Abstract Pose estimation requires optimally estimating translation and rotation. Here, we focus on rotation, since it involves nonlinear analysis. We show that the computation can be done systematically if we exploit the fact that the set of rotations forms a group of transformations, called the “special orthogonal group,” denoted by SO(3). For optimizing a function J(R) of a rotation R, we need not parameterize R in any way; we only need to add to R a small rotation so that J(R) decreases. To this end, we define a linear space spanned by infinitesimal rotations, called the “Lie algebra” of SO(3). We describe the computational procedure for minimizing J(R) based on the Lie algebra formulation, which we call the “Lie algebra method.” We apply it to three computer vision problems: (1) Given two sets of 3D points, we optimally estimate the translation and rotation between them in the presence of inhomogeneous anisotropic noise. (2) Given corresponding points between two images, we optimally compute the fundamental matrix. (3) We describe the procedure of bundle adjustment for computing, from images of multiple points in the scene taken by multiple cameras, the 3D locations of all the points and the postures of all the cameras as well as their internal parameters. Finally, we overview the role of Lie algebra in various computer vision applications.
Lie Algebra Method for Pose Optimization Computation
Machine Vision and Navigation ; 293-319
2019-10-01
27 pages
Aufsatz/Kapitel (Buch)
Elektronische Ressource
Englisch
Pose estimation , 3D rotation , Infinitesimal rotation , Lie algebra , Maximum likelihood , Fundamental Matrix , Bundle adjustment Engineering , Communications Engineering, Networks , Signal, Image and Speech Processing , Computational Intelligence , Control, Robotics, Mechatronics , Health Informatics
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