# OSLO: On-the-Sphere Learning for Omnidirectional images and its application to 360-degree image compression

arXiv: https://arxiv.org/abs/2107.09179 · HTML: https://mlsanity.com/paper/2107.09179/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 54 references that are in the map.
- First posted on arXiv 19 Jul 2021.

## Builds on (most cited first, 26 of 26)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Variational image compression with a scale hyperprior](https://mlsanity.com/paper/1802.01436/) (2018)
- [Representation Learning on Graphs with Jumping Knowledge Networks](https://mlsanity.com/paper/1806.03536/) (2018)
- [End-to-end Optimized Image Compression](https://mlsanity.com/paper/1611.01704/) (2016)
- [Learned Image Compression with Discretized Gaussian Mixture Likelihoods and Attention Modules](https://mlsanity.com/paper/2001.01568/) (2020)
- [Spherical CNNs](https://mlsanity.com/paper/1801.10130/) (2018)
- [CompressAI: a PyTorch library and evaluation platform for end-to-end compression research](https://mlsanity.com/paper/2011.03029/) (2020)
- [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)
- [Density Modeling of Images using a Generalized Normalization Transformation](https://mlsanity.com/paper/1511.06281/) (2015)
- [Spherical CNNs on Unstructured Grids](https://mlsanity.com/paper/1901.02039/) (2019)
- [End-to-end optimization of nonlinear transform codes for perceptual quality](https://mlsanity.com/paper/1607.05006/) (2016)
- [DeepSphere: Efficient spherical Convolutional Neural Network with HEALPix sampling for cosmological applications](https://mlsanity.com/paper/1810.12186/) (2018)
- [Learning End-to-End Lossy Image Compression: A Benchmark](https://mlsanity.com/paper/2002.03711/) (2020)
- [Orientation-aware Semantic Segmentation on Icosahedron Spheres](https://mlsanity.com/paper/1907.12849/) (2019)
- [Spin-Weighted Spherical CNNs](https://mlsanity.com/paper/2006.10731/) (2020)
- [Artistic style transfer for videos and spherical images](https://mlsanity.com/paper/1708.04538/) (2017)
- [Restricted Deformable Convolution based Road Scene Semantic Segmentation Using Surround View Cameras](https://mlsanity.com/paper/1801.00708/) (2018)
- [SpherePHD: Applying CNNs on a Spherical PolyHeDron Representation of 360 degree Images](https://mlsanity.com/paper/1811.08196/) (2018)
- [Learning Spherical Convolution for Fast Features from 360deg Imagery](https://mlsanity.com/paper/1708.00919/) (2017)
- [SalNet360: Saliency Maps for omni-directional images with CNN](https://mlsanity.com/paper/1709.06505/) (2017)
- [Is the deconvolution layer the same as a convolutional layer?](https://mlsanity.com/paper/1609.07009/) (2016)
- [Graph-Based Classification of Omnidirectional Images](https://mlsanity.com/paper/1707.08301/) (2017)

## Built on by (most cited first, 7 of 7)

- [Deep Learning for Omnidirectional Vision: A Survey and New Perspectives](https://mlsanity.com/paper/2205.10468/) (2022)
- [Pseudocylindrical Convolutions for Learned Omnidirectional Image Compression](https://mlsanity.com/paper/2112.13227/) (2021)
- [Hierarchical Spherical CNNs with Lifting-based Adaptive Wavelets for Pooling and Unpooling](https://mlsanity.com/paper/2205.15571/) (2022)
- [Viewport-based Neural 360deg Image Compression](https://mlsanity.com/paper/2603.22776/) (2026)
- [Spectral Diffusion Models on the Sphere](https://mlsanity.com/paper/2601.20498/) (2026)
- [Rate-Distortion Adaptive Primitive Selection for Omnidirectional Gaussian Splatting](https://mlsanity.com/paper/2609.34367/) (2026)
- [S3N: A Spherical Spiral Scanning Network for Weather Forecasting](https://mlsanity.com/paper/2610.04338/) (2026)

## Abstract (arXiv)

State-of-the-art 2D image compression schemes rely on the power of convolutional neural networks (CNNs). Although CNNs offer promising perspectives for 2D image compression, extending such models to omnidirectional images is not straightforward. First, omnidirectional images have specific spatial and statistical properties that can not be fully captured by current CNN models. Second, basic mathematical operations composing a CNN architecture, e.g., translation and sampling, are not well-defined on the sphere. In this paper, we study the learning of representation models for omnidirectional images and propose to use the properties of HEALPix uniform sampling of the sphere to redefine the mathematical tools used in deep learning models for omnidirectional images. In particular, we: i) propose the definition of a new convolution operation on the sphere that keeps the high expressiveness and the low complexity of a classical 2D convolution; ii) adapt standard CNN techniques such as stride, iterative aggregation, and pixel shuffling to the spherical domain; and then iii) apply our new framework to the task of omnidirectional image compression. Our experiments show that our proposed on-the-sphere solution leads to a better compression gain that can save 13.7% of the bit rate compared to similar learned models applied to equirectangular images. Also, compared to learning models based on graph convolutional networks, our solution supports more expressive filters that can preserve high frequencies and provide a better perceptual quality of the compressed images. Such results demonstrate the efficiency of the proposed framework, which opens new research venues for other omnidirectional vision tasks to be effectively implemented on the sphere manifold.