无需训练，用流形正则化解决3D重建的长期漂移问题
SSR: A Training-Free Approach for Streaming 3D Reconstruction
- 将状态序列视为流形上的轨迹，通过自表达特性计算关联矩阵
- 在多个长序列任务中减少几何漂移，提升重建精度
- 即插即用、推理时无额外开销，适合实时3D系统
流式3D重建需在严格延迟约束下实现长时间状态更新，但有记忆的循环模型常因误差累积导致几何漂移。本文从Grassmann流形视角重新审视该问题：潜在持久状态可视为子空间表示，即在流形上演化的一个点，时间一致性意味着状态轨迹应保持在（或靠近）该流形。基于此，我们提出自表达序列正则化（SSR），一种可即插即用、无需训练的推理时算子，用于强制序列在流形上的正则性。给定历史状态窗口，SSR通过自表达性质解析计算亲和矩阵，并用于正则化当前更新，有效将噪声预测拉回流形一致轨迹，且开销极低。在多个长序列基准测试中，SSR一致降低漂移，提升多种流式3D重建任务的重建质量。
原文摘要 · Abstract (English)
Streaming 3D reconstruction demands long-horizon state updates under strict latency constraints, yet stateful recurrent models often suffer from geometric drift as errors accumulate over time. We revisit this problem from a Grassmannian manifold perspective: the latent persistent state can be viewed as a subspace representation, i.e., a point evolving on a Grassmannian manifold, where temporal coherence implies the state trajectory should remain on (or near) this manifold.Based on this view, we propose Self-expressive Sequence Regularization (SSR), a plug-and-play, training-free operator that enforces Grassmannian sequence regularity during inference.Given a window of historical states, SSR computes an analytical affinity matrix via the self-expressive property and uses it to regularize the current update, effectively pulling noisy predictions back toward the manifold-consistent trajectory with minimal overhead. Experiments on long-sequence benchmarks demonstrate that SSR consistently reduces drift and improves reconstruction quality across multiple streaming 3D reconstruction tasks.
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