Related papers: Triangulation of Points Constrained to a Plane

We present a novel method to reconstruct the 3D layout of a room (walls, floors, ceilings) from a single perspective view in challenging conditions, by contrast with previous single-view methods restricted to cuboid-shaped layouts. This…

We present a novel method to estimate the motion matrix between overlapping pairs of 3D views in the context of indoor scenes. We use the Manhattan world assumption to introduce lightweight geometric constraints under the form of planes…

To address the issue of increased triangulation uncertainty caused by selecting views with small camera baselines in Structure from Motion (SFM) view selection, this paper proposes a robust error-resistant view selection method. The method…

We show that among any $n$ points in the unit cube one can find a triangle of area at most $n^{-2/3-c}$ for some absolute constant $c >0$. This gives the first non-trivial upper bound for the three-dimensional version of Heilbronn's…

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…

State of the art methods in astronomical image reconstruction rely on the resolution of a regularized or constrained optimization problem. Solving this problem can be computationally intensive and usually leads to a quadratic or at least…

The Perspective-Three-Point Problem (P3P) is solved by first focusing on determining the directions of the lines through pairs of control points, relative to the camera, rather than the distances from the camera to the control points. The…

Multi-camera systems offer rich observation capabilities for visual navigation and 3D scene reconstruction; however, the resulting feature redundancy often compromises computational efficiency. This challenge is particularly pronounced…

Let $P$ be a set of $n$ points in the plane. A crossing-free structure on $P$ is a plane graph with vertex set $P$. Examples of crossing-free structures include triangulations of $P$, spanning cycles of $P$, also known as polygonalizations…

Structure from motion using uncalibrated multi-camera systems is a challenging task. This paper proposes a bundle adjustment solution that implements a baseline constraint respecting that these cameras are static to each other. We assume…

This paper proposes a new approach for monocular dense 3D reconstruction of a complex dynamic scene from two perspective frames. By applying superpixel over-segmentation to the image, we model a generically dynamic (hence non-rigid) scene…

We refine the bit complexity analysis of an algorithm for the computation of at least one point per connected component of a smooth real algebraic set, yielding exponential speedup (with respect to the number of variables) compared to prior…

A simple, yet general, formalism for the optimized linear combination of astrophysical images is constructed and demonstrated. The formalism allows the user to combine multiple undersampled images to provide oversampled output at high…

We solve three enumerative problems concerning families of planar maps. More precisely, we establish algebraic equations for the generating function of non-separable triangulations in which all vertices have degree at least d, for a certain…

In this paper we study the problem of augmenting a planar graph such that it becomes 3-regular and remains planar. We show that it is NP-hard to decide whether such an augmentation exists. On the other hand, we give an efficient algorithm…

We target the problem of sparse 3D reconstruction of dynamic objects observed by multiple unsynchronized video cameras with unknown temporal overlap. To this end, we develop a framework to recover the unknown structure without sequencing…

A triangulation of a surface is irreducible if there is no edge whose contraction produces another triangulation of the surface. In this work we propose an algorithm that constructs the set of irreducible triangulations of any surface with…

Reconstructing surfaces from normals is a key component of photometric stereo. This work introduces an adaptive surface triangulation in the image domain and afterwards performs the normal integration on a triangle mesh. Our key insight is…

The multi-dissipative photogravitational triaxial elliptic restricted three body problem is treated. The perturbed locations of triangular points are computed. The stability of the triangular points under changing one or more perturbing…

Solving the challenging problem of 3D object reconstruction from a single image appropriately gives existing technologies the ability to perform with a single monocular camera rather than requiring depth sensors. In recent years, thanks to…