# Structure from Recurrent Motion: From Rigidity to Recurrency

arXiv: https://arxiv.org/abs/1804.06510 · HTML: https://mlsanity.com/paper/1804.06510/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Apr 2018.

## Built on by (most cited first, 16 of 16)

- [Generating Smooth Pose Sequences for Diverse Human Motion Prediction](https://mlsanity.com/paper/2108.08422/) (2021)
- [TransRAC: Encoding Multi-scale Temporal Correlation with Transformers for Repetitive Action Counting](https://mlsanity.com/paper/2204.01018/) (2022)
- [Multi-level Motion Attention for Human Motion Prediction](https://mlsanity.com/paper/2106.09300/) (2021)
- [Diverse Human Motion Prediction Guided by Multi-Level Spatial-Temporal Anchors](https://mlsanity.com/paper/2302.04860/) (2023)
- [Human Joint Kinematics Diffusion-Refinement for Stochastic Motion Prediction](https://mlsanity.com/paper/2210.05976/) (2022)
- [Contact-aware Human Motion Forecasting](https://mlsanity.com/paper/2210.03954/) (2022)
- [PoseRAC: Pose Saliency Transformer for Repetitive Action Counting](https://mlsanity.com/paper/2303.08450/) (2023)
- [Learning Semantic Latent Directions for Accurate and Controllable Human Motion Prediction](https://mlsanity.com/paper/2407.11494/) (2024)
- [CountLLM: Towards Generalizable Repetitive Action Counting via Large Language Model](https://mlsanity.com/paper/2503.17690/) (2025)
- [Repetitive Action Counting with Hybrid Temporal Relation Modeling](https://mlsanity.com/paper/2412.07233/) (2024)
- [PR-RRN: Pairwise-Regularized Residual-Recursive Networks for Non-rigid Structure-from-Motion](https://mlsanity.com/paper/2108.07506/) (2021)
- [Scene-aware Human Motion Forecasting via Mutual Distance Prediction](https://mlsanity.com/paper/2310.00615/) (2023)
- [DivDiff: A Conditional Diffusion Model for Diverse Human Motion Prediction](https://mlsanity.com/paper/2409.00014/) (2024)
- [A Spatio-temporal Continuous Network for Stochastic 3D Human Motion Prediction](https://mlsanity.com/paper/2508.01585/) (2025)
- [FCA-RAC: First Cycle Annotated Repetitive Action Counting](https://mlsanity.com/paper/2406.12178/) (2024)
- [IVAC-P2L: Leveraging Irregular Repetition Priors for Improving Video Action Counting](https://mlsanity.com/paper/2403.11959/) (2024)

## Abstract (arXiv)

This paper proposes a new method for Non-Rigid Structure-from-Motion (NRSfM) from a long monocular video sequence observing a non-rigid object performing recurrent and possibly repetitive dynamic action. Departing from the traditional idea of using linear low-order or lowrank shape model for the task of NRSfM, our method exploits the property of shape recurrency (i.e., many deforming shapes tend to repeat themselves in time). We show that recurrency is in fact a generalized rigidity. Based on this, we reduce NRSfM problems to rigid ones provided that certain recurrency condition is satisfied. Given such a reduction, standard rigid-SfM techniques are directly applicable (without any change) to the reconstruction of non-rigid dynamic shapes. To implement this idea as a practical approach, this paper develops efficient algorithms for automatic recurrency detection, as well as camera view clustering via a rigidity-check. Experiments on both simulated sequences and real data demonstrate the effectiveness of the method. Since this paper offers a novel perspective on rethinking structure-from-motion, we hope it will inspire other new problems in the field.