# Learning Continuous Environment Fields via Implicit Functions

arXiv: https://arxiv.org/abs/2111.13997 · HTML: https://mlsanity.com/paper/2111.13997/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 54 references that are in the map.
- First posted on arXiv 27 Nov 2021.

## Builds on (most cited first, 30 of 34)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [Fully Convolutional Networks for Semantic Segmentation](https://mlsanity.com/paper/1411.4038/) (2014)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [HyperNetworks](https://mlsanity.com/paper/1609.09106/) (2016)
- [Scene Representation Networks: Continuous 3D-Structure-Aware Neural Scene Representations](https://mlsanity.com/paper/1906.01618/) (2019)
- [PIFu: Pixel-Aligned Implicit Function for High-Resolution Clothed Human Digitization](https://mlsanity.com/paper/1905.05172/) (2019)
- [Convolutional Occupancy Networks](https://mlsanity.com/paper/2003.04618/) (2020)
- [PIFuHD: Multi-Level Pixel-Aligned Implicit Function for High-Resolution 3D Human Digitization](https://mlsanity.com/paper/2004.00452/) (2020)
- [SAL: Sign Agnostic Learning of Shapes from Raw Data](https://mlsanity.com/paper/1911.10414/) (2019)
- [Local Implicit Grid Representations for 3D Scenes](https://mlsanity.com/paper/2003.08981/) (2020)
- [Learning from Synthetic Humans](https://mlsanity.com/paper/1701.01370/) (2017)
- [DISN: Deep Implicit Surface Network for High-quality Single-view 3D Reconstruction](https://mlsanity.com/paper/1905.10711/) (2019)
- [Resolving 3D Human Pose Ambiguities with 3D Scene Constraints](https://mlsanity.com/paper/1908.06963/) (2019)
- [Stochastic Scene-Aware Motion Prediction](https://mlsanity.com/paper/2108.08284/) (2021)
- [Long-term Human Motion Prediction with Scene Context](https://mlsanity.com/paper/2007.03672/) (2020)
- [Cyclical Annealing Schedule: A Simple Approach to Mitigating KL Vanishing](https://mlsanity.com/paper/1903.10145/) (2019)
- [Grasping Field: Learning Implicit Representations for Human Grasps](https://mlsanity.com/paper/2008.04451/) (2020)
- [Value Iteration Networks](https://mlsanity.com/paper/1602.02867/) (2016)
- [Generating 3D People in Scenes without People](https://mlsanity.com/paper/1912.02923/) (2019)
- [Fully Convolutional Instance-aware Semantic Segmentation](https://mlsanity.com/paper/1611.07709/) (2016)
- [Learning with AMIGo: Adversarially Motivated Intrinsic Goals](https://mlsanity.com/paper/2006.12122/) (2020)
- [Learning to Act Properly: Predicting and Explaining Affordances from Images](https://mlsanity.com/paper/1712.07576/) (2017)
- [Putting Humans in a Scene: Learning Affordance in 3D Indoor Environments](https://mlsanity.com/paper/1903.05690/) (2019)
- [Does computer vision matter for action?](https://mlsanity.com/paper/1905.12887/) (2019)
- [Learning to See before Learning to Act: Visual Pre-training for Manipulation](https://mlsanity.com/paper/2107.00646/) (2021)

## Built on by (most cited first, 8 of 8)

- [Learning Continuous Grasping Function with a Dexterous Hand from Human Demonstrations](https://mlsanity.com/paper/2207.05053/) (2022)
- [VL-Fields: Towards Language-Grounded Neural Implicit Spatial Representations](https://mlsanity.com/paper/2305.12427/) (2023)
- [NTFields: Neural Time Fields for Physics-Informed Robot Motion Planning](https://mlsanity.com/paper/2210.00120/) (2022)
- [Multi-Object Navigation with dynamically learned neural implicit representations](https://mlsanity.com/paper/2210.05129/) (2022)
- [Progressive Learning for Physics-informed Neural Motion Planning](https://mlsanity.com/paper/2306.00616/) (2023)
- [Physics-informed Temporal Difference Metric Learning for Robot Motion Planning](https://mlsanity.com/paper/2505.05691/) (2025)
- [Multi-Object Navigation in real environments using hybrid policies](https://mlsanity.com/paper/2401.13800/) (2024)
- [Neural Navigation Functions for Zero-Shot Generalizable Motion Planning](https://mlsanity.com/paper/2606.03756/) (2026)

## Abstract (arXiv)

We propose a novel scene representation that encodes reaching distance -- the distance between any position in the scene to a goal along a feasible trajectory. We demonstrate that this environment field representation can directly guide the dynamic behaviors of agents in 2D mazes or 3D indoor scenes. Our environment field is a continuous representation and learned via a neural implicit function using discretely sampled training data. We showcase its application for agent navigation in 2D mazes, and human trajectory prediction in 3D indoor environments. To produce physically plausible and natural trajectories for humans, we additionally learn a generative model that predicts regions where humans commonly appear, and enforce the environment field to be defined within such regions. Extensive experiments demonstrate that the proposed method can generate both feasible and plausible trajectories efficiently and accurately.