# Deep Learning-Based Quasi-Conformal Surface Registration for Partial 3D Faces Applied to Facial Recognition

arXiv: https://arxiv.org/abs/2405.09880 · HTML: https://mlsanity.com/paper/2405.09880/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 27 of its 53 references that are in the map.
- First posted on arXiv 16 May 2024.

## Builds on (most cited first, 27 of 27)

- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [FaceNet: A Unified Embedding for Face Recognition and Clustering](https://mlsanity.com/paper/1503.03832/) (2015)
- [Accurate 3D Face Reconstruction with Weakly-Supervised Learning: From Single Image to Image Set](https://mlsanity.com/paper/1903.08527/) (2019)
- [MagFace: A Universal Representation for Face Recognition and Quality Assessment](https://mlsanity.com/paper/2103.06627/) (2021)
- [Nonlinear 3D Face Morphable Model](https://mlsanity.com/paper/1804.03786/) (2018)
- [Adaptive Wing Loss for Robust Face Alignment via Heatmap Regression](https://mlsanity.com/paper/1904.07399/) (2019)
- [Wing Loss for Robust Facial Landmark Localisation with Convolutional Neural Networks](https://mlsanity.com/paper/1711.06753/) (2017)
- [i3DMM: Deep Implicit 3D Morphable Model of Human Heads](https://mlsanity.com/paper/2011.14143/) (2020)
- [AvatarMe: Realistically Renderable 3D Facial Reconstruction "in-the-wild"](https://mlsanity.com/paper/2003.13845/) (2020)
- [Facial Landmark Detection: a Literature Survey](https://mlsanity.com/paper/1805.05563/) (2018)
- [DeepID3: Face Recognition with Very Deep Neural Networks](https://mlsanity.com/paper/1502.00873/) (2015)
- [Unsupervised Learning of Robust Spectral Shape Matching](https://mlsanity.com/paper/2304.14419/) (2023)
- [Deeply learned face representations are sparse, selective, and robust](https://mlsanity.com/paper/1412.1265/) (2014)
- [Supervision-by-Registration: An Unsupervised Approach to Improve the Precision of Facial Landmark Detectors](https://mlsanity.com/paper/1807.00966/) (2018)
- [Deep Alignment Network: A convolutional neural network for robust face alignment](https://mlsanity.com/paper/1706.01789/) (2017)
- [Face Super-Resolution Guided by 3D Facial Priors](https://mlsanity.com/paper/2007.09454/) (2020)
- [Learning Deep Representation for Face Alignment with Auxiliary Attributes](https://mlsanity.com/paper/1408.3967/) (2014)
- [Supervision by Registration and Triangulation for Landmark Detection](https://mlsanity.com/paper/2101.09866/) (2021)
- [PFLD: A Practical Facial Landmark Detector](https://mlsanity.com/paper/1902.10859/) (2019)
- [Fast Facial Landmark Detection and Applications: A Survey](https://mlsanity.com/paper/2101.10808/) (2021)
- [On Unsupervised Partial Shape Correspondence](https://mlsanity.com/paper/2310.14692/) (2023)
- [MobileFAN: Transferring Deep Hidden Representation for Face Alignment](https://mlsanity.com/paper/1908.03839/) (2019)
- [A Deep Learning Framework for Diffeomorphic Mapping Problems via Quasi-conformal Geometry applied to Imaging](https://mlsanity.com/paper/2110.10580/) (2021)
- [Automatic Landmark Detection and Registration of Brain Cortical Surfaces via Quasi-Conformal Geometry and Convolutional Neural Networks](https://mlsanity.com/paper/2208.07010/) (2022)
- [Computing quasiconformal folds](https://mlsanity.com/paper/1804.03936/) (2018)
- [Inconsistent Surface Registration via Optimization of Mapping Distortions](https://mlsanity.com/paper/1908.09098/) (2019)
- [Quasi-conformal Geometry based Local Deformation Analysis of Lateral Cephalogram for Childhood OSA Classification](https://mlsanity.com/paper/2006.11408/) (2020)

## Abstract (arXiv)

3D face registration is an important process in which a 3D face model is aligned and mapped to a template face. However, the task of 3D face registration becomes particularly challenging when dealing with partial face data, where only limited facial information is available. To address this challenge, this paper presents a novel deep learning-based approach that combines quasi-conformal geometry with deep neural networks for partial face registration. The proposed framework begins with a Landmark Detection Network that utilizes curvature information to detect the presence of facial features and estimate their corresponding coordinates. These facial landmark features serve as essential guidance for the registration process. To establish a dense correspondence between the partial face and the template surface, a registration network based on quasiconformal theories is employed. The registration network establishes a bijective quasiconformal surface mapping aligning corresponding partial faces based on detected landmarks and curvature values. It consists of the Coefficients Prediction Network, which outputs the optimal Beltrami coefficient representing the surface mapping. The Beltrami coefficient quantifies the local geometric distortion of the mapping. By controlling the magnitude of the Beltrami coefficient through a suitable activation function, the bijectivity and geometric distortion of the mapping can be controlled. The Beltrami coefficient is then fed into the Beltrami solver network to reconstruct the corresponding mapping. The surface registration enables the acquisition of corresponding regions and the establishment of point-wise correspondence between different partial faces, facilitating precise shape comparison through the evaluation of point-wise geometric differences at these corresponding regions. Experimental results demonstrate the effectiveness of the proposed method.