# Perspective-Equivariance for Unsupervised Imaging with Camera Geometry

arXiv: https://arxiv.org/abs/2403.09327 · HTML: https://mlsanity.com/paper/2403.09327/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 74 references that are in the map.
- First posted on arXiv 14 Mar 2024.

## Builds on (most cited first, 29 of 29)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [Solving Linear Inverse Problems Provably via Posterior Sampling with Latent Diffusion Models](https://mlsanity.com/paper/2307.00619/) (2023)
- [Noisier2Noise: Learning to Denoise from Unpaired Noisy Data](https://mlsanity.com/paper/1910.11908/) (2019)
- [Deep Scale-spaces: Equivariance Over Scale](https://mlsanity.com/paper/1905.11697/) (2019)
- [Ambient Diffusion: Learning Clean Distributions from Corrupted Data](https://mlsanity.com/paper/2305.19256/) (2023)
- [Mask-guided Spectral-wise Transformer for Efficient Hyperspectral Image Reconstruction](https://mlsanity.com/paper/2111.07910/) (2021)
- [Equivariant Imaging: Learning Beyond the Range Space](https://mlsanity.com/paper/2103.14756/) (2021)
- [Robust Equivariant Imaging: a fully unsupervised framework for learning to image from noisy and partial measurements](https://mlsanity.com/paper/2111.12855/) (2021)
- [A Multi-Scale and Multi-Depth Convolutional Neural Network for Remote Sensing Imagery Pan-Sharpening](https://mlsanity.com/paper/1712.09809/) (2017)
- [Super-resolution of Sentinel-2 images: Learning a globally applicable deep neural network](https://mlsanity.com/paper/1803.04271/) (2018)
- [Imaging with Equivariant Deep Learning](https://mlsanity.com/paper/2209.01725/) (2022)
- [SpaceNet MVOI: a Multi-View Overhead Imagery Dataset](https://mlsanity.com/paper/1903.12239/) (2019)
- [Sensing Theorems for Unsupervised Learning in Linear Inverse Problems](https://mlsanity.com/paper/2203.12513/) (2022)
- [Guided Deep Decoder: Unsupervised Image Pair Fusion](https://mlsanity.com/paper/2007.11766/) (2020)
- [PanFormer: a Transformer Based Model for Pan-sharpening](https://mlsanity.com/paper/2203.02916/) (2022)
- [Learning Geocentric Object Pose in Oblique Monocular Images](https://mlsanity.com/paper/2007.00729/) (2020)
- [PanFlowNet: A Flow-Based Deep Network for Pan-sharpening](https://mlsanity.com/paper/2305.07774/) (2023)
- [Pansharpening by convolutional neural networks in the full resolution framework](https://mlsanity.com/paper/2111.08334/) (2021)
- [Scale-Equivariant Imaging: Self-Supervised Learning for Image Super-Resolution and Deblurring](https://mlsanity.com/paper/2312.11232/) (2023)
- [Self-Supervised Super-Resolution for Multi-Exposure Push-Frame Satellites](https://mlsanity.com/paper/2205.02031/) (2022)
- [Unsupervised Deep Learning-based Pansharpening with Jointly-Enhanced Spectral and Spatial Fidelity](https://mlsanity.com/paper/2307.14403/) (2023)
- [Progressive Content-aware Coded Hyperspectral Compressive Imaging](https://mlsanity.com/paper/2303.09773/) (2023)
- [Computational Spectral Imaging: A Contemporary Overview](https://mlsanity.com/paper/2303.04848/) (2023)
- [Unsupervised Spectral Demosaicing with Lightweight Spectral Attention Networks](https://mlsanity.com/paper/2307.01990/) (2023)
- [Unsupervised Spatial-spectral Network Learning for Hyperspectral Compressive Snapshot Reconstruction](https://mlsanity.com/paper/2012.12086/) (2020)
- [Near Real-Time Social Distance Estimation in London](https://mlsanity.com/paper/2012.07751/) (2020)

## Built on by (most cited first, 5 of 5)

- [Equivariant Imaging for Self-supervised Hyperspectral Image Inpainting](https://mlsanity.com/paper/2404.13159/) (2024)
- [Benchmarking Self-Supervised Learning Methods for Accelerated MRI Reconstruction](https://mlsanity.com/paper/2502.14009/) (2025)
- [Fully Unsupervised Dynamic MRI Reconstruction via Diffeo-Temporal Equivariance](https://mlsanity.com/paper/2410.08646/) (2024)
- [Equivariant Splitting: Self-supervised learning from incomplete data](https://mlsanity.com/paper/2510.00929/) (2025)
- [Perspective-Equivariant Fine-tuning for Multispectral Demosaicing without Ground Truth](https://mlsanity.com/paper/2603.01332/) (2026)

## Abstract (arXiv)

Ill-posed image reconstruction problems appear in many scenarios such as remote sensing, where obtaining high quality images is crucial for environmental monitoring, disaster management and urban planning. Deep learning has seen great success in overcoming the limitations of traditional methods. However, these inverse problems rarely come with ground truth data, highlighting the importance of unsupervised learning from partial and noisy measurements alone. We propose perspective-equivariant imaging (EI), a framework that leverages classical projective camera geometry in optical imaging systems, such as satellites or handheld cameras, to recover information lost in ill-posed camera imaging problems. We show that our much richer non-linear class of group transforms, derived from camera geometry, generalises previous EI work and is an excellent prior for satellite and urban image data. Perspective-EI achieves state-of-the-art results in multispectral pansharpening, outperforming other unsupervised methods in the literature. Code at https://github.com/Andrewwango/perspective-equivariant-imaging.