# Real-World Repetition Estimation by Div, Grad and Curl

arXiv: https://arxiv.org/abs/1802.09971 · HTML: https://mlsanity.com/paper/1802.09971/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Feb 2018.

## Built on by (most cited first, 21 of 21)

- [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)
- [ViLMA: A Zero-Shot Benchmark for Linguistic and Temporal Grounding in Video-Language Models](https://mlsanity.com/paper/2311.07022/) (2023)
- [PoseRAC: Pose Saliency Transformer for Repetitive Action Counting](https://mlsanity.com/paper/2303.08450/) (2023)
- [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)
- [OVR: A Dataset for Open Vocabulary Temporal Repetition Counting in Videos](https://mlsanity.com/paper/2407.17085/) (2024)
- [Every Shot Counts: Using Exemplars for Repetition Counting in Videos](https://mlsanity.com/paper/2403.18074/) (2024)
- [CycleCL: Self-supervised Learning for Periodic Videos](https://mlsanity.com/paper/2311.03402/) (2023)
- [Viewpoint-Invariant Exercise Repetition Counting](https://mlsanity.com/paper/2107.13760/) (2021)
- [Count What You Want: Exemplar Identification and Few-shot Counting of Human Actions in the Wild](https://mlsanity.com/paper/2312.17330/) (2023)
- [Efficient Action Counting with Dynamic Queries](https://mlsanity.com/paper/2403.01543/) (2024)
- [Is end-to-end learning enough for fitness activity recognition?](https://mlsanity.com/paper/2305.08191/) (2023)
- [Skim then Focus: Integrating Contextual and Fine-grained Views for Repetitive Action Counting](https://mlsanity.com/paper/2406.08814/) (2024)
- [MultiCounter: Multiple Action Agnostic Repetition Counting in Untrimmed Videos](https://mlsanity.com/paper/2409.04035/) (2024)
- [Localization-Aware Multi-Scale Representation Learning for Repetitive Action Counting](https://mlsanity.com/paper/2501.07312/) (2025)
- [HoloEv-Net: Efficient Event-based Action Recognition via Holographic Spatial Embedding and Global Spectral Gating](https://mlsanity.com/paper/2602.04182/) (2026)
- [Detecting Biological Locomotion in Video: A Computational Approach](https://mlsanity.com/paper/2105.12661/) (2021)
- [IVAC-P2L: Leveraging Irregular Repetition Priors for Improving Video Action Counting](https://mlsanity.com/paper/2403.11959/) (2024)
- [GMFL-Net: A Global Multi-geometric Feature Learning Network for Repetitive Action Counting](https://mlsanity.com/paper/2409.00330/) (2024)
- [TReViS: Temporal Repetition Structure Aware Video Synthesis for Self-supervised Repetitive Action Counting](https://mlsanity.com/paper/2609.24367/) (2026)

## Abstract (arXiv)

We consider the problem of estimating repetition in video, such as performing push-ups, cutting a melon or playing violin. Existing work shows good results under the assumption of static and stationary periodicity. As realistic video is rarely perfectly static and stationary, the often preferred Fourier-based measurements is inapt. Instead, we adopt the wavelet transform to better handle non-static and non-stationary video dynamics. From the flow field and its differentials, we derive three fundamental motion types and three motion continuities of intrinsic periodicity in 3D. On top of this, the 2D perception of 3D periodicity considers two extreme viewpoints. What follows are 18 fundamental cases of recurrent perception in 2D. In practice, to deal with the variety of repetitive appearance, our theory implies measuring time-varying flow and its differentials (gradient, divergence and curl) over segmented foreground motion. For experiments, we introduce the new QUVA Repetition dataset, reflecting reality by including non-static and non-stationary videos. On the task of counting repetitions in video, we obtain favorable results compared to a deep learning alternative.