Jung, YucheolKim, HyominYoon, HyejeongLee, SeungyongBousseau, AdrienDay, Angela2025-05-092025-05-0920251467-8659https://doi.org/10.1111/cgf.70035https://diglib.eg.org/handle/10.1111/cgf70035Non-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.CCS Concepts: Computing methodologies->Mesh models; Reconstruction; Mathematics of computing->Continuous optimizationComputing methodologiesMesh modelsReconstructionMathematics of computingContinuous optimization10.1111/cgf.7003516 pages