Year: 2026
Type: article
Abstract: . We present an analytic approximation model for nonrigid point set registration, grounded in the multivariate Taylor expansion of vector-valued functions. By exploiting the algebraic structure of Taylor expansions, we construct a structured function space spanned by truncated basis terms, allowing smooth deformations to be represented with low complexity and explicit form. To estimate mappings within this space, we develop a quasi-Newton optimization algorithm that progressively lifts the identity map into higher-order analytic forms. This structured framework unifies rigid, affine, and nonlinear deformations under a single closed-form formulation, without relying on kernel functions or high-dimensional parameterizations. The proposed model is embedded into a standard ICP loop—using (by default) nearest-neighbor correspondences—resulting in Analytic-ICP, an efficient registration algorithm with quasi-linear time complexity. Experiments on 2D and 3D datasets demonstrate that Analytic-ICP achieves higher accuracy and faster convergence than classical methods such as CPD and TPS-RPM, particularly for small and smooth deformations.
Source: SIAM Journal on Imaging Sciences
DOI: 10.1137/25m1752080
Authors: Wei Feng, Tengda Wei, Haiyong Zheng
Institutions: Ocean University of China, Shandong Normal University
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: green
Awards: G2367420292, G4025526384, G6761395902
OpenAlex ID: W7170055649