Related papers: A polynomial formula for the perspective four poin…

The direct or algorithmic approach for the Jacobian problem, consisting of the direct construction of the inverse polynomials is proposed. The so called principle and derived Jacobi conditions are proposed and discussed. The algorithmic…

Evaluating a polynomial on a set of points is a fundamental task in computer algebra. In this work, we revisit a particular variant called trimmed multipoint evaluation: given an $n$-variate polynomial with bounded individual degree $d$ and…

Estimating relative camera poses between images has been a central problem in computer vision. Methods that find correspondences and solve for the fundamental matrix offer high precision in most cases. Conversely, methods predicting pose…

We present a new insight into the systematic generation of minimal solvers in computer vision, which leads to smaller and faster solvers. Many minimal problem formulations are coupled sets of linear and polynomial equations where image…

Two-view relative pose estimation and structure reconstruction is a classical problem in computer vision. The typical methods usually employ the singular value decomposition of the essential matrix to get multiple solutions of the relative…

In this paper we study the problem of estimating the semi-generalized pose of a partially calibrated camera, i.e., the pose of a perspective camera with unknown focal length w.r.t. a generalized camera, from a hybrid set of 2D-2D and 2D-3D…

This paper presents a generic 6DOF camera pose estimation method, which can be used for both the pinhole camera and the fish-eye camera. Different from existing methods, relative positions of 3D points rather than absolute coordinates in…

6D pose estimation of textureless objects is a valuable but challenging task for many robotic applications. In this work, we propose a framework to address this challenge using only RGB images acquired from multiple viewpoints. The core…

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…

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…

This paper introduces a new approach for the automated reconstruction - reassembly of fragmented objects having one surface near to plane, on the basis of the 3D representation of their constituent fragments. The whole process starts by 3D…

The starting point of this work is the principle that all movement of particles and photons in the observable Universe must follow geodesics of a 4-dimensional space where time intervals are always a measure of geodesic arc lengths, i.e.…

Accurate reconstruction and tracking of dynamic human faces from image sequences is challenging because non-rigid deformations, expression changes, and viewpoint variations occur simultaneously, creating significant ambiguity in geometry…

Traditionally, the P3P problem is solved by firstly transforming its 3 quadratic equations into a quartic one, then by locating the roots of the resulting quartic equation and verifying whether a root does really correspond to a true…

We introduce new linear mathematical formulations to calculate the focal length of a camera in an active platform. Through mathematical derivations, we show that the focal lengths in each direction can be estimated using only one point…

In this paper, we study a 2D tomography problem for point source models with random unknown view angles. Rather than recovering the projection angles, we reconstruct the model through a set of rotation-invariant features that are estimated…

This paper studies the complex task of simultaneous multi-object 3D reconstruction, 6D pose and size estimation from a single-view RGB-D observation. In contrast to instance-level pose estimation, we focus on a more challenging problem…

Point matching refers to the process of finding spatial transformation and correspondences between two sets of points. In this paper, we focus on the case that there is only partial overlap between two point sets. Following the approach of…

We propose a modified normalized direct linear transform (DLT) algorithm for solving the perspective-n-point (PnP) problem with much better behavior than the conventional DLT. The modification consists of analytically weighting the…

We propose a novel 3D human pose detector using two panoramic cameras. We show that transforming fisheye perspectives to rectilinear views allows a direct application of two-dimensional deep-learning pose estimation methods, without the…