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.

Despite the importance of unsupervised object detection, to the best of our knowledge, there is no previous work addressing this problem. One main issue, widely known to the community, is that object boundaries derived only from 2D image appearance are ambiguous and unreliable. To address this, we exploit LiDAR clues to aid unsupervised object detection. By exploiting the 3D scene structure, the issue of localization can be considerably mitigated. We further identify another major issue, seldom noticed by the community, that the long-tailed and open-ended (sub-)category distribution should be accommodated.