5 papers
Explicit Solutions of the Singular Yang--Baxter-like Matrix Equation and Their Numerical Computation
Ashim Kumar, João R. Cardoso, Gurjinder Singh
We derive several explicit formulae for finding infinitely many solutions of the equation , when is singular. We start by splitting the equation into a couple of linea…
Solving the Discrete Euler-Arnold Equations for the Generalized Rigid Body Motion
Joao R. Cardoso, Pedro Miraldo
We propose three iterative methods for solving the Moser-Veselov equation, which arises in the discretization of the Euler-Arnold differential equations governing the motion of a g…
POSEAMM: A Unified Framework for Solving Pose Problems using an Alternating Minimization Method
Joao Campos, Joao R. Cardoso, Pedro Miraldo
Pose estimation is one of the most important problems in computer vision. It can be divided in two different categories -- absolute and relative -- and may involve two different ty…
Plücker Correction Problem: Analysis and Improvements in Efficiency
João R. Cardoso, Pedro Miraldo, Helder Araujo
A given six dimensional vector represents a 3D straight line in Plucker coordinates if its coordinates satisfy the Klein quadric constraint. In many problems aiming to find the Pl…
An Explicit Formula for the Matrix Logarithm
Joao R. Cardoso
We present an explicit polynomial formula for evaluating the principal logarithm of all matrices lying on the line segment joining the identity matrix $I…