PAGF: Short-Horizon Forecasting of 3D Facial Landmarks

Short-term facial landmark forecasting is important for anticipatory facial behavior in human–robot interaction, yet models trained with pointwise reconstruction losses often suffer from mean reversion, producing low-error predictions with weakened motion dynamics. To address this issue, we propose a peak-aware gated recurrent unit (GRU) framework that separates forecasting into peak planning and peak-conditioned trajectory generation. The planning stage estimates the timing and intensity of a salient motion peak within the forecast horizon together with a global motion direction, and the generation stage produces short-horizon landmark displacements through temporal gating and structured motion composition. The model is trained with reconstruction loss, peak supervision, peak-integrity regularization, and correlation-based temporal-shape regularization. Experiments on the MEAD dataset using 3D facial landmarks under a subject-independent protocol show a clear distortion–dynamics trade-off. Compared with static and sequence-to-sequence baselines, the proposed method better preserves peak-related facial dynamics while maintaining competitive 24-step prediction accuracy.

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Publication Details

Journal
Mathematics
Published
2026-04-06
DOI
https://doi.org/10.3390/math14071222
Primary Topic
Face recognition and analysis
Type
article
Field-Weighted Citation Impact
0.00

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article

PAGF: Short-Horizon Forecasting of 3D Facial Landmarks

Mingzhu Yan, Jian Liu, Y. X. Yuan, Fangyan Yang
Mathematics
Face recognition and analysis
article

PAGF: Short-Horizon Forecasting of 3D Facial Landmarks

Mingzhu Yan, Jian Liu, Y. X. Yuan, Fangyan Yang
article en

Abstract

Short-term facial landmark forecasting is important for anticipatory facial behavior in human–robot interaction, yet models trained with pointwise reconstruction losses often suffer from mean reversion, producing low-error predictions with weakened motion dynamics. To address this issue, we propose a peak-aware gated recurrent unit (GRU) framework that separates forecasting into peak planning and peak-conditioned trajectory generation. The planning stage estimates the timing and intensity of a salient motion peak within the forecast horizon together with a global motion direction, and the generation stage produces short-horizon landmark displacements through temporal gating and structured motion composition. The model is trained with reconstruction loss, peak supervision, peak-integrity regularization, and correlation-based temporal-shape regularization. Experiments on the MEAD dataset using 3D facial landmarks under a subject-independent protocol show a clear distortion–dynamics trade-off. Compared with static and sequence-to-sequence baselines, the proposed method better preserves peak-related facial dynamics while maintaining competitive 24-step prediction accuracy.

MathematicsVol. 14(7)
University of Shanghai for Science and Technology (CN), Shanghai Research Center for Acupuncture and Meridians (CN)
Shanghai Science and Technology Development Foundation, National Science and Technology Major Project, Key Technologies Research and Development Program, National Key Research and Development Program of China
Sustainable cities and communities
Openalex Percentile: Top 31%
Face recognition and analysis
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