This library implements Gaussian Process Regression (GPR) on point cloud data using a kernel that employs geodesic distance as the metric instead of the traditional Euclidean distance. This approach is particularly useful for applications where the underlying geometry of the data is non-Euclidean, such as surfaces embedded in 3D space.
- Geodesic Distance Kernel: A custom kernel that computes geodesic distances on point clouds.
- Point Cloud Support: Designed to work directly with 3D point cloud data.
- Gaussian Process Regression: Provides a flexible and probabilistic framework for regression tasks.
Clone the repository and install the required dependencies:
git clone https://github.com/lucabeber/gpr-on-point-cloud.git
cd gpr-on-point-cloudIf you are using uv environment manager, you can create a virtual environment and install the library with the following commands:
uv syncOtherwise, you can install the required dependencies manually.
An example on how to use this library is provided in example.py.
Here you can see the reconstruction of the distribution on a point cloud.
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| Cup with a red X draw on it | Reconstruction of the X |
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| Plate with different shapes | Reconstriction of the shapes |
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| Bunny with the X | Reconstriction of the X |
This project is licensed under the MIT License. See the LICENSE file for details.
This library was inspired by the need for non-Euclidean regression techniques in 3D geometry processing tasks.
This library is based on the following paper:
@article{borovitskiy2020matern,
title={Mat{\'e}rn Gaussian processes on Riemannian manifolds},
author={Borovitskiy, Viacheslav and Terenin, Alexander and Mostowsky, Peter and others},
journal={Advances in Neural Information Processing Systems},
volume={33},
pages={12426--12437},
year={2020}
}