# Learning Continuous Implicit Representation for Near-Periodic Patterns

arXiv: https://arxiv.org/abs/2208.12278 · HTML: https://mlsanity.com/paper/2208.12278/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 79 references that are in the map.
- First posted on arXiv 25 Aug 2022.

## Builds on (most cited first, 30 of 35)

- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017)
- [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)
- [Describing Textures in the Wild](https://mlsanity.com/paper/1311.3618/) (2013)
- [Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Network](https://mlsanity.com/paper/1609.04802/) (2016)
- [Deep High-Resolution Representation Learning for Human Pose Estimation](https://mlsanity.com/paper/1902.09212/) (2019)
- [NeRF in the Wild: Neural Radiance Fields for Unconstrained Photo Collections](https://mlsanity.com/paper/2008.02268/) (2020)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [Multi-Stage Progressive Image Restoration](https://mlsanity.com/paper/2102.02808/) (2021)
- [Resolution-robust Large Mask Inpainting with Fourier Convolutions](https://mlsanity.com/paper/2109.07161/) (2021)
- [Learning Continuous Image Representation with Local Implicit Image Function](https://mlsanity.com/paper/2012.09161/) (2020)
- [Learning Shape Templates with Structured Implicit Functions](https://mlsanity.com/paper/1904.06447/) (2019)
- [A General and Adaptive Robust Loss Function](https://mlsanity.com/paper/1701.03077/) (2017)
- [How Neural Networks Extrapolate: From Feedforward to Graph Neural Networks](https://mlsanity.com/paper/2009.11848/) (2020)
- [The Contextual Loss for Image Transformation with Non-Aligned Data](https://mlsanity.com/paper/1803.02077/) (2018)
- [Adversarial Generation of Continuous Images](https://mlsanity.com/paper/2011.12026/) (2020)
- [Neural Blind Deconvolution Using Deep Priors](https://mlsanity.com/paper/1908.02197/) (2019)
- [Recurrent Feature Reasoning for Image Inpainting](https://mlsanity.com/paper/2008.03737/) (2020)
- [Neural Networks Fail to Learn Periodic Functions and How to Fix It](https://mlsanity.com/paper/2006.08195/) (2020)
- [Learning Pyramid-Context Encoder Network for High-Quality Image Inpainting](https://mlsanity.com/paper/1904.07475/) (2019)
- [High-Resolution Image Inpainting with Iterative Confidence Feedback and Guided Upsampling](https://mlsanity.com/paper/2005.11742/) (2020)
- [Single-Image Piece-wise Planar 3D Reconstruction via Associative Embedding](https://mlsanity.com/paper/1902.09777/) (2019)
- [TransFill: Reference-guided Image Inpainting by Merging Multiple Color and Spatial Transformations](https://mlsanity.com/paper/2103.15982/) (2021)
- [Texture Synthesis with Spatial Generative Adversarial Networks](https://mlsanity.com/paper/1611.08207/) (2016)
- [Rethinking Positional Encoding](https://mlsanity.com/paper/2107.02561/) (2021)
- [X-Fields: Implicit Neural View-, Light- and Time-Image Interpolation](https://mlsanity.com/paper/2010.00450/) (2020)
- [Learning a Sketch Tensor Space for Image Inpainting of Man-made Scenes](https://mlsanity.com/paper/2103.15087/) (2021)
- [Image Inpainting with External-internal Learning and Monochromic Bottleneck](https://mlsanity.com/paper/2104.09068/) (2021)

## Built on by (most cited first, 4 of 4)

- [Virtual Home Staging: Inverse Rendering and Editing an Indoor Panorama under Natural Illumination](https://mlsanity.com/paper/2311.12265/) (2023)
- [Neural Functions for Learning Periodic Signal](https://mlsanity.com/paper/2506.09526/) (2025)
- [Direct Motif Extraction from High Resolution Crystalline STEM Images](https://mlsanity.com/paper/2303.07438/) (2023)
- [Bottom-up Modeling of Repeated Elements via Single Image Analysis-by-Synthesis](https://mlsanity.com/paper/2609.07939/) (2026)

## Abstract (arXiv)

Near-Periodic Patterns (NPP) are ubiquitous in man-made scenes and are composed of tiled motifs with appearance differences caused by lighting, defects, or design elements. A good NPP representation is useful for many applications including image completion, segmentation, and geometric remapping. But representing NPP is challenging because it needs to maintain global consistency (tiled motifs layout) while preserving local variations (appearance differences). Methods trained on general scenes using a large dataset or single-image optimization struggle to satisfy these constraints, while methods that explicitly model periodicity are not robust to periodicity detection errors. To address these challenges, we learn a neural implicit representation using a coordinate-based MLP with single image optimization. We design an input feature warping module and a periodicity-guided patch loss to handle both global consistency and local variations. To further improve the robustness, we introduce a periodicity proposal module to search and use multiple candidate periodicities in our pipeline. We demonstrate the effectiveness of our method on more than 500 images of building facades, friezes, wallpapers, ground, and Mondrian patterns on single and multi-planar scenes.