# Bayesian Spatial Kernel Smoothing for Scalable Dense Semantic Mapping

arXiv: https://arxiv.org/abs/1909.04631 · HTML: https://mlsanity.com/paper/1909.04631/

## Key facts

- Cited by 35 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Sep 2019.

## Built on by (most cited first, 30 of 35)

- [(AF)2-S3Net: Attentive Feature Fusion with Adaptive Feature Selection for Sparse Semantic Segmentation Network](https://mlsanity.com/paper/2102.04530/) (2021)
- [FIDNet: LiDAR Point Cloud Semantic Segmentation with Fully Interpolation Decoding](https://mlsanity.com/paper/2109.03787/) (2021)
- [ConDA: Unsupervised Domain Adaptation for LiDAR Segmentation via Regularized Domain Concatenation](https://mlsanity.com/paper/2111.15242/) (2021)
- [LESS: Label-Efficient Semantic Segmentation for LiDAR Point Clouds](https://mlsanity.com/paper/2210.08064/) (2022)
- [MotionSC: Data Set and Network for Real-Time Semantic Mapping in Dynamic Environments](https://mlsanity.com/paper/2203.07060/) (2022)
- [Grid-Centric Traffic Scenario Perception for Autonomous Driving: A Comprehensive Review](https://mlsanity.com/paper/2303.01212/) (2023)
- [Modeling Uncertainty in 3D Gaussian Splatting through Continuous Semantic Splatting](https://mlsanity.com/paper/2411.02547/) (2024)
- [MEM: Multi-Modal Elevation Mapping for Robotics and Learning](https://mlsanity.com/paper/2309.16818/) (2023)
- [ConvBKI: Real-Time Probabilistic Semantic Mapping Network with Quantifiable Uncertainty](https://mlsanity.com/paper/2310.16020/) (2023)
- [The Bare Necessities: Designing Simple, Effective Open-Vocabulary Scene Graphs](https://mlsanity.com/paper/2412.01539/) (2024)
- [S3Net: 3D LiDAR Sparse Semantic Segmentation Network](https://mlsanity.com/paper/2103.08745/) (2021)
- [Convolutional Bayesian Kernel Inference for 3D Semantic Mapping](https://mlsanity.com/paper/2209.10663/) (2022)
- [Depth from Camera Motion and Object Detection](https://mlsanity.com/paper/2103.01468/) (2021)
- [PanopticNDT: Efficient and Robust Panoptic Mapping](https://mlsanity.com/paper/2309.13635/) (2023)
- [Evidential Semantic Mapping in Off-road Environments with Uncertainty-aware Bayesian Kernel Inference](https://mlsanity.com/paper/2403.14138/) (2024)
- [Energy-based Legged Robots Terrain Traversability Modeling via Deep Inverse Reinforcement Learning](https://mlsanity.com/paper/2207.03034/) (2022)
- [UFO: Uncertainty-aware LiDAR-image Fusion for Off-road Semantic Terrain Map Estimation](https://mlsanity.com/paper/2403.02642/) (2024)
- [Dynamic Semantic Occupancy Mapping using 3D Scene Flow and Closed-Form Bayesian Inference](https://mlsanity.com/paper/2108.03180/) (2021)
- [Inverse reinforcement learning for autonomous navigation via differentiable semantic mapping and planning](https://mlsanity.com/paper/2101.00186/) (2021)
- [SEAL: Simultaneous Exploration and Localization in Multi-Robot Systems](https://mlsanity.com/paper/2306.12623/) (2023)
- [EvidMTL: Evidential Multi-Task Learning for Uncertainty-Aware Semantic Surface Mapping from Monocular RGB Images](https://mlsanity.com/paper/2503.04441/) (2025)
- [ZeST: A VLM-based Zero-Shot Traversability Navigation for Unknown Environments](https://mlsanity.com/paper/2508.19131/) (2025)
- [Mapping High-level Semantic Regions in Indoor Environments without Object Recognition](https://mlsanity.com/paper/2403.07076/) (2024)
- [Uncertainty-aware Semantic Mapping in Off-road Environments with Dempster-Shafer Theory of Evidence](https://mlsanity.com/paper/2405.06265/) (2024)
- [LatentBKI: Open-Dictionary Continuous Mapping in Visual-Language Latent Spaces with Quantifiable Uncertainty](https://mlsanity.com/paper/2410.11783/) (2024)
- [Real-Time Metric-Semantic Mapping for Autonomous Navigation in Outdoor Environments](https://mlsanity.com/paper/2412.00291/) (2024)
- [PSG-Nav: Probabilistic Scene Graph Navigation via Multiverse Decision Making](https://mlsanity.com/paper/2606.01313/) (2026)
- [Efficient Prediction of Dense Visual Embeddings via Distillation and RGB-D Transformers](https://mlsanity.com/paper/2601.00359/) (2026)
- [CARE: Confidence-rich Autonomous Robot Exploration using Bayesian Kernel Inference and Optimization](https://mlsanity.com/paper/2309.05200/) (2023)
- [3DTTNet: Multimodal Fusion-Based 3D Traversable Terrain Modeling for Off-Road Environments](https://mlsanity.com/paper/2412.08195/) (2024)

## Abstract (arXiv)

This paper develops a Bayesian continuous 3D semantic occupancy map from noisy point clouds by generalizing the Bayesian kernel inference model for building occupancy maps, a binary problem, to semantic maps, a multi-class problem. The proposed method provides a unified probabilistic model for both occupancy and semantic probabilities and nicely reverts to the original occupancy mapping framework when only one occupied class exists in obtained measurements. The Bayesian spatial kernel inference relaxes the independent grid assumption and brings smoothness and continuity to the map inference, enabling to exploit local correlations present in the environment and increasing the performance. The accompanying software uses multi-threading and vectorization, and runs at about 2 Hz on a laptop CPU. Evaluations using multiple sequences of stereo camera and LiDAR datasets show that the proposed method consistently outperforms current baselines. We also present a qualitative evaluation using data collected with a bipedal robot platform on the University of Michigan - North Campus.