# Learning Graph Regularisation for Guided Super-Resolution

arXiv: https://arxiv.org/abs/2203.14297 · HTML: https://mlsanity.com/paper/2203.14297/

## Key facts

- Cited by 27 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 63 references that are in the map.
- First posted on arXiv 27 Mar 2022.

## Builds on (most cited first, 24 of 24)

- [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)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [Fully Convolutional Networks for Semantic Segmentation](https://mlsanity.com/paper/1411.4038/) (2014)
- [Vision Transformers for Dense Prediction](https://mlsanity.com/paper/2103.13413/) (2021)
- [Towards Robust Monocular Depth Estimation: Mixing Datasets for Zero-shot Cross-dataset Transfer](https://mlsanity.com/paper/1907.01341/) (2019)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [Accurate Image Super-Resolution Using Very Deep Convolutional Networks](https://mlsanity.com/paper/1511.04587/) (2015)
- [Conditional Random Fields as Recurrent Neural Networks](https://mlsanity.com/paper/1502.03240/) (2015)
- [Pixel-Adaptive Convolutional Neural Networks](https://mlsanity.com/paper/1904.05373/) (2019)
- [The Fast Bilateral Solver](https://mlsanity.com/paper/1511.03296/) (2015)
- [Towards Fast and Accurate Real-World Depth Super-Resolution: Benchmark Dataset and Baseline](https://mlsanity.com/paper/2104.06174/) (2021)
- [Deformable Kernel Networks for Joint Image Filtering](https://mlsanity.com/paper/1910.08373/) (2019)
- [Joint Image Filtering with Deep Convolutional Networks](https://mlsanity.com/paper/1710.04200/) (2017)
- [Super-resolution of Sentinel-2 images: Learning a globally applicable deep neural network](https://mlsanity.com/paper/1803.04271/) (2018)
- [Channel Attention based Iterative Residual Learning for Depth Map Super-Resolution](https://mlsanity.com/paper/2006.01469/) (2020)
- [Learning Scene Structure Guidance via Cross-Task Knowledge Transfer for Single Depth Super-Resolution](https://mlsanity.com/paper/2103.12955/) (2021)
- [A Large RGB-D Dataset for Semi-supervised Monocular Depth Estimation](https://mlsanity.com/paper/1904.10230/) (2019)
- [Guided Deep Decoder: Unsupervised Image Pair Fusion](https://mlsanity.com/paper/2007.11766/) (2020)
- [A Deep Primal-Dual Network for Guided Depth Super-Resolution](https://mlsanity.com/paper/1607.08569/) (2016)
- [Joint Graph-based Depth Refinement and Normal Estimation](https://mlsanity.com/paper/1912.01306/) (2019)
- [Unpaired Depth Super-Resolution in the Wild](https://mlsanity.com/paper/2105.12038/) (2021)

## Built on by (most cited first, 27 of 27)

- [Guided Depth Super-Resolution by Deep Anisotropic Diffusion](https://mlsanity.com/paper/2211.11592/) (2022)
- [PatchFusion: An End-to-End Tile-Based Framework for High-Resolution Monocular Metric Depth Estimation](https://mlsanity.com/paper/2312.02284/) (2023)
- [Spherical Space Feature Decomposition for Guided Depth Map Super-Resolution](https://mlsanity.com/paper/2303.08942/) (2023)
- [SGNet: Structure Guided Network via Gradient-Frequency Awareness for Depth Map Super-Resolution](https://mlsanity.com/paper/2312.05799/) (2023)
- [Guided Depth Map Super-resolution: A Survey](https://mlsanity.com/paper/2302.09598/) (2023)
- [Consistent Direct Time-of-Flight Video Depth Super-Resolution](https://mlsanity.com/paper/2211.08658/) (2022)
- [URCDC-Depth: Uncertainty Rectified Cross-Distillation with CutFlip for Monocular Depth Estimation](https://mlsanity.com/paper/2302.08149/) (2023)
- [PatchRefiner: Leveraging Synthetic Data for Real-Domain High-Resolution Monocular Metric Depth Estimation](https://mlsanity.com/paper/2406.06679/) (2024)
- [DORNet: A Degradation Oriented and Regularized Network for Blind Depth Super-Resolution](https://mlsanity.com/paper/2410.11666/) (2024)
- [Learning Mutual Modulation for Self-Supervised Cross-Modal Super-Resolution](https://mlsanity.com/paper/2207.09156/) (2022)
- [DuCos: Duality Constrained Depth Super-Resolution via Foundation Model](https://mlsanity.com/paper/2503.04171/) (2025)
- [RGB Guided ToF Imaging System: A Survey of Deep Learning-based Methods](https://mlsanity.com/paper/2405.10357/) (2024)
- [Depth Super-Resolution from Explicit and Implicit High-Frequency Features](https://mlsanity.com/paper/2303.09307/) (2023)
- [Scene Prior Filtering for Depth Super-Resolution](https://mlsanity.com/paper/2402.13876/) (2024)
- [PatchRefiner V2: Fast and Lightweight Real-Domain High-Resolution Metric Depth Estimation](https://mlsanity.com/paper/2501.01121/) (2025)
- [SEMPART: Self-supervised Multi-resolution Partitioning of Image Semantics](https://mlsanity.com/paper/2309.10972/) (2023)
- [Self-Distilled Depth Refinement with Noisy Poisson Fusion](https://mlsanity.com/paper/2409.17880/) (2024)
- [SuperInpaint: Learning Detail-Enhanced Attentional Implicit Representation for Super-resolutional Image Inpainting](https://mlsanity.com/paper/2307.14489/) (2023)
- [Advancing 3D Gaussian Splatting Editing with Complementary and Consensus Information](https://mlsanity.com/paper/2503.11601/) (2025)
- [Scene Structure Guidance Network: Unfolding Graph Partitioning into Pixel-Wise Feature Learning](https://mlsanity.com/paper/2301.00555/) (2023)
- [Adaptive Multi-modal Fusion of Spatially Variant Kernel Refinement with Diffusion Model for Blind Image Super-Resolution](https://mlsanity.com/paper/2403.05808/) (2024)
- [Multi-Order Matching Network for Alignment-Free Depth Super-Resolution](https://mlsanity.com/paper/2511.16361/) (2025)
- [SuperF: Neural Implicit Fields for Multi-Image Super-Resolution](https://mlsanity.com/paper/2512.09115/) (2025)
- [NAIMA: Semantics Aware RGB Guided Depth Super-Resolution](https://mlsanity.com/paper/2604.04407/) (2026)
- [2D Representation for Unguided Single-View 3D Super-Resolution in Real-Time](https://mlsanity.com/paper/2511.08224/) (2025)
- [Four decades of circumpolar super-resolved satellite land surface temperature data](https://mlsanity.com/paper/2511.17134/) (2025)
- [DegBins: Degradation-Driven Binning for Depth Super-Resolution](https://mlsanity.com/paper/2605.09628/) (2026)

## Abstract (arXiv)

We introduce a novel formulation for guided super-resolution. Its core is a differentiable optimisation layer that operates on a learned affinity graph. The learned graph potentials make it possible to leverage rich contextual information from the guide image, while the explicit graph optimisation within the architecture guarantees rigorous fidelity of the high-resolution target to the low-resolution source. With the decision to employ the source as a constraint rather than only as an input to the prediction, our method differs from state-of-the-art deep architectures for guided super-resolution, which produce targets that, when downsampled, will only approximately reproduce the source. This is not only theoretically appealing, but also produces crisper, more natural-looking images. A key property of our method is that, although the graph connectivity is restricted to the pixel lattice, the associated edge potentials are learned with a deep feature extractor and can encode rich context information over large receptive fields. By taking advantage of the sparse graph connectivity, it becomes possible to propagate gradients through the optimisation layer and learn the edge potentials from data. We extensively evaluate our method on several datasets, and consistently outperform recent baselines in terms of quantitative reconstruction errors, while also delivering visually sharper outputs. Moreover, we demonstrate that our method generalises particularly well to new datasets not seen during training.