Related papers: Exploring the Adjugate Matrix Approach to Quaterni…
We study matrix forms of quaternionic versions of the Fourier Transform and Convolution operations. Quaternions offer a powerful representation unit, however they are related to difficulties in their use that stem foremost from…
This article presents and compares four approaches for computing the rotation of a point about an axis by an angle in $\mathbb{R}^3$. We illustrate these methods by computing, by hand, the rotation of point $P=(1,0,1)^T$ about axis…
This paper presents a dual quaternion framework for 6-DOF visual target tracking that addresses key limitations of perspective-n-point (P$n$P) solvers: sensitivity to noise and outliers, and inability to propagate estimates through…
We explain the use of dual quaternions to represent poses, twists, and wrenches.
In this work, we propose a method for object recognition and pose estimation from depth images using convolutional neural networks. Previous methods addressing this problem rely on manifold learning to learn low dimensional viewpoint…
Quaternions were appeared through Lagrangian formulation of mechanics in Symplectic vector space. Its general form was obtained from the Clifford algebra, and Frobenius' theorem, which says that "the only finite-dimensional real division…
Planar markers are useful in robotics and computer vision for mapping and localisation. Given a detected marker in an image, a frequent task is to estimate the 6DOF pose of the marker relative to the camera, which is an instance of planar…
We study the problem of rotating a simple polygon to contain the maximum number of elements from a given point set in the plane. We consider variations of this problem where the rotation center is a given point or lies on a line segment, a…
An arbitrary rigid transformation in $\mathbf{SE}(3)$ can be separated into two parts, namely, a translation and a rigid rotation. This technical report reviews, under a unifying viewpoint, three common alternatives to representing the…
A key question in many low-rank problems throughout optimization, machine learning, and statistics is to characterize the convex hulls of simple low-rank sets and judiciously apply these convex hulls to obtain strong yet computationally…
The $\mathrm{SE}(3)$ invariants of a pose include its rotation angle and screw translation. In this paper, we present a complete comprehensive study of the relative pose estimation problem for a calibrated camera constrained by known…
The use of quaternions as a novel tool for color image representation has yielded impressive results in color image processing. By considering the color image as a unified entity rather than separate color space components, quaternions can…
This paper presents a new dual quaternion-based formulation for pose-based visual servoing. Extending our previous work on local contact moment (LoCoMo) based grasp planning, we demonstrate grasping of arbitrarily moving objects in 3D…
3D human pose estimation is a vital task in computer vision, involving the prediction of human joint positions from images or videos to reconstruct a skeleton of a human in three-dimensional space. This technology is pivotal in various…
This paper revisits the topic of rotation estimation through the lens of special unitary matrices. We begin by reformulating Wahba's problem using $SU(2)$ to derive multiple solutions that yield linear constraints on corresponding…
Capsules are grouping of neurons that allow to represent sophisticated information of a visual entity such as pose and features. In the view of this property, Capsule Networks outperform CNNs in challenging tasks like object recognition in…
We give a new algorithmic solution to the well-known five-point relative pose problem. Our approach does not deal with the famous cubic constraint on an essential matrix. Instead, we use the Cayley representation of rotations in order to…
This work proposes a quaternion-based sliding variable that describes exponentially convergent error dynamics for any forward complete desired attitude trajectory. The proposed sliding variable directly operates on the non-Euclidean space…
The numerical optimization of continuous functions is a fundamental task in many scientific and engineering domains, ranging from mechanical design to training of artificial intelligence models. Among the most effective and widely used…
Learning about the three-dimensional world from two-dimensional images is a fundamental problem in computer vision. An ideal neural network architecture for such tasks would leverage the fact that objects can be rotated and translated in…