Related papers: Exploring the Adjugate Matrix Approach to Quaterni…
We present a novel solution to the camera pose estimation problem, where rotation and translation of a camera between two views are estimated from matched feature points in the images. The camera pose estimation problem is traditionally…
We review the general problem of finding a global rotation that transforms a given set of points and/or coordinate frames (the "test" data) into the best possible alignment with a corresponding set (the "reference" data). For 3D point data,…
The attitude space has been parameterized in various ways for practical purposes. Different representations gain preferences over others based on their intuitive understanding, ease of implementation, formulaic simplicity, and physical as…
This paper presents an experimental study on the application of quaternions in several machine learning algorithms. Quaternion is a mathematical representation of rotation in three-dimensional space, which can be used to represent complex…
In this paper, we present a novel algorithm to extract a quaternion from a two dimensional camera frame for estimating a contained human skeletal pose. The problem of pose estimation is usually tackled through the usage of stereo cameras…
Objects' rigid motions in 3D space are described by rotations and translations of a highly-correlated set of points, each with associated $x,y,z$ coordinates that real-valued networks consider as separate entities, losing information.…
The purpose of this effort is to investigate if the use of quaternion mathematics can be used to better model and simulate the electromagnetic fields that occur from moving electromagnetic charges. One observed deficiency with the commonly…
Rotation representations are foundational in fields such as computer graphics, robotics, and machine learning, where precise and efficient modeling of 3D orientations is critical. This paper comprehensively investigates diverse…
Quaternion matrices are employed successfully in many color image processing applications. In particular, a pure quaternion matrix can be used to represent red, green and blue channels of color images. A low-rank approximation for a pure…
Numerous attempts have been made to replicate the success of complex-valued algebra in engineering and science to other hypercomplex domains such as quaternions, tessarines, biquaternions, and octonions. Perhaps, none have matched the…
In this paper, we present a simple but powerful method to tackle the problem of estimating the 6D pose of objects from a single RGB image. Our system trains a novel convolutional neural network to regress the unit quaternion, which…
Relative pose estimation, a fundamental computer vision problem, has been extensively studied for decades. Existing methods either estimate and decompose the essential matrix or directly estimate the rotation and translation to obtain the…
Time-varying, smooth trajectory estimation is of great interest to the vision community for accurate and well behaving 3D systems. In this paper, we propose a novel principal component local regression filter acting directly on the…
Dual quaternions and dual quaternion matrices have garnered widespread applications in robotic research, and its spectral theory has been extensively studied in recent years. This paper introduces the novel concept of the dual complex…
Quaternion optimization has attracted significant interest due to its broad applications, including color face recognition, video compression, and signal processing. Despite the growing literature on quadratic and matrix quaternion…
Quaternions are an important tool to describe the orientation of a molecule. This paper considers the use of quaternions in matching two conformations of a molecule, in interpolating rotations, in performing statistics on orientational…
Many machine learning problems involve regressing variables on a non-Euclidean manifold -- e.g. a discrete probability distribution, or the 6D pose of an object. One way to tackle these problems through gradient-based learning is to use a…
Solving non-linear least-squares problem for pose estimation (rotation and translation) is often a time consuming yet fundamental problem in several real-time computer vision applications. With an adequate rotation parametrization, the…
This paper presents solutions to the following two common quaternion attitude estimation problems: (i) estimation of attitude using measurement of two reference vectors, and (ii) estimation of attitude using rate measurement and measurement…
Vision-based 3D human motion capture from videos remains a challenge in computer vision. Traditional 3D pose estimation approaches often ignore the temporal consistency between frames, causing implausible and jittery motion. The emerging…