# HIIF: Hierarchical Encoding based Implicit Image Function for Continuous Super-resolution

arXiv: https://arxiv.org/abs/2412.03748 · HTML: https://mlsanity.com/paper/2412.03748/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Builds on 49 of its 66 references that are in the map.
- First posted on arXiv 4 Dec 2024.

## Builds on (most cited first, 30 of 49)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [SwinIR: Image Restoration Using Swin Transformer](https://mlsanity.com/paper/2108.10257/) (2021)
- [Enhanced Deep Residual Networks for Single Image Super-Resolution](https://mlsanity.com/paper/1707.02921/) (2017)
- [Image Super-Resolution via Iterative Refinement](https://mlsanity.com/paper/2104.07636/) (2021)
- [Image Super-Resolution Using Very Deep Residual Channel Attention Networks](https://mlsanity.com/paper/1807.02758/) (2018)
- [ESRGAN: Enhanced Super-Resolution Generative Adversarial Networks](https://mlsanity.com/paper/1809.00219/) (2018)
- [Image Super-Resolution Using Deep Convolutional Networks](https://mlsanity.com/paper/1501.00092/) (2014)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [Accurate Image Super-Resolution Using Very Deep Convolutional Networks](https://mlsanity.com/paper/1511.04587/) (2015)
- [Uformer: A General U-Shaped Transformer for Image Restoration](https://mlsanity.com/paper/2106.03106/) (2021)
- [Residual Dense Network for Image Super-Resolution](https://mlsanity.com/paper/1802.08797/) (2018)
- [Nerfstudio: A Modular Framework for Neural Radiance Field Development](https://mlsanity.com/paper/2302.04264/) (2023)
- [Learning Continuous Image Representation with Local Implicit Image Function](https://mlsanity.com/paper/2012.09161/) (2020)
- [SAL: Sign Agnostic Learning of Shapes from Raw Data](https://mlsanity.com/paper/1911.10414/) (2019)
- [Efficient Attention: Attention with Linear Complexities](https://mlsanity.com/paper/1812.01243/) (2018)
- [MambaIR: A Simple Baseline for Image Restoration with State-Space Model](https://mlsanity.com/paper/2402.15648/) (2024)
- [Implicit Functions in Feature Space for 3D Shape Reconstruction and Completion](https://mlsanity.com/paper/2003.01456/) (2020)
- [XCiT: Cross-Covariance Image Transformers](https://mlsanity.com/paper/2106.09681/) (2021)
- [Deep Local Shapes: Learning Local SDF Priors for Detailed 3D Reconstruction](https://mlsanity.com/paper/2003.10983/) (2020)
- [NeRV: Neural Representations for Videos](https://mlsanity.com/paper/2110.13903/) (2021)
- [VRT: A Video Restoration Transformer](https://mlsanity.com/paper/2201.12288/) (2022)
- [Implicit Diffusion Models for Continuous Super-Resolution](https://mlsanity.com/paper/2303.16491/) (2023)
- [Meta-SR: A Magnification-Arbitrary Network for Super-Resolution](https://mlsanity.com/paper/1903.00875/) (2019)
- [Local Texture Estimator for Implicit Representation Function](https://mlsanity.com/paper/2111.08918/) (2021)
- [VideoINR: Learning Video Implicit Neural Representation for Continuous Space-Time Super-Resolution](https://mlsanity.com/paper/2206.04647/) (2022)
- [VmambaIR: Visual State Space Model for Image Restoration](https://mlsanity.com/paper/2403.11423/) (2024)

## Built on by (most cited first, 17 of 17)

- [The Tenth NTIRE 2025 Efficient Super-Resolution Challenge Report](https://mlsanity.com/paper/2504.10686/) (2025)
- [NTIRE 2025 Challenge on Short-form UGC Video Quality Assessment and Enhancement: Methods and Results](https://mlsanity.com/paper/2504.13131/) (2025)
- [GIViC: Generative Implicit Video Compression](https://mlsanity.com/paper/2503.19604/) (2025)
- [C2D-ISR: Optimizing Attention-based Image Super-resolution from Continuous to Discrete Scales](https://mlsanity.com/paper/2503.13740/) (2025)
- [Continuous Space-Time Video Super-Resolution with 3D Fourier Fields](https://mlsanity.com/paper/2509.26325/) (2025)
- [Instance Data Condensation for Image Super-Resolution](https://mlsanity.com/paper/2505.21099/) (2025)
- [Compressed Video Super-Resolution based on Hierarchical Encoding](https://mlsanity.com/paper/2506.14381/) (2025)
- [Self-Supervised Image Super-Resolution Quality Assessment based on Content-Free Multi-Model Oriented Representation Learning](https://mlsanity.com/paper/2602.10744/) (2026)
- [Content-Aware Frequency Encoding for Implicit Neural Representations with Fourier-Chebyshev Features](https://mlsanity.com/paper/2603.01028/) (2026)
- [Implicit Neural Representation-Based Continuous Single Image Super-Resolution: An Empirical Benchmark](https://mlsanity.com/paper/2601.17723/) (2026)
- [Single Image Super-Resolution via Bivariate `A Trous Wavelet Diffusion](https://mlsanity.com/paper/2603.07234/) (2026)
- [GB-LSR: Local Spectral Decoding with a Learned Global Bandwidth for Arbitrary-Scale Super-Resolution](https://mlsanity.com/paper/2606.19617/) (2026)
- [Fidelity- and Perception-Aware Local Implicit Attention for Arbitrary-Scale Image Super-Resolution](https://mlsanity.com/paper/2606.21910/) (2026)
- [Dual-Prior Guided Null-Space Learning with Mixture-of-Splines for Arbitrary Medical Slice Super-Resolution](https://mlsanity.com/paper/2606.26716/) (2026)
- [PixelSR: Efficient Screen Content Super-Resolution via Pixel Classification](https://mlsanity.com/paper/2608.00646/) (2026)
- [From Multi-Resolution Cells to Gigapixel Whole Slide Images Foundation Model for Computational Pathology](https://mlsanity.com/paper/2608.03508/) (2026)
- [How Far Can INRs Go? Cross-Domain Parameter-efficient INR-Based Semantic Segmentation for Brain MRI](https://mlsanity.com/paper/2609.31573/) (2026)

## Abstract (arXiv)

Recent advances in implicit neural representations (INRs) have shown significant promise in modeling visual signals for various low-vision tasks including image super-resolution (ISR). INR-based ISR methods typically learn continuous representations, providing flexibility for generating high-resolution images at any desired scale from their low-resolution counterparts. However, existing INR-based ISR methods utilize multi-layer perceptrons for parameterization in the network; this does not take account of the hierarchical structure existing in local sampling points and hence constrains the representation capability. In this paper, we propose a new Hierarchical encoding based Implicit Image Function for continuous image super-resolution, HIIF, which leverages a novel hierarchical positional encoding that enhances the local implicit representation, enabling it to capture fine details at multiple scales. Our approach also embeds a multi-head linear attention mechanism within the implicit attention network by taking additional non-local information into account. Our experiments show that, when integrated with different backbone encoders, HIIF outperforms the state-of-the-art continuous image super-resolution methods by up to 0.17dB in PSNR. The source code of HIIF will be made publicly available at urlwww.github.com.