Unsupervised Object Detection with Theoretical Guarantees

TL;DR

This paper introduces the first unsupervised object detection method with proven theoretical guarantees, ensuring accurate object position recovery within quantifiable bounds, validated through synthetic and real data experiments.

Contribution

The paper presents a novel unsupervised object detection architecture with theoretical guarantees on position accuracy, a first in the field.

Findings

Method's predictions are within theoretical error bounds on CLEVR data.

Error bounds depend on encoder/decoder receptive fields, object sizes, and Gaussian widths.

Synthetic experiments validate theoretical predictions up to pixel-level precision.

Abstract

Unsupervised object detection using deep neural networks is typically a difficult problem with few to no guarantees about the learned representation. In this work we present the first unsupervised object detection method that is theoretically guaranteed to recover the true object positions up to quantifiable small shifts. We develop an unsupervised object detection architecture and prove that the learned variables correspond to the true object positions up to small shifts related to the encoder and decoder receptive field sizes, the object sizes, and the widths of the Gaussians used in the rendering process. We perform detailed analysis of how the error depends on each of these variables and perform synthetic experiments validating our theoretical predictions up to a precision of individual pixels. We also perform experiments on CLEVR-based data and show that, unlike current SOTA object detection methods (SAM, CutLER), our method's prediction errors always lie within our theoretical bounds. We hope that this work helps open up an avenue of research into object detection methods with theoretical guarantees.