Preconditioned Single-step Transforms for Non-rigid ICP
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Date
2025
Journal Title
Journal ISSN
Volume Title
Publisher
The Eurographics Association and John Wiley & Sons Ltd.
Abstract
Non-rigid iterative closest point (ICP) is a popular framework for shape alignment, typically formulated as alternating iteration of correspondence search and shape transformation. A common approach in the shape transformation stage is to solve a linear least squares problem to find a smoothness-regularized transform that fits the target shape. However, completely solving the linear least squares problem to obtain a transform is wasteful because the correspondences used for constructing the problem are imperfect, especially at early iterations. In this work, we design a novel framework to compute a transform in single step without the exact linear solve. Our key idea is to use only a single step of an iterative linear system solver, conjugate gradient, at each shape transformation stage. For this single-step scheme to be effective, appropriate preconditioning of the linear system is required. We design a novel adaptive Sobolev-Jacobi preconditioning method for our single-step transform to produce a large and regularized shape update suitable for correspondence search in the next iteration. We demonstrate that our preconditioned single-step transform stably accelerates challenging 3D surface registration tasks.
Description
CCS Concepts: Computing methodologies->Mesh models; Reconstruction; Mathematics of computing->Continuous optimization
@article{10.1111:cgf.70035,
journal = {Computer Graphics Forum},
title = {{Preconditioned Single-step Transforms for Non-rigid ICP}},
author = {Jung, Yucheol and Kim, Hyomin and Yoon, Hyejeong and Lee, Seungyong},
year = {2025},
publisher = {The Eurographics Association and John Wiley & Sons Ltd.},
ISSN = {1467-8659},
DOI = {10.1111/cgf.70035}
}