# 3QFP: Efficient neural implicit surface reconstruction using Tri-Quadtrees and Fourier feature Positional encoding

arXiv: https://arxiv.org/abs/2401.07164 · HTML: https://mlsanity.com/paper/2401.07164/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Jan 2024.

## Built on by (most cited first, 3 of 3)

- [Neural Implicit Representation for Highly Dynamic LiDAR Mapping and Odometry](https://mlsanity.com/paper/2409.17729/) (2024)
- [HessianForge: Scalable LiDAR reconstruction with Physics-Informed Neural Representation and Smoothness Energy Constraints](https://mlsanity.com/paper/2503.08929/) (2025)
- [Unpaired RGB-Thermal Gaussian-Splatting Using Visual Geometric Transformers](https://mlsanity.com/paper/2606.05491/) (2026)

## Abstract (arXiv)

Neural implicit surface representations are currently receiving a lot of interest as a means to achieve high-fidelity surface reconstruction at a low memory cost, compared to traditional explicit representations.However, state-of-the-art methods still struggle with excessive memory usage and non-smooth surfaces. This is particularly problematic in large-scale applications with sparse inputs, as is common in robotics use cases. To address these issues, we first introduce a sparse structure, tri-quadtrees, which represents the environment using learnable features stored in three planar quadtree projections. Secondly, we concatenate the learnable features with a Fourier feature positional encoding. The combined features are then decoded into signed distance values through a small multi-layer perceptron. We demonstrate that this approach facilitates smoother reconstruction with a higher completion ratio with fewer holes. Compared to two recent baselines, one implicit and one explicit, our approach requires only 10%--50% as much memory, while achieving competitive quality.