# Exemplar-based Pattern Synthesis with Implicit Periodic Field Network

arXiv: https://arxiv.org/abs/2204.01671 · HTML: https://mlsanity.com/paper/2204.01671/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 43 references that are in the map.
- First posted on arXiv 4 Apr 2022.

## Builds on (most cited first, 21 of 21)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [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)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [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)
- [Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/1511.06434/) (2015)
- [pixelNeRF: Neural Radiance Fields from One or Few Images](https://mlsanity.com/paper/2012.02190/) (2020)
- [Image Super-Resolution Using Deep Convolutional Networks](https://mlsanity.com/paper/1501.00092/) (2014)
- [PIFu: Pixel-Aligned Implicit Function for High-Resolution Clothed Human Digitization](https://mlsanity.com/paper/1905.05172/) (2019)
- [SinGAN: Learning a Generative Model from a Single Natural Image](https://mlsanity.com/paper/1905.01164/) (2019)
- [Precomputed Real-Time Texture Synthesis with Markovian Generative Adversarial Networks](https://mlsanity.com/paper/1604.04382/) (2016)
- [Frequency Bias in Neural Networks for Input of Non-Uniform Density](https://mlsanity.com/paper/2003.04560/) (2020)
- [Learning to Infer Implicit Surfaces without 3D Supervision](https://mlsanity.com/paper/1911.00767/) (2019)
- [Non-Stationary Texture Synthesis by Adversarial Expansion](https://mlsanity.com/paper/1805.04487/) (2018)
- [Learning Texture Manifolds with the Periodic Spatial GAN](https://mlsanity.com/paper/1705.06566/) (2017)
- [Learning a Neural 3D Texture Space from 2D Exemplars](https://mlsanity.com/paper/1912.04158/) (2019)
- [TextureGAN: Controlling Deep Image Synthesis with Texture Patches](https://mlsanity.com/paper/1706.02823/) (2017)
- [Texture Synthesis with Spatial Generative Adversarial Networks](https://mlsanity.com/paper/1611.08207/) (2016)
- [GramGAN: Deep 3D Texture Synthesis From 2D Exemplars](https://mlsanity.com/paper/2006.16112/) (2020)

## Built on by (most cited first, 3 of 3)

- [Multiresolution Neural Networks for Imaging](https://mlsanity.com/paper/2208.11813/) (2022)
- [Learning Continuous Implicit Representation for Near-Periodic Patterns](https://mlsanity.com/paper/2208.12278/) (2022)
- [NeRF-Texture: Synthesizing Neural Radiance Field Textures](https://mlsanity.com/paper/2412.10004/) (2024)

## Abstract (arXiv)

Synthesis of ergodic, stationary visual patterns is widely applicable in texturing, shape modeling, and digital content creation. The wide applicability of this technique thus requires the pattern synthesis approaches to be scalable, diverse, and authentic. In this paper, we propose an exemplar-based visual pattern synthesis framework that aims to model the inner statistics of visual patterns and generate new, versatile patterns that meet the aforementioned requirements. To this end, we propose an implicit network based on generative adversarial network (GAN) and periodic encoding, thus calling our network the Implicit Periodic Field Network (IPFN). The design of IPFN ensures scalability: the implicit formulation directly maps the input coordinates to features, which enables synthesis of arbitrary size and is computationally efficient for 3D shape synthesis. Learning with a periodic encoding scheme encourages diversity: the network is constrained to model the inner statistics of the exemplar based on spatial latent codes in a periodic field. Coupled with continuously designed GAN training procedures, IPFN is shown to synthesize tileable patterns with smooth transitions and local variations. Last but not least, thanks to both the adversarial training technique and the encoded Fourier features, IPFN learns high-frequency functions that produce authentic, high-quality results. To validate our approach, we present novel experimental results on various applications in 2D texture synthesis and 3D shape synthesis.