KernelGPA: A Deformable SLAM Back-end

Abstract

Simultaneous localization and mapping (SLAM) in the deformable environment has encountered several barricades. One of them is the lack of a global registration technique. Thus current SLAM systems heavily rely on template based methods. We propose KernelGPA, a novel global registration technique to bridge the gap. We define nonrigid transformations using a kernel method, and show that the principal axes of the map can be solved globally in closed-form, up to a global scale ambiguity along each axis. We propose to solve both the global scale ambiguity and rigid poses in a unified optimization framework, yielding a cost that can be readily incorporated in sensor fusion frameworks. We demonstrate the registration performance of KernelGPA using various datasets, with a special focus on computerized tomography (CT) registration. We release our code 1 and data to foster future research in this direction.

Kernel-GPA: A globally optimal solution to deformable SLAM in closed-form

“…Connection to the Result in Bai and Bartoli (2022a) In Bai and Bartoli (2022a), Q t was defined as equation ( 52) which can be simplified to the form in equation ( 25).…”

“…The expression of Q t in equation (25) is much more elegant than the one in Bai and Bartoli (2022a). See Appendix I for details.…”

“…Performance improvements of the proposed boldΛ estimation method over the one in Bai and Bartoli (2022b). We gradually remove the correspondences in the HandBag dataset Gallardo et al (2017) (with 155 × 8 correspondences in total) and report statistics of 20-trial Monte-Carlo runs based on leave-1 and 20-fold cross-validations Bai and Bartoli (2022a), for five transformation models: affine, TPS with 3 × 3, 5 × 5, and 7 × 7 control points, and the proposed KBT.…”

“…This article is an extension to the Kernel-GPA method initially appeared in the proceedings of Robotics: Science and Systems (RSS) Bai and Bartoli (2022a). Concretely, this work contains the following contributions:1.…”

“…This article makes several improvements over the initial version appeared in RSS Bai and Bartoli (2022a). We have rewritten most of the text for better clarity, for instance, the exposition of the constraints in Section 5 and the special eigenvalue problem in Section 6.…”