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Chonghyuk Song

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TMLR Journal 2025 Journal Article

SIRE: SE(3) Intrinsic Rigidity Embeddings

Cameron Omid Smith
Basile Van Hoorick
Chonghyuk Song
Vincent Sitzmann
Vitor Campagnolo Guizilini
Yue Wang

Motion serves as a powerful cue for scene perception and understanding by separating independently moving surfaces and organizing the physical world into distinct entities. We introduce SIRE, a self-supervised method for motion discovery of objects and dynamic scene reconstruction from casual scenes by learning intrinsic rigidity embeddings from videos. Our method trains an image encoder to estimate scene rigidity and geometry, supervised by a simple 4D reconstruction loss: a least-squares solver uses the estimated geometry and rigidity to lift 2D point track trajectories into SE(3) tracks, which are simply re-projected back to 2D and compared against the original 2D trajectories for supervision. Crucially, our framework is fully end-to-end differentiable and can be optimized either on video datasets to learn generalizable image priors, or even on a single video to capture scene-specific structure -- highlighting strong data efficiency. We demonstrate the effectiveness of our rigidity embeddings and geometry across multiple settings, including downstream object segmentation, SE(3) rigid motion estimation, and self-supervised depth estimation. Our findings suggest that SIRE can pave the way towards self-supervised learning of priors over geometry and motion rigidity from large-scale video data.

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AAAI Conference 2021 Conference Paper

Improving Gradient Flow with Unrolled Highway Expectation Maximization

Chonghyuk Song
Eunseok Kim
Inwook Shim

Integrating model-based machine learning methods into deep neural architectures allows one to leverage both the expressive power of deep neural nets and the ability of model-based methods to incorporate domain-specific knowledge. In particular, many works have employed the expectation maximization (EM) algorithm in the form of an unrolled layerwise structure that is jointly trained with a backbone neural network. However, it is difficult to discriminatively train the backbone network by backpropagating through the EM iterations as they are prone to the vanishing gradient problem. To address this issue, we propose Highway Expectation Maximization Networks (HEMNet), which is comprised of unrolled iterations of the generalized EM (GEM) algorithm based on the Newton-Rahpson method. HEMNet features scaled skip connections, or highways, along the depths of the unrolled architecture, resulting in improved gradient flow during backpropagation while incurring negligible additional computation and memory costs compared to standard unrolled EM. Furthermore, HEMNet preserves the underlying EM procedure, thereby fully retaining the convergence properties of the original EM algorithm. We achieve significant improvement in performance on several semantic segmentation benchmarks and empirically show that HEMNet effectively alleviates gradient decay.

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