Diffused Fields

This package is supplementary material for the paper "Object-centric Task Representation and Transfer using Diffused Orientation Fields".

This is the core package that provides fundamental diffusion algorithms and geometric manifold operations for computing Diffused Orienation Fields (DOF).

For robot manipulation experiments using DOF, see the companion package:

• diffused_fields_robotics (depends on this package) - Object-centric robot manipulation applications: local action primitives (peeling, slicing and tactile coverage), trajectory optimization, and reinforcement learning using DOF.

Features

Core package for solving orientation valued diffusion PDE (i.e., heat equation) on geometric manifolds.

This package provides implementations of both traditional diffusion solvers and walk-on-spheres methods on point clouds for various data types (scalars, vectors, quaternions).

• Diffusion on Manifolds: Scalar, vector, and quaternion diffusion on point clouds
• Walk-on-Spheres Methods: Monte Carlo-based diffusion solvers for point clouds and various geometric primitives
• Visualization Tools: Interactive 3D visualization with Polyscope
• Comparisons to Baselines: Comparison to nearest frame projection, tangent vector projection and Euclidean diffusion baselines

Installation

Complete Installation (Recommended)

Follow the installation instructions of the diffused_fields_robotics

Stand-alone Installation Using Python 3.12 virtual environment

# Create a virtual environment named 'df' with Python 3.12
python3.12 -m venv df

# Activate the virtual environment
source df/bin/activate

# Install the package in editable mode
pip install -e .

Repository Structure

diffused_fields/
├── src/diffused_fields/     # Main package source code
│   ├── core/                # Core algorithms and data structures
│   ├── diffusion/           # Diffusion solvers (scalar, vector, quaternion)
│   ├── manifold/            # Manifold operations and geometry
│   ├── utils/               # Utility functions
│   ├── visualization/       # Visualization tools
│   └── baselines/           # Baseline methods for comparison
├── scripts/                 # Example scripts and demonstrations
├── data/                    # Sample point clouds and meshes
│   ├── pointclouds/         # .ply and .pcd files
│   └── meshes/              # .obj and .stl files
└── config/                  # Configuration files

Paper and Citation

If you use this package in your research, please cite:

@online{bilalogluTactileErgodicControl2024,
  title = {Tactile {{Ergodic Control Using Diffusion}} and {{Geometric Algebra}}},
  author = {Bilaloglu, Cem and Löw, Tobias and Calinon, Sylvain},
  date = {2024-02-07},
  eprint = {2402.04862},
  eprinttype = {arxiv},
  eprintclass = {cs},
  url = {http://arxiv.org/abs/2402.04862}
}

Reproducing Paper Results

Simulation data and plots from the paper can be generated using the scripts in this repository.

Dependencies

To compute the discrete Laplacian on point clouds (and also meshes if you want) robust_laplacian: https://github.com/nmwsharp/robust-laplacians-py

For basic point cloud operations (another library can be easily used instead): open3d: https://www.open3d.org

For visualizations: plotly: https://polyscope.run/py/

For sparse matrix operations: scipy: https://scipy.org

For linear algebra operations: numpy: https://numpy.org

This code is maintained by Cem Bilaloglu and licensed under the MIT License.

Copyright (c) 2025 Idiap Research Institute [email protected]