Related papers: Exploring the Adjugate Matrix Approach to Quaterni…

This paper establishes the basis of the quaternionic differential geometry ($\mathbbm H$DG) initiated in a previous article. The usual concepts of curves and surfaces are generalized to quaternionic constraints, as well as the curvature and…

Full 3D estimation of human pose from a single image remains a challenging task despite many recent advances. In this paper, we explore the hypothesis that strong prior information about scene geometry can be used to improve pose estimation…

Multiview 3D face modeling has attracted increasing attention recently and has become one of the potential avenues in future video systems. We aim to make more reliable and robust automatic feature extraction and natural 3D feature…

We discuss the relationship between quaternion algebras and quadratic forms with a focus on computational aspects. Our basic motivating problem is to determine if a given algebra of rank 4 over a commutative ring R embeds in the 2x2-matrix…

In this paper we consider the localization problem for a visual sensor network. Inspired by the alternate attitude and position distributed optimization framework discussed in [1], we propose an estimation scheme that exploits the unit dual…

Estimating the relative camera pose from $n \geq 5$ correspondences between two calibrated views is a fundamental task in computer vision. This process typically involves two stages: 1) estimating the essential matrix between the views, and…

Rotation estimation plays a fundamental role in computer vision and robot tasks, and extremely robust rotation estimation is significantly useful for safety-critical applications. Typically, estimating a rotation is considered a non-linear…

There are many space subdivision and space partitioning techniques used in many algorithms to speed up computations. They mostly rely on orthogonal space subdivision, resp. using hierarchical data structures, e.g. BSP trees, quadtrees,…

This paper introduces a new architecture for human pose estimation using a multi- layer convolutional network architecture and a modified learning technique that learns low-level features and higher-level weak spatial models. Unconstrained…

We present a practical Newton-based method for computing left eigenvalues of quaternion matrices. It uses only standard real/complex linear-algebra kernels via embeddings and applies to matrices of any size. Extensive tests on literature…

The Grassmann manifold of linear subspaces is important for the mathematical modelling of a multitude of applications, ranging from problems in machine learning, computer vision and image processing to low-rank matrix optimization problems,…

In this paper, we propose a lower rank quaternion decomposition algorithm and apply it to color image inpainting. We introduce a concise form for the gradient of a real function in quaternion matrix variables. The optimality conditions of…

In computer vision, camera pose estimation from correspondences between 3D geometric entities and their projections into the image has been a widely investigated problem. Although most state-of-the-art methods exploit low-level primitives…

Accurate 6D object pose estimation is fundamental to robotic manipulation and grasping. Previous methods follow a local optimization approach which minimizes the distance between closest point pairs to handle the rotation ambiguity of…

6D object pose estimation aims to infer the relative pose between the object and the camera using a single image or multiple images. Most works have focused on predicting the object pose without associated uncertainty under occlusion and…

We propose an approach for estimating the relative pose between calibrated image pairs by jointly exploiting points, lines, and their coincidences in a hybrid manner. We investigate all possible configurations where these data modalities…

Randomized algorithms for low-rank approximation of quaternion matrices have gained increasing attention in recent years. However, existing methods overlook pass efficiency, the ability to limit the number of passes over the input…

The paper explains how a unit generalized quaternion is used to represent a rotation of a vector in 3-dimensional space. We review of some algebraic properties of generalized quaternions and operations between them and then show their…

Robotics and computer vision problems commonly require handling rigid-body motions comprising translation and rotation - together referred to as pose. In some situations, a vectorial parameterization of pose can be useful, where elements of…

Rotation invariance has been studied in the computer vision community primarily in the context of small in-plane rotations. This is usually achieved by building invariant image features. However, the problem of achieving invariance for…