# Nonparametric Continuous Sensor Registration

arXiv: https://arxiv.org/abs/2001.04286 · HTML: https://mlsanity.com/paper/2001.04286/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Jan 2020.

## Built on by (most cited first, 5 of 5)

- [Correspondence-Free SE(3) Point Cloud Registration in RKHS via Unsupervised Equivariant Learning](https://mlsanity.com/paper/2407.20223/) (2024)
- [Scale-Invariant Fast Functional Registration](https://mlsanity.com/paper/2209.12763/) (2022)
- [DynaWeightPnP: Toward global real-time 3D-2D solver in PnP without correspondences](https://mlsanity.com/paper/2409.18457/) (2024)
- [Generalized-CVO: Fast and Correspondence-Free Local Point Cloud Registration with Second Order Riemannian Optimization](https://mlsanity.com/paper/2606.10019/) (2026)
- [Spectral Consistency-Guided Multiview Point Cloud Registration for Low-Overlap Scenes](https://mlsanity.com/paper/2609.12417/) (2026)

## Abstract (arXiv)

This paper develops a new mathematical framework that enables nonparametric joint semantic and geometric representation of continuous functions using data. The joint embedding is modeled by representing the processes in a reproducing kernel Hilbert space. The functions can be defined on arbitrary smooth manifolds where the action of a Lie group aligns them. The continuous functions allow the registration to be independent of a specific signal resolution. The framework is fully analytical with a closed-form derivation of the Riemannian gradient and Hessian. We study a more specialized but widely used case where the Lie group acts on functions isometrically. We solve the problem by maximizing the inner product between two functions defined over data, while the continuous action of the rigid body motion Lie group is captured through the integration of the flow in the corresponding Lie algebra. Low-dimensional cases are derived with numerical examples to show the generality of the proposed framework. The high-dimensional derivation for the special Euclidean group acting on the Euclidean space showcases the point cloud registration and bird's-eye view map registration abilities. An implementation of this framework for RGB-D cameras outperforms the state-of-the-art robust visual odometry and performs well in texture and structure-scarce environments.