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Learned Trajectory Embedding for Subspace Clustering
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Learns a PointNet-style trajectory encoder with contrastive and geometric losses so that trajectory embeddings identify motion subspaces, then clusters them for fast motion segmentation.
Problem
Segmenting multiple rigid or non-rigid motions from occluded point trajectories is hard because cluster assignment and subspace estimation are coupled as a chicken-and-egg problem.
Approach
Train a feed-forward trajectory encoder with an InfoNCE metric-learning loss so features cluster by motion, plus a coordinate-MLP decoder that predicts the generating subspace basis, using residual and feature-difference losses for geometric consistency and noise invariance; clustering is then done purely in feature space.
Key results
- On Hopkins155 the method reaches 0.63% mean classification error with 7ms runtime, the best among compared methods on fully visible trajectories.
- On KT3DMoSeg it achieves 5.85% mean and 0.80% median error, outperforming prior methods on the mean metric over the reported baselines (e.g., SSC 33.88% under a different column layout is not comparable; Subset gets 8.08% mean).
- On Hopkins12 with missing data it reports 0.60% mean error, competitive with state-of-the-art methods.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use learned trajectory embeddings for motion segmentation instead of Subset | Trajectory-based motion segmentation · Hopkins155 | classification error (%): 0.31 -> 0.62 | Hurt |
| Use learned trajectory embeddings for motion segmentation instead of ALCsp | Trajectory-based motion segmentation · Hopkins12 | classification error (%): 1.28 -> 5.12 | Hurt |
| Use learned trajectory embeddings for motion segmentation instead of CoReg | Trajectory-based motion segmentation · KT3DMoSeg | classification error (%): 7.92 -> 5.85 | Helped |
Surprising findings
- The disjoint-subspace assumption was checked empirically: concatenated subspace ranks reached 82, implying the subspaces in Hopkins155 do not intersect numerically.
Limitations
- Focuses only on linear subspace motion models, tied to affine cameras.
- Performance on Hopkins12 and KT3DMoSeg with heavy occlusion is less dominant; trajectory completion is local and may fail for short sub-trajectories.
- Requires known ranks and number of motions via hierarchical clustering.
Experimental setup
Datasets: Hopkins155 KT3DMoSeg
Benchmarks: Hopkins155 Hopkins12 KT3DMoSeg
Metrics: classification error (%) mean pixel error angle between features runtime
Baselines: RANSAC GPCA MSL LSA ALC5 ALCsp LRR SSC RSIM MultiConsensus KerAdd CoReg
Builds on: PointNet InfoNCE sparse subspace clustering
Closest papers by meaning
- Learning Segmentation from Point Trajectories (NeurIPS 2024 · similarity 0.90)
- GTR: A General, Multi-View, and Dynamic Framework for Trajectory Representation Learning (ICML 2025 · similarity 0.85)
- Segment Any Motion in Videos (CVPR 2025 · similarity 0.84)
- TrajLoc: Trajectory-Attention Localization for Multi-Object Motion Control (NeurIPS 2026 · similarity 0.84)
- Generative Human Trajectory Recovery via Embedding-Space Conditional Diffusion (ICML 2025 · similarity 0.84)
- FLD: Fourier Latent Dynamics for Structured Motion Representation and Learning (ICLR 2024 · similarity 0.84)
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