiple views. Our primary focus is a novel approach to autocalibration, a long-standing problem in computer vision. Traditional approaches to this problem, such as…
We introduce an alternative approach for constrained mathematical programming problems. It rests on two main aspects: an efficient way to compute optimal solutions for unconstrained problems, and multipliers regarded as variables for a…