# An Algorithm for the SE(3)-Transformation on Neural Implicit Maps for Remapping Functions

arXiv: https://arxiv.org/abs/2206.08712 · HTML: https://mlsanity.com/paper/2206.08712/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 40 references that are in the map.
- First posted on arXiv 17 Jun 2022.

## Builds on (most cited first, 25 of 25)

- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [The Replica Dataset: A Digital Replica of Indoor Spaces](https://mlsanity.com/paper/1906.05797/) (2019)
- [ORB-SLAM2: an Open-Source SLAM System for Monocular, Stereo and RGB-D Cameras](https://mlsanity.com/paper/1610.06475/) (2016)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks](https://mlsanity.com/paper/2006.10503/) (2020)
- [NICE-SLAM: Neural Implicit Scalable Encoding for SLAM](https://mlsanity.com/paper/2112.12130/) (2021)
- [iMAP: Implicit Mapping and Positioning in Real-Time](https://mlsanity.com/paper/2103.12352/) (2021)
- [Conditional Neural Processes](https://mlsanity.com/paper/1807.01613/) (2018)
- [Local Implicit Grid Representations for 3D Scenes](https://mlsanity.com/paper/2003.08981/) (2020)
- [3D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Data](https://mlsanity.com/paper/1807.02547/) (2018)
- [Deep Local Shapes: Learning Local SDF Priors for Detailed 3D Reconstruction](https://mlsanity.com/paper/2003.10983/) (2020)
- [Vector Neurons: A General Framework for SO(3)-Equivariant Networks](https://mlsanity.com/paper/2104.12229/) (2021)
- [Neural Unsigned Distance Fields for Implicit Function Learning](https://mlsanity.com/paper/2010.13938/) (2020)
- [Learning SO(3) Equivariant Representations with Spherical CNNs](https://mlsanity.com/paper/1711.06721/) (2017)
- [PointNetLK: Robust & Efficient Point Cloud Registration using PointNet](https://mlsanity.com/paper/1903.05711/) (2019)
- [Clebsch-Gordan Nets: a Fully Fourier Space Spherical Convolutional Neural Network](https://mlsanity.com/paper/1806.09231/) (2018)
- [BundleFusion: Real-time Globally Consistent 3D Reconstruction using On-the-fly Surface Re-integration](https://mlsanity.com/paper/1604.01093/) (2016)
- [DI-Fusion: Online Implicit 3D Reconstruction with Deep Priors](https://mlsanity.com/paper/2012.05551/) (2020)
- [NeuralBlox: Real-Time Neural Representation Fusion for Robust Volumetric Mapping](https://mlsanity.com/paper/2110.09415/) (2021)
- [Self-supervised Point Set Local Descriptors for Point Cloud Registration](https://mlsanity.com/paper/2003.05199/) (2020)
- [Indirect Point Cloud Registration: Aligning Distance Fields using a Pseudo Third Point Ses](https://mlsanity.com/paper/2205.15954/) (2022)

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

- [PIN-SLAM: LiDAR SLAM Using a Point-Based Implicit Neural Representation for Achieving Global Map Consistency](https://mlsanity.com/paper/2401.09101/) (2024)
- [MIPS-Fusion: Multi-Implicit-Submaps for Scalable and Robust Online Neural RGB-D Reconstruction](https://mlsanity.com/paper/2308.08741/) (2023)
- [Uni-Fusion: Universal Continuous Mapping](https://mlsanity.com/paper/2303.12678/) (2023)
- [SceneFactory: A Workflow-centric and Unified Framework for Incremental Scene Modeling](https://mlsanity.com/paper/2405.07847/) (2024)
- [NSLF-OL: Online Learning of Neural Surface Light Fields alongside Real-time Incremental 3D Reconstruction](https://mlsanity.com/paper/2305.00282/) (2023)

## Abstract (arXiv)

Implicit representations are widely used for object reconstruction due to their efficiency and flexibility. In 2021, a novel structure named neural implicit map has been invented for incremental reconstruction. A neural implicit map alleviates the problem of inefficient memory cost of previous online 3D dense reconstruction while producing better quality. % However, the neural implicit map suffers the limitation that it does not support remapping as the frames of scans are encoded into a deep prior after generating the neural implicit map. This means, that neither this generation process is invertible, nor a deep prior is transformable. The non-remappable property makes it not possible to apply loop-closure techniques. % We present a neural implicit map based transformation algorithm to fill this gap. As our neural implicit map is transformable, our model supports remapping for this special map of latent features. % Experiments show that our remapping module is capable to well-transform neural implicit maps to new poses. Embedded into a SLAM framework, our mapping model is able to tackle the remapping of loop closures and demonstrates high-quality surface reconstruction. % Our implementation is available at githubfootnoteurlhttps://github.com/Jarrome/IMTMapping for the research community.