# GeoSAM-3D: Geodesic Prompt Propagation for Open-Vocabulary 3D Scene Segmentation from Monocular Video

arXiv: https://arxiv.org/abs/2606.00447 · HTML: https://mlsanity.com/paper/2606.00447/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 39 references that are in the map.
- First posted on arXiv 30 May 2026.

## Builds on (most cited first, 21 of 21)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Segment Anything](https://mlsanity.com/paper/2304.02643/) (2023)
- [Emerging Properties in Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.14294/) (2021)
- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Vision Transformers for Dense Prediction](https://mlsanity.com/paper/2103.13413/) (2021)
- [4D Spatio-Temporal ConvNets: Minkowski Convolutional Neural Networks](https://mlsanity.com/paper/1904.08755/) (2019)
- [KPConv: Flexible and Deformable Convolution for Point Clouds](https://mlsanity.com/paper/1904.08889/) (2019)
- [ORB-SLAM2: an Open-Source SLAM System for Monocular, Stereo and RGB-D Cameras](https://mlsanity.com/paper/1610.06475/) (2016)
- [DROID-SLAM: Deep Visual SLAM for Monocular, Stereo, and RGB-D Cameras](https://mlsanity.com/paper/2108.10869/) (2021)
- [RandLA-Net: Efficient Semantic Segmentation of Large-Scale Point Clouds](https://mlsanity.com/paper/1911.11236/) (2019)
- [Convex Optimization: Algorithms and Complexity](https://mlsanity.com/paper/1405.4980/) (2014)
- [OpenScene: 3D Scene Understanding with Open Vocabularies](https://mlsanity.com/paper/2211.15654/) (2022)
- [LERF: Language Embedded Radiance Fields](https://mlsanity.com/paper/2303.09553/) (2023)
- [Decomposing NeRF for Editing via Feature Field Distillation](https://mlsanity.com/paper/2205.15585/) (2022)
- [Mask3D: Mask Transformer for 3D Semantic Instance Segmentation](https://mlsanity.com/paper/2210.03105/) (2022)
- [OpenMask3D: Open-Vocabulary 3D Instance Segmentation](https://mlsanity.com/paper/2306.13631/) (2023)
- [CLIP-Fields: Weakly Supervised Semantic Fields for Robotic Memory](https://mlsanity.com/paper/2210.05663/) (2022)
- [OpenSplat3D: Open-Vocabulary 3D Instance Segmentation using Gaussian Splatting](https://mlsanity.com/paper/2506.07697/) (2025)

## Abstract (arXiv)

Open-vocabulary 3D scene segmentation usually assumes RGB-D video, calibrated multi-view imagery, or a reconstructed mesh. GeoSAM-3D studies a lighter setting: a user uploads a short monocular video, clicks or names an object in one frame, and receives a propagated 3D mask over a Gaussian scene. The implementation combines frozen image and video foundation models with a monocular 3D Gaussian Splatting reconstruction and a differentiable graph-geodesic propagation kernel over Gaussian centroids. The central design choice is to propagate prompts by heat-kernel distance on the reconstructed scene graph, rather than by Euclidean nearest neighbors in 3D. This preserves continuity around curved surfaces and reduces leakage across nearby but disconnected objects. This paper describes the repository state, the mathematical kernel implemented in geosam3d.propagate, the feature head trained from Segment Anything masks, and the validation already present in the codebase. The evaluation protocol separates implementation validation, graph propagation quality, leakage control, and interactive latency.