# Direction of Arrival Estimation of Sound Sources Using Icosahedral CNNs

arXiv: https://arxiv.org/abs/2203.16940 · HTML: https://mlsanity.com/paper/2203.16940/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 52 references that are in the map.
- First posted on arXiv 31 Mar 2022.

## Builds on (most cited first, 28 of 28)

- [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)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Spherical CNNs](https://mlsanity.com/paper/1801.10130/) (2018)
- [Gauge Equivariant Convolutional Networks and the Icosahedral CNN](https://mlsanity.com/paper/1902.04615/) (2019)
- [Learning SO(3) Equivariant Representations with Spherical CNNs](https://mlsanity.com/paper/1711.06721/) (2017)
- [Sound Event Localization and Detection of Overlapping Sources Using Convolutional Recurrent Neural Networks](https://mlsanity.com/paper/1807.00129/) (2018)
- [DeepSphere: a graph-based spherical CNN](https://mlsanity.com/paper/2012.15000/) (2020)
- [DeepSphere: Efficient spherical Convolutional Neural Network with HEALPix sampling for cosmological applications](https://mlsanity.com/paper/1810.12186/) (2018)
- [gpuRIR: A Python Library for Room Impulse Response Simulation with GPU Acceleration](https://mlsanity.com/paper/1810.11359/) (2018)
- [A Survey of Sound Source Localization with Deep Learning Methods](https://mlsanity.com/paper/2109.03465/) (2021)
- [Efficient Generalized Spherical CNNs](https://mlsanity.com/paper/2010.11661/) (2020)
- [Direction of arrival estimation for multiple sound sources using convolutional recurrent neural network](https://mlsanity.com/paper/1710.10059/) (2017)
- [Scattering Networks on the Sphere for Scalable and Rotationally Equivariant Spherical CNNs](https://mlsanity.com/paper/2102.02828/) (2021)
- [Graph-Based Classification of Omnidirectional Images](https://mlsanity.com/paper/1707.08301/) (2017)
- [Robust Sound Source Tracking Using SRP-PHAT and 3D Convolutional Neural Networks](https://mlsanity.com/paper/2006.09006/) (2020)
- [Towards End-to-End Acoustic Localization using Deep Learning: from Audio Signal to Source Position Coordinates](https://mlsanity.com/paper/1807.11094/) (2018)
- [Multi-Speaker DOA Estimation Using Deep Convolutional Networks Trained with Noise Signals](https://mlsanity.com/paper/1807.11722/) (2018)
- [Sound source detection, localization and classification using consecutive ensemble of CRNN models](https://mlsanity.com/paper/1908.00766/) (2019)
- [Differentiable Tracking-Based Training of Deep Learning Sound Source Localizers](https://mlsanity.com/paper/2111.00030/) (2021)
- [Regression and Classification for Direction-of-Arrival Estimation with Convolutional Recurrent Neural Networks](https://mlsanity.com/paper/1904.08452/) (2019)
- [Indoor Sound Source Localization with Probabilistic Neural Network](https://mlsanity.com/paper/1712.07814/) (2017)
- [Time Difference of Arrival Estimation from Frequency-Sliding Generalized Cross-Correlations Using Convolutional Neural Networks](https://mlsanity.com/paper/2002.00641/) (2020)
- [Data-Efficient Framework for Real-world Multiple Sound Source 2D Localization](https://mlsanity.com/paper/2012.05533/) (2020)
- [SALADnet: Self-Attentive multisource Localization in the Ambisonics Domain](https://mlsanity.com/paper/2107.11066/) (2021)
- [Sound Source Localization in a Multipath Environment Using Convolutional Neural Networks](https://mlsanity.com/paper/1710.10948/) (2017)
- [BeamLearning: an end-to-end Deep Learning approach for the angular localization of sound sources using raw multichannel acoustic pressure data](https://mlsanity.com/paper/2104.13347/) (2021)

## Built on by (most cited first, 3 of 3)

- [AtlasD: Automatic Local Symmetry Discovery](https://mlsanity.com/paper/2504.10777/) (2025)
- [Position tracking of a varying number of sound sources with sliding permutation invariant training](https://mlsanity.com/paper/2210.14536/) (2022)
- [Permutation Invariant Recurrent Neural Networks for Sound Source Tracking Applications](https://mlsanity.com/paper/2306.08510/) (2023)

## Abstract (arXiv)

In this paper, we present a new model for Direction of Arrival (DOA) estimation of sound sources based on an Icosahedral Convolutional Neural Network (CNN) applied over SRP-PHAT power maps computed from the signals received by a microphone array. This icosahedral CNN is equivariant to the 60 rotational symmetries of the icosahedron, which represent a good approximation of the continuous space of spherical rotations, and can be implemented using standard 2D convolutional layers, having a lower computational cost than most of the spherical CNNs. In addition, instead of using fully connected layers after the icosahedral convolutions, we propose a new soft-argmax function that can be seen as a differentiable version of the argmax function and allows us to solve the DOA estimation as a regression problem interpreting the output of the convolutional layers as a probability distribution. We prove that using models that fit the equivariances of the problem allows us to outperform other state-of-the-art models with a lower computational cost and more robustness, obtaining root mean square localization errors lower than 10deg even in scenarios with a reverberation time T60 of 1.5 s.