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Unsupervised Object Detection with Theoretical Guarantees
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Proposes a translation-equivariant CNN autoencoder (softargmax encoder, Gaussian rendering decoder) and proves bounds on the position error of unsupervised object detection, validated on synthetic, CLEVR and real video data against SAM and CutLER.
Problem
Unsupervised object detection with deep networks offers few or no guarantees about whether learned representations match true object positions.
Approach
Make a CNN autoencoder exactly translation-equivariant via a softargmax encoder and Gaussian-rendering decoder, then prove that learned latent positions match true object positions up to a maximum error set by encoder/decoder receptive fields, object size, and Gaussian width.
Key results
- Synthetic experiments: all measured position errors lie at or below the theoretical bounds across encoder RF, decoder RF, object size and Gaussian s.d. sweeps, with some encoder-bound cases hitting the maximum exactly.
- On CLEVR data, the proposed method's position errors always lie within the theoretical bounds, whereas SAM and CutLER sometimes exceed them by large margins.
- Real video experiments reach test MSE of 7.2e-5 (traffic car) and 8.2e-3 (mini pool balls) in normalised units.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| increase the Gaussian standard deviation | Proposed method · Synthetic object-position experiments | position error | Hurt |
| use larger encoder and decoder receptive fields than necessary | Proposed method · Mini pool video | position error | Hurt |
Surprising findings
- SAM and CutLER, although generally achieving low position errors, sometimes have errors much larger than the proposed method's theoretical bound.
Limitations
- Only detects dynamic objects (moving or appearing at multiple locations); static objects are not learned.
- Guarantees are conditional on successful image reconstruction, which depends on architecture and optimisation.
- Representations do not transfer to videos with different backgrounds unless decoder is conditioned on a nearby frame.
Experimental setup
Datasets: synthetic white-square dataset (80x80 px) CLEVR-generated images overhead traffic video (YouTube) mini pool video (YouTube)
Benchmarks: synthetic white-square experiments CLEVR-based experiments
Metrics: position error (px) proportion of errors within 2 std of theoretical bound mean squared error on normalised positions reconstruction accuracy
Baselines: SAM CutLER
Builds on: autoencoder soft argmax Jakab et al. unsupervised keypoint detection (conditional U-Net)
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