Related papers: Exploring the Adjugate Matrix Approach to Quaterni…
6D object pose estimation problem has been extensively studied in the field of Computer Vision and Robotics. It has wide range of applications such as robot manipulation, augmented reality, and 3D scene understanding. With the advent of…
In recent years, a deep learning framework has been widely used for object pose estimation. While quaternion is a common choice for rotation representation of 6D pose, it cannot represent an uncertainty of the observation. In order to…
Image representation is an important topic in computer vision and pattern recognition. It plays a fundamental role in a range of applications towards understanding visual contents. Moment-based image representation has been reported to be…
Over the last decades quaternions have become a crucial and very successful tool for attitude representation in robotics and aerospace. However, there is a major problem that is continuously causing trouble in practice when it comes to…
Estimating 3D from 2D is one of the central tasks in computer vision. In this work, we consider the monocular setting, i.e. single-view input, for 3D human pose estimation (HPE). Here, the task is to predict a 3D point set of human skeletal…
We present in this paper some fundamental tools for developing matrix analysis over the complex quaternion algebra. As applications, we consider generalized inverses, eigenvalues and eigenvectors, similarity, determinants of complex…
The paper aims to adopt the complex quaternion and octonion to formulate the field equations for electromagnetic and gravitational fields. Applying the octonionic representation enables one single definition to combine some physics contents…
This article investigates Kak neural networks, which can be instantaneously trained, for complex and quaternion inputs. The performance of the basic algorithm has been analyzed and shown how it provides a plausible model of human perception…
The constrained orthogonal Procrustes problem is the least-squares problem that calls for a rotation matrix that optimally aligns two corresponding sets of points in d-dimensional Euclidean space. This problem generalizes to the so-called…
The point correspondence (PC) and affine correspondence (AC) are widely used for relative pose estimation. An AC consists of a PC across two views and an affine transformation between the small patches around this PC. Previous work…
A common representation of a three dimensional object in computer applications, such as graphics and design, is in the form of a triangular mesh. In many instances, individual or groups of triangles in such representation need to satisfy…
Quaternions have an (over a century-old) extensive and quite complicated interaction with special relativity. Since quaternions are intrinsically 4-dimensional, and do such a good job of handling 3-dimensional rotations, the hope has always…
Multivalued projections are applied to the study of weighted least squares solutions of linear relations equations (or inclusions) and some of its applications. To this end a matrix representation of multivalued projections with respect to…
Accurate registration of 2D imagery with point clouds is a key technology for image-LiDAR point cloud fusion, camera to laser scanner calibration and camera localization. Despite continuous improvements, automatic registration of 2D and 3D…
Robustly estimating camera poses from a set of images is a fundamental task which remains challenging for differentiable methods, especially in the case of small and sparse camera pose graphs. To overcome this challenge, we propose…
Quaternion-valued differential equations (QDEs) is a new kind of differential equations which have many applications in physics and life sciences. The largest difference between QDEs and ODEs is the algebraic structure. On the…
6D pose estimation of rigid objects from RGB-D images is crucial for object grasping and manipulation in robotics. Although RGB channels and the depth (D) channel are often complementary, providing respectively the appearance and geometry…
A novel framework for a unifying treatment of quaternion valued adaptive filtering algorithms is introduced. This is achieved based on a rigorous account of quaternion differentiability, the proposed I-gradient, and the use of augmented…
6D pose estimation is a central problem in robot vision. Compared with pose estimation based on point correspondences or its robust versions, correspondence-free methods are often more flexible. However, existing correspondence-free methods…
The goal of this paper is to estimate directly the rotation and translation between two stereoscopic images with the help of five homologous points. The methodology presented does not mix the rotation and translation parameters, which is…