# Structured Analytic Mappings for Point Set Registration

arXiv: https://arxiv.org/abs/2602.16753 · HTML: https://mlsanity.com/paper/2602.16753/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Feb 2026.

## Built on by (most cited first, 1 of 1)

- [Structured Analytic Coherent Point Drift for Non-Rigid Point Set Registration](https://mlsanity.com/paper/2605.00934/) (2026)

## Abstract (arXiv)

We present an analytic approximation model for non-rigid 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.