# Bottom-up Modeling of Repeated Elements via Single Image Analysis-by-Synthesis

arXiv: https://arxiv.org/abs/2609.07939 · HTML: https://mlsanity.com/paper/2609.07939/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 52 of its 70 references that are in the map.
- First posted on arXiv 7 Sep 2026.

## Builds on (most cited first, 30 of 52)

- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Segment Anything](https://mlsanity.com/paper/2304.02643/) (2023)
- [End-to-End Object Detection with Transformers](https://mlsanity.com/paper/2005.12872/) (2020)
- [Emerging Properties in Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.14294/) (2021)
- [Spatial Transformer Networks](https://mlsanity.com/paper/1506.02025/) (2015)
- [DINOv3](https://mlsanity.com/paper/2508.10104/) (2025)
- [Object-Centric Learning with Slot Attention](https://mlsanity.com/paper/2006.15055/) (2020)
- [Dynamic Routing Between Capsules](https://mlsanity.com/paper/1710.09829/) (2017)
- [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)
- [SinGAN: Learning a Generative Model from a Single Natural Image](https://mlsanity.com/paper/1905.01164/) (2019)
- [Deep ViT Features as Dense Visual Descriptors](https://mlsanity.com/paper/2112.05814/) (2021)
- [Bridging the Gap to Real-World Object-Centric Learning](https://mlsanity.com/paper/2209.14860/) (2022)
- [Attend, Infer, Repeat: Fast Scene Understanding with Generative Models](https://mlsanity.com/paper/1603.08575/) (2016)
- [SPACE: Unsupervised Object-Oriented Scene Representation via Spatial Attention and Decomposition](https://mlsanity.com/paper/2001.02407/) (2020)
- [Learning To Count Everything](https://mlsanity.com/paper/2104.08391/) (2021)
- [Illiterate DALL-E Learns to Compose](https://mlsanity.com/paper/2110.11405/) (2021)
- [3D Shape Induction from 2D Views of Multiple Objects](https://mlsanity.com/paper/1612.05872/) (2016)
- [ClevrTex: A Texture-Rich Benchmark for Unsupervised Multi-Object Segmentation](https://mlsanity.com/paper/2111.10265/) (2021)
- [Class-Agnostic Counting](https://mlsanity.com/paper/1811.00472/) (2018)
- [Stacked Capsule Autoencoders](https://mlsanity.com/paper/1906.06818/) (2019)
- [CounTR: Transformer-based Generalised Visual Counting](https://mlsanity.com/paper/2208.13721/) (2022)
- [A Low-Shot Object Counting Network With Iterative Prototype Adaptation](https://mlsanity.com/paper/2211.08217/) (2022)
- [GAN-Supervised Dense Visual Alignment](https://mlsanity.com/paper/2112.05143/) (2021)
- [Improving Object-centric Learning with Query Optimization](https://mlsanity.com/paper/2210.08990/) (2022)
- [SinDDM: A Single Image Denoising Diffusion Model](https://mlsanity.com/paper/2211.16582/) (2022)
- [CountGD: Multi-Modal Open-World Counting](https://mlsanity.com/paper/2407.04619/) (2024)
- [Few-shot Object Counting and Detection](https://mlsanity.com/paper/2207.10988/) (2022)
- [Invariant Slot Attention: Object Discovery with Slot-Centric Reference Frames](https://mlsanity.com/paper/2302.04973/) (2023)

## Abstract (arXiv)

We address the problem of discovering repeated elements from a single image. In contrast to existing approaches that depend on large annotated datasets, curated multi-image collections, or object segmentation masks, we show that a single image can suffice to learn a meaningful object model in a completely bottom-up fashion, without any prior knowledge beyond a coarse scale prior. Our method learns a tunable image-space prototype of the repeated elements through a reconstruction objective, enabling the model to identify and synthesize consistent object instances within the same image. Experiments on 116 real images from the FSC-147 dataset demonstrate that our method successfully learns coherent element models and captures intra-category variation on challenging images. Qualitative results reveal superior reconstructions and interpretable decompositions compared to classical decomposition, joint alignment, and 3D object modeling methods, while maintaining a simple 2D formulation. These results suggest that meaningful object discovery can emerge from single image learning alone.