# Robust Facial Landmark Detection by Multi-order Multi-constraint Deep Networks

arXiv: https://arxiv.org/abs/2012.04927 · HTML: https://mlsanity.com/paper/2012.04927/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Dec 2020.

## Built on by (most cited first, 14 of 14)

- [Sparse to Dense Dynamic 3D Facial Expression Generation](https://mlsanity.com/paper/2105.07463/) (2021)
- [Precise Facial Landmark Detection by Reference Heatmap Transformer](https://mlsanity.com/paper/2303.07840/) (2023)
- [Generating Multiple 4D Expression Transitions by Learning Face Landmark Trajectories](https://mlsanity.com/paper/2208.00050/) (2022)
- [Robust and Precise Facial Landmark Detection by Self-Calibrated Pose Attention Network](https://mlsanity.com/paper/2112.12328/) (2021)
- [Geometric Graph Representation with Learnable Graph Structure and Adaptive AU Constraint for Micro-Expression Recognition](https://mlsanity.com/paper/2205.00380/) (2022)
- [Proto-Former: Unified Facial Landmark Detection by Prototype Transformer](https://mlsanity.com/paper/2510.15338/) (2025)
- [Multi-Prior Learning via Neural Architecture Search for Blind Face Restoration](https://mlsanity.com/paper/2206.13962/) (2022)
- [LSF-Animation: Label-Free Speech-Driven Facial Animation via Implicit Feature Representation](https://mlsanity.com/paper/2510.21864/) (2025)
- [FGTBT: Frequency-Guided Task-Balancing Transformer for Unified Facial Landmark Detection](https://mlsanity.com/paper/2601.12863/) (2026)
- [Supervision-by-Hallucination-and-Transfer: A Weakly-Supervised Approach for Robust and Precise Facial Landmark Detection](https://mlsanity.com/paper/2601.12919/) (2026)
- [FreqFLD: Towards All-in-One Facial Landmark Detection via Frequency Modulation](https://mlsanity.com/paper/2609.10278/) (2026)
- [LocalEyenet: Deep Attention framework for Localization of Eyes](https://mlsanity.com/paper/2303.12728/) (2023)
- [Dual-Stream Collaborative Transformer for Image Captioning](https://mlsanity.com/paper/2601.12926/) (2026)
- [FAHCD-Net: Frequency-Adaptive Heatmap-Conditional Diffusion Networks for Robust Facial Landmark Detection](https://mlsanity.com/paper/2609.16842/) (2026)

## Abstract (arXiv)

Recently, heatmap regression has been widely explored in facial landmark detection and obtained remarkable performance. However, most of the existing heatmap regression-based facial landmark detection methods neglect to explore the high-order feature correlations, which is very important to learn more representative features and enhance shape constraints. Moreover, no explicit global shape constraints have been added to the final predicted landmarks, which leads to a reduction in accuracy. To address these issues, in this paper, we propose a Multi-order Multi-constraint Deep Network (MMDN) for more powerful feature correlations and shape constraints learning. Specifically, an Implicit Multi-order Correlating Geometry-aware (IMCG) model is proposed to introduce the multi-order spatial correlations and multi-order channel correlations for more discriminative representations. Furthermore, an Explicit Probability-based Boundary-adaptive Regression (EPBR) method is developed to enhance the global shape constraints and further search the semantically consistent landmarks in the predicted boundary for robust facial landmark detection. It's interesting to show that the proposed MMDN can generate more accurate boundary-adaptive landmark heatmaps and effectively enhance shape constraints to the predicted landmarks for faces with large pose variations and heavy occlusions. Experimental results on challenging benchmark datasets demonstrate the superiority of our MMDN over state-of-the-art facial landmark detection methods. The code has been publicly available at https://github.com/junwan2014/MMDN-master.