相关论文: Special Unitary Parameterized Estimators of Rotati…

The Wahba problem, also known as rotation search, seeks to find the best rotation to align two sets of vector observations given putative correspondences, and is a fundamental routine in many computer vision and robotics applications. This…

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…

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…

A novel single-frame quaternion estimator processing two vector observations is introduced. The singular cases are examined, and appropriate rotational solutions are provided. Additionally, an alternative method involving sequential…

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…

We revisit the relative perturbation theory for invariant subspaces of positive definite matrix pairs. As a prototype model problem for our results we consider parameter dependent families of eigenvalue problems. We show that new estimates…

Machine learning techniques are used to predict theoretical constraints such as unitarity and boundedness from below in extensions of the Standard Model. This approach has proven effective for models incorporating additional SU(2) scalar…

Accurate estimates of rotation are crucial to vision-based motion estimation in augmented reality and robotics. In this work, we present a method to extract probabilistic estimates of rotation from deep regression models. First, we build on…

Existing methods for rotation estimation between two spherical ($\mathbb{S}^2$) patterns typically rely on spherical cross-correlation maximization between two spherical function. However, these approaches exhibit computational complexities…

We consider the problem of jointly estimating the attitude and spin-rate of a spinning spacecraft. Psiaki (J. Astronautical Sci., 57(1-2):73--92, 2009) has formulated a family of optimization problems that generalize the classical…

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…

A modified Gibbs's rotation matrix is derived and the connection with the Euler angles, quaternions, and Cayley$-$Klein parameters is established. As particular cases, the Rodrigues and Gibbs parameterizations of the rotation are obtained.…

Recently, the supersymmetry method was extended from Gaussian ensembles to arbitrary unitarily invariant matrix ensembles by generalizing the Hubbard-Stratonovich transformation. Here, we complete this extension by including arbitrary…

The linearization of the equations of motion of a robotics system about a given state-input trajectory, including a controlled equilibrium state, is a valuable tool for model-based planning, closed-loop control, gain tuning, and state…

Recently, Zhuang, Roth, \& Sudhakar [1] proposed a method that allows simultaneous computation of the rigid transformations from world frame to robot base frame and from hand frame to camera frame. Their method attempts to solve a…

We introduce motions as real six-dimensional vectors. A motion means a rotation and a translation. We define a motion operator which maps unit dual quaternions to motions, and a UDQ operator which maps motions to unit dual quaternions. By…

In this paper, we provide some careful analysis of certain pathological behavior of Euler angles and unit quaternions encountered in previous works related to rotation representation in neural networks. In particular, we show that for…

In this paper we study the Rotor Model of Martins and Nienhuis. After introducing spectral parameters, a combined use of integrability, polynomiality of the ground state wave function and a mapping into the fully-packed O(1)-model allows us…

Matrix functions are utilized to rewrite smooth spectral constrained matrix optimization problems as smooth unconstrained problems over the set of symmetric matrices which are then solved via the cubic-regularized Newton method. A…

We describe an algorithm to compute the extremal eigenvalues and corresponding eigenvectors of a symmetric matrix by solving a sequence of Quadratic Binary Optimization problems. This algorithm is robust across many different classes of…