Radial Distortion in Face Images: Detection and Impact

TL;DR

Radial distortion is modeled via a center $(x_c,y_c)$ and a distortion function $oldsymbol{\\delta(r_d)}$, with the Division Model giving $oldsymbol{\delta(r_d)=1+\lambda r_d^2}$ (plus higher-order terms) and the Kannala-Brandt model using angle-based projections $oldsymbol{\delta(r_d)}=\lambda_1\theta+\lambda_2\theta^3+\ldots$, enabling synthetic distortion datasets on base face sets. The authors train a ResNet34-based RD detector, convert its outputs into a FIQA-native quality measure via $\text{NQM}=\text{softmax}(\beta)$, and evaluate the effect on FR using ArcFace with EDC curves on distorted LFW variants. Key contributions include a practical RD detection model for unsupervised self-enrolment, a FIQA formulation for radial distortion, and synthetic/mobile datasets to evaluate generalization. Findings suggest RD checks should run before preprocessing in enrolment pipelines to avoid accepting distorted reference data, with the work offering valuable datasets and a framework for future refinements of distortion-aware FIQA in real-world systems.

Abstract

Acquiring face images of sufficiently high quality is important for online ID and travel document issuance applications using face recognition systems (FRS). Low-quality, manipulated (intentionally or unintentionally), or distorted images degrade the FRS performance and facilitate documents' misuse. Securing quality for enrolment images, especially in the unsupervised self-enrolment scenario via a smartphone, becomes important to assure FRS performance. In this work, we focus on the less studied area of radial distortion (a.k.a., the fish-eye effect) in face images and its impact on FRS performance. We introduce an effective radial distortion detection model that can detect and flag radial distortion in the enrolment scenario. We formalize the detection model as a face image quality assessment (FIQA) algorithm and provide a careful inspection of the effect of radial distortion on FRS performance. Evaluation results show excellent detection results for the proposed models, and the study on the impact on FRS uncovers valuable insights into how to best use these models in operational systems.

Figures (6)

• Figure 1: Radial distortion effect in face images. The left column shows the original, undistorted images. The middle column shows images with a mild level of distortion. The right column shows the images with a more pronounced level of distortion. Distortion is introduced synthetically using the Division Model (DM) but with different values for the distortion coefficient $\lambda$. Images from the FRLL dataset DeBruine2021.
• Figure 2: Illustration of the radial distortion effect on a face image using different distortion models and different distortion coefficient values. DM refers to the Division Model. KBp, KBs, KBe, and KBo refer to the Kannala-Brandt model of types perspective, stereographic, equisolid, and orthogonal, respectively. $\lambda$ is the distortion coefficient. Image from LFW dataset LFWTech.
• Figure 3: Sample distorted and undistorted images from the collected Mobile Fisheye Dataset (MFD)
• Figure 4: Evaluation results for the five distortion detection models on datasets with different base datasets, distortion models, and distortion coefficient values. Figure \ref{['fig:eval-ep-dm-0.4']} to \ref{['fig:eval-lfw-kbe-1.5']} show evaluation results on the synthetic datasets. Figure \ref{['fig:eval-mfd']} shows evaluation results on the self-collected Mobile Fisheye Dataset (MFD).
• Figure 5: EDC curves on two synthetically distorted versions of the LFW dataset, created with random distortion levels ranging from very mild to very severe distortion. ArcFace is used as the FRS, and 0.05 is the starting error rate.