# Unsupervised Image Decomposition with Phase-Correlation Networks

arXiv: https://arxiv.org/abs/2110.03473 · HTML: https://mlsanity.com/paper/2110.03473/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 55 references that are in the map.
- First posted on arXiv 7 Oct 2021.

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

- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Spatial Transformer Networks](https://mlsanity.com/paper/1506.02025/) (2015)
- [Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations](https://mlsanity.com/paper/1811.12359/) (2018)
- [Object-Centric Learning with Slot Attention](https://mlsanity.com/paper/2006.15055/) (2020)
- [Prototypical Contrastive Learning of Unsupervised Representations](https://mlsanity.com/paper/2005.04966/) (2020)
- [MONet: Unsupervised Scene Decomposition and Representation](https://mlsanity.com/paper/1901.11390/) (2019)
- [Multi-Object Representation Learning with Iterative Variational Inference](https://mlsanity.com/paper/1903.00450/) (2019)
- [Understanding disentangling in β-VAE](https://mlsanity.com/paper/1804.03599/) (2018)
- [GENESIS: Generative Scene Inference and Sampling with Object-Centric Latent Representations](https://mlsanity.com/paper/1907.13052/) (2019)
- [Recurrent Independent Mechanisms](https://mlsanity.com/paper/1909.10893/) (2019)
- [Attend, Infer, Repeat: Fast Scene Understanding with Generative Models](https://mlsanity.com/paper/1603.08575/) (2016)
- [Learning in the Frequency Domain](https://mlsanity.com/paper/2002.12416/) (2020)
- [SPACE: Unsupervised Object-Oriented Scene Representation via Spatial Attention and Decomposition](https://mlsanity.com/paper/2001.02407/) (2020)
- [Sequential Attend, Infer, Repeat: Generative Modelling of Moving Objects](https://mlsanity.com/paper/1806.01794/) (2018)
- [Frequency Separation for Real-World Super-Resolution](https://mlsanity.com/paper/1911.07850/) (2019)
- [Entity Abstraction in Visual Model-Based Reinforcement Learning](https://mlsanity.com/paper/1910.12827/) (2019)
- [GENESIS-V2: Inferring Unordered Object Representations without Iterative Refinement](https://mlsanity.com/paper/2104.09958/) (2021)
- [ST-GAN: Spatial Transformer Generative Adversarial Networks for Image Compositing](https://mlsanity.com/paper/1803.01837/) (2018)
- [Fast Training of Convolutional Networks through FFTs](https://mlsanity.com/paper/1312.5851/) (2013)
- [Stacked Capsule Autoencoders](https://mlsanity.com/paper/1906.06818/) (2019)
- [Learning Unsupervised Hierarchical Part Decomposition of 3D Objects from a Single RGB Image](https://mlsanity.com/paper/2004.01176/) (2020)
- [Unsupervised Layered Image Decomposition into Object Prototypes](https://mlsanity.com/paper/2104.14575/) (2021)
- [LR-GAN: Layered Recursive Generative Adversarial Networks for Image Generation](https://mlsanity.com/paper/1703.01560/) (2017)
- [Object Discovery with a Copy-Pasting GAN](https://mlsanity.com/paper/1905.11369/) (2019)
- [Benchmarking Unsupervised Object Representations for Video Sequences](https://mlsanity.com/paper/2006.07034/) (2020)
- [Deep Transformation-Invariant Clustering](https://mlsanity.com/paper/2006.11132/) (2020)
- [Tracking by Animation: Unsupervised Learning of Multi-Object Attentive Trackers](https://mlsanity.com/paper/1809.03137/) (2018)
- [The Atari Grand Challenge Dataset](https://mlsanity.com/paper/1705.10998/) (2017)
- [Copy and Paste GAN: Face Hallucination from Shaded Thumbnails](https://mlsanity.com/paper/2002.10650/) (2020)

## Built on by (most cited first, 6 of 6)

- [Compositional Scene Representation Learning via Reconstruction: A Survey](https://mlsanity.com/paper/2202.07135/) (2022)
- [Object-Centric Video Prediction via Decoupling of Object Dynamics and Interactions](https://mlsanity.com/paper/2302.11850/) (2023)
- [Compositional Scene Modeling with Global Object-Centric Representations](https://mlsanity.com/paper/2211.11500/) (2022)
- [TextOCVP: Object-Centric Video Prediction with Language Guidance](https://mlsanity.com/paper/2502.11655/) (2025)
- [VideoPCDNet: Video Parsing and Prediction with Phase Correlation Networks](https://mlsanity.com/paper/2506.19621/) (2025)
- [SlotDiT: Object-Centric Representations for Diffusion Transformers](https://mlsanity.com/paper/2609.17414/) (2026)

## Abstract (arXiv)

The ability to decompose scenes into their object components is a desired property for autonomous agents, allowing them to reason and act in their surroundings. Recently, different methods have been proposed to learn object-centric representations from data in an unsupervised manner. These methods often rely on latent representations learned by deep neural networks, hence requiring high computational costs and large amounts of curated data. Such models are also difficult to interpret. To address these challenges, we propose the Phase-Correlation Decomposition Network (PCDNet), a novel model that decomposes a scene into its object components, which are represented as transformed versions of a set of learned object prototypes. The core building block in PCDNet is the Phase-Correlation Cell (PC Cell), which exploits the frequency-domain representation of the images in order to estimate the transformation between an object prototype and its transformed version in the image. In our experiments, we show how PCDNet outperforms state-of-the-art methods for unsupervised object discovery and segmentation on simple benchmark datasets and on more challenging data, while using a small number of learnable parameters and being fully interpretable.