Related papers: Optimal Triangulation Method is Not Really Optimal
For decades, it has been widely accepted that the gold standard for two-view triangulation is to minimize the cost based on reprojection errors. In this work, we challenge this idea. We propose a novel alternative to the classic midpoint…
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…
This paper proposes a method to compute camera 6Dof poses to achieve a user defined coverage. The camera placement problem is modeled as a combinatorial optimization where given the maximum number of cameras, a camera set is selected from a…
Determining the position and orientation of a calibrated camera from a single image with respect to a 3D model is an essential task for many applications. When 2D-3D correspondences can be obtained reliably, perspective-n-point solvers can…
In this paper, a statistically optimal solution to the Perspective-n-Point (PnP) problem is presented. Many solutions to the PnP problem are geometrically optimal, but do not consider the uncertainties of the observations. In addition, it…
In this note, we show that the L2 optimal solutions to most real multiple view L2 triangulation problems can be efficiently obtained by two-stage Newton-like iterative methods, while the difficulty of such problems mainly lies in how to…
In this work, we address the problem of refining the geometry of local image features from multiple views without known scene or camera geometry. Current approaches to local feature detection are inherently limited in their keypoint…
We study the accuracy of triangulation in multi-camera systems with respect to the number of cameras. We show that, under certain conditions, the optimal achievable reconstruction error decays quadratically as more cameras are added to the…
This work proposes a non-iterative, scalable, and statistically optimal way to triangulate called \texttt{LOSTU}. Unlike triangulation algorithms that minimize the reprojection ($L_2$) error, LOSTU will still provide the maximum likelihood…
Images are an important source of information for spacecraft navigation and for three-dimensional reconstruction of observed space objects. Both of these applications take the form of a triangulation problem when the camera has a known…
We propose a robust and efficient method for multiview triangulation and uncertainty estimation. Our contribution is threefold: First, we propose an outlier rejection scheme using two-view RANSAC with the midpoint method. By prescreening…
In this paper, it is proposed to solve the problem of triangulation for calibrated omnidirectional cameras through the optimisation of ray-pairs on the projective sphere. The proposed solution boils down to finding the roots of a quadratic…
Triangulation of a three-dimensional point from at least two noisy 2-D images can be formulated as a quadratically constrained quadratic program. We propose an algorithm to extract candidate solutions to this problem from its semidefinite…
We address the problem of generalizability for multi-view 3D human pose estimation. The standard approach is to first detect 2D keypoints in images and then apply triangulation from multiple views. Even though the existing methods achieve…
3D human pose estimation has been a long-standing challenge in computer vision and graphics, where multi-view methods have significantly progressed but are limited by the tedious calibration processes. Existing multi-view methods are…
Flying Triangulation sensors enable a free-hand and motion-robust 3D data acquisition of complex shaped objects. The measurement principle is based on a multi-line light-sectioning approach and uses sophisticated algorithms for real-time…
Nonlinear lens distortion rectification is a common first step in image processing applications where the assumption of a linear camera model is essential. For rectifying the lens distortion, forward distortion model needs to be known.…
We propose a novel iterative method for optimally placing and orienting multiple cameras in a 3D scene. Sample applications include improving the accuracy of 3D reconstruction, maximizing the covered area for surveillance, or improving the…
Two-view triangulation is a problem of minimizing a quadratic polynomial under an equality constraint. We derive a polynomial that encodes the local minimizers of this problem using the theory of Lagrange multipliers. This offers a simpler…
We introduce a novel concept for motion robust optical 3D-sensing. The concept is based on multi-line triangulation. The aim is to evaluate a large number of projected lines (high data density) in a large measurement volume with high…