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

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.