# Automatic Estimation of Self-Reported Pain by Trajectory Analysis in the Manifold of Fixed Rank Positive Semi-Definite Matrices

arXiv: https://arxiv.org/abs/2209.01813 · HTML: https://mlsanity.com/paper/2209.01813/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 51 references that are in the map.
- First posted on arXiv 5 Sep 2022.

## Builds on (most cited first, 7 of 7)

- [Realtime Multi-Person 2D Pose Estimation using Part Affinity Fields](https://mlsanity.com/paper/1611.08050/) (2016)
- [A Novel Geometric Framework on Gram Matrix Trajectories for Human Behavior Understanding](https://mlsanity.com/paper/1807.00676/) (2018)
- [Personalized Automatic Estimation of Self-reported Pain Intensity from Facial Expressions](https://mlsanity.com/paper/1706.07154/) (2017)
- [Automatic Estimation of Self-Reported Pain by Interpretable Representations of Motion Dynamics](https://mlsanity.com/paper/2006.13882/) (2020)
- [DeepFaceLIFT: Interpretable Personalized Models for Automatic Estimation of Self-Reported Pain](https://mlsanity.com/paper/1708.04670/) (2017)
- [Physiological and behavioral profiling for nociceptive pain estimation using personalized multitask learning](https://mlsanity.com/paper/1711.04036/) (2017)
- [Fitting, Comparison, and Alignment of Trajectories on Positive Semi-Definite Matrices with Application to Action Recognition](https://mlsanity.com/paper/1908.00646/) (2019)

## Built on by (most cited first, 4 of 4)

- [QAFE-Net: Quality Assessment of Facial Expressions with Landmark Heatmaps](https://mlsanity.com/paper/2312.00856/) (2023)
- [Trajectory-guided Motion Perception for Facial Expression Quality Assessment in Neurological Disorders](https://mlsanity.com/paper/2504.09530/) (2025)
- [PainNet: Statistical Relation Network with Episode-Based Training for Pain Estimation](https://mlsanity.com/paper/2504.06257/) (2025)
- [TraMP-LLaMA: Generative Interpretability with Decoupled Instruction Tuning for Facial Expression Quality Assessment](https://mlsanity.com/paper/2606.26942/) (2026)

## Abstract (arXiv)

We propose an automatic method to estimate self-reported pain based on facial landmarks extracted from videos. For each video sequence, we decompose the face into four different regions and the pain intensity is measured by modeling the dynamics of facial movement using the landmarks of these regions. A formulation based on Gram matrices is used for representing the trajectory of landmarks on the Riemannian manifold of symmetric positive semi-definite matrices of fixed rank. A curve fitting algorithm is used to smooth the trajectories and temporal alignment is performed to compute the similarity between the trajectories on the manifold. A Support Vector Regression classifier is then trained to encode extracted trajectories into pain intensity levels consistent with self-reported pain intensity measurement. Finally, a late fusion of the estimation for each region is performed to obtain the final predicted pain level. The proposed approach is evaluated on two publicly available datasets, the UNBCMcMaster Shoulder Pain Archive and the Biovid Heat Pain dataset. We compared our method to the state-of-the-art on both datasets using different testing protocols, showing the competitiveness of the proposed approach.