# Learning Local Implicit Fourier Representation for Image Warping

arXiv: https://arxiv.org/abs/2207.01831 · HTML: https://mlsanity.com/paper/2207.01831/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 60 references that are in the map.
- First posted on arXiv 5 Jul 2022.

## Builds on (most cited first, 30 of 39)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [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)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (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)
- [Spatial Transformer Networks](https://mlsanity.com/paper/1506.02025/) (2015)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [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)
- [Real-Time Single Image and Video Super-Resolution Using an Efficient Sub-Pixel Convolutional Neural Network](https://mlsanity.com/paper/1609.05158/) (2016)
- [PWC-Net: CNNs for Optical Flow Using Pyramid, Warping, and Cost Volume](https://mlsanity.com/paper/1709.02371/) (2017)
- [Accurate Image Super-Resolution Using Very Deep Convolutional Networks](https://mlsanity.com/paper/1511.04587/) (2015)
- [Pre-Trained Image Processing Transformer](https://mlsanity.com/paper/2012.00364/) (2020)
- [Scene Representation Networks: Continuous 3D-Structure-Aware Neural Scene Representations](https://mlsanity.com/paper/1906.01618/) (2019)
- [Residual Dense Network for Image Super-Resolution](https://mlsanity.com/paper/1802.08797/) (2018)
- [Learning Continuous Image Representation with Local Implicit Image Function](https://mlsanity.com/paper/2012.09161/) (2020)
- [Local Implicit Grid Representations for 3D Scenes](https://mlsanity.com/paper/2003.08981/) (2020)
- [BasicVSR: The Search for Essential Components in Video Super-Resolution and Beyond](https://mlsanity.com/paper/2012.02181/) (2020)
- [Single Image Super-Resolution via a Holistic Attention Network](https://mlsanity.com/paper/2008.08767/) (2020)
- [NeRV: Neural Representations for Videos](https://mlsanity.com/paper/2110.13903/) (2021)
- [How Neural Networks Extrapolate: From Feedforward to Graph Neural Networks](https://mlsanity.com/paper/2009.11848/) (2020)
- [COTR: Correspondence Transformer for Matching Across Images](https://mlsanity.com/paper/2103.14167/) (2021)
- [Meta-SR: A Magnification-Arbitrary Network for Super-Resolution](https://mlsanity.com/paper/1903.00875/) (2019)
- [Frame-Recurrent Video Super-Resolution](https://mlsanity.com/paper/1801.04590/) (2018)
- [Local Texture Estimator for Implicit Representation Function](https://mlsanity.com/paper/2111.08918/) (2021)

## Built on by (most cited first, 14 of 14)

- [Implicit Neural Representation for Cooperative Low-light Image Enhancement](https://mlsanity.com/paper/2303.11722/) (2023)
- [Learning A Physical-aware Diffusion Model Based on Transformer for Underwater Image Enhancement](https://mlsanity.com/paper/2403.01497/) (2024)
- [Fast Context-Based Low-Light Image Enhancement via Neural Implicit Representations](https://mlsanity.com/paper/2407.12511/) (2024)
- [BF-STVSR: B-Splines and Fourier-Best Friends for High Fidelity Spatial-Temporal Video Super-Resolution](https://mlsanity.com/paper/2501.11043/) (2025)
- [OmniZoomer: Learning to Move and Zoom in on Sphere at High-Resolution](https://mlsanity.com/paper/2308.08114/) (2023)
- [JDEC: JPEG Decoding via Enhanced Continuous Cosine Coefficients](https://mlsanity.com/paper/2404.05558/) (2024)
- [Scene Matters: Model-based Deep Video Compression](https://mlsanity.com/paper/2303.04557/) (2023)
- [ResVR: Joint Rescaling and Viewport Rendering of Omnidirectional Images](https://mlsanity.com/paper/2404.16825/) (2024)
- [Towards Lossless Implicit Neural Representation via Bit Plane Decomposition](https://mlsanity.com/paper/2502.21001/) (2025)
- [Implicit Neural Image Stitching](https://mlsanity.com/paper/2309.01409/) (2023)
- [LeRF: Learning Resampling Function for Adaptive and Efficient Image Interpolation](https://mlsanity.com/paper/2407.09935/) (2024)
- [Unwarping Screen Content Images via Structure-texture Enhancement Network and Transformation Self-estimation](https://mlsanity.com/paper/2504.15108/) (2025)
- [JPEG Processing Neural Operator for Backward-Compatible Coding](https://mlsanity.com/paper/2507.23521/) (2025)
- [D2R2OSR: Degradation-Disentangled Representation for Real-World Omnidirectional Image Super-Resolution](https://mlsanity.com/paper/2606.29314/) (2026)

## Abstract (arXiv)

Image warping aims to reshape images defined on rectangular grids into arbitrary shapes. Recently, implicit neural functions have shown remarkable performances in representing images in a continuous manner. However, a standalone multi-layer perceptron suffers from learning high-frequency Fourier coefficients. In this paper, we propose a local texture estimator for image warping (LTEW) followed by an implicit neural representation to deform images into continuous shapes. Local textures estimated from a deep super-resolution (SR) backbone are multiplied by locally-varying Jacobian matrices of a coordinate transformation to predict Fourier responses of a warped image. Our LTEW-based neural function outperforms existing warping methods for asymmetric-scale SR and homography transform. Furthermore, our algorithm well generalizes arbitrary coordinate transformations, such as homography transform with a large magnification factor and equirectangular projection (ERP) perspective transform, which are not provided in training.