Face recognition has evolved as a widely used biometric modality. However, its vulnerability against presentation attacks poses a significant security threat. Though presentation attack detection (PAD) methods try to address this issue, they often fail in generalizing to unseen attacks. In this work, we propose a new framework for PAD using a one-class classifier, where the representation used is learned with a Multi-Channel Convolutional Neural Network (MCCNN). A novel loss function is introduced, which forces the network to learn a compact embedding for bonafide class while being far from the representation of attacks. A one-class Gaussian Mixture Model is used on top of these embeddings for the PAD task. The proposed framework introduces a novel approach to learn a robust PAD system from bonafide and available (known) attack classes. This is particularly important as collecting bonafide data and simpler attacks are much easier than collecting a wide variety of expensive attacks. The proposed system is evaluated on the publicly available WMCA multi-channel face PAD database, which contains a wide variety of 2D and 3D attacks. Further, we have performed experiments with MLFP and SiW-M datasets using RGB channels only. Superior performance in unseen attack protocols shows the effectiveness of the proposed approach. Software, data, and protocols to reproduce the results are made available publicly.
Compared to 2D face presentation attacks (e.g. printed photos and video replays), 3D type attacks are more challenging to face recognition systems (FRS) by presenting 3D characteristics or materials similar to real faces. Existing 3D face spoofing databases, however, mostly based on 3D masks, are restricted to small data size or poor authenticity due to the production difficulty and high cost. In this work, we introduce the first wax figure face database, WFFD, as one type of super-realistic 3D presentation attacks to spoof the FRS. This database consists of 2200 images with both real and wax …
In a typical face recognition pipeline, the task of the face detector is to localize the face region. However, the face detector localizes regions that look like a face, irrespective of the liveliness of the face, which makes the entire system susceptible to presentation attacks. In this work, we try to reformulate the task of the face detector to detect real faces, thus eliminating the threat of presentation attacks. While this task could be challenging with visible spectrum images alone, we leverage the multi-channel information available from off the shelf devices (such as color, depth, and…
Nanyang Technological University(南洋理工大学);SailYond Technology(赛扬科技);Institute of Automation, Chinese Academy of Sciences(中国科学院自动化研究所);University of Chinese Academy of Sciences(中国科学院大学);Hong Kong Institute of Science & Innovation, Chinese Academy of Sciences(中国科学院香港创新研究院)
Face recognition technology has been widely used in daily interactive applications such as checking-in and mobile payment due to its convenience and high accuracy. However, its vulnerability to presentation attacks (PAs) limits its reliable use in ultra-secure applicational scenarios. A presentation attack is first defined in ISO standard as: a presentation to the biometric data capture subsystem with the goal of interfering with the operation of the biometric system. Specifically, PAs range from simple 2D print, replay and more sophisticated 3D masks and partial masks. To defend the face reco…
Fraunhofer Institute for Computer Graphics Research IGD(弗劳恩霍夫计算机图形研究所);TU Darmstadt(达姆施塔特工业大学)
Face masks have become one of the main methods for reducing the transmission of COVID-19. This makes face recognition (FR) a challenging task because masks hide several discriminative features of faces. Moreover, face presentation attack detection (PAD) is crucial to ensure the security of FR systems. In contrast to the growing number of masked FR studies, the impact of face masked attacks on PAD has not been explored. Therefore, we present novel attacks with real face masks placed on presentations and attacks with subjects wearing masks to reflect the current real-world situation. Furthermore…
School of Electronics and Information, Northwestern Polytechnical University(西北工业大学电子信息学院);Department of Electrical and Electronic Engineering, University of Cagliari(卡利亚里大学电气与电子工程系)
Face presentation attacks have become a major threat to face recognition systems and many countermeasures have been proposed in the past decade. However, most of them are devoted to 2D face presentation attacks, rather than 3D face masks. Unlike the real face, the 3D face mask is usually made of resin materials and has a smooth surface, resulting in reflectance differences. So, we propose a novel detection method for 3D face mask presentation attack by modeling reflectance differences based on intrinsic image analysis. In the proposed method, the face image is first processed with intrinsic im…
Hong Kong Baptist University(香港浸会大学);Johns Hopkins University(约翰斯·霍普金斯大学)
Face presentation attack detection (fPAD) plays a critical role in the modern face recognition pipeline. A face presentation attack detection model with good generalization can be obtained when it is trained with face images from different input distributions and different types of spoof attacks. In reality, training data (both real face images and spoof images) are not directly shared between data owners due to legal and privacy issues. In this paper, with the motivation of circumventing this challenge, we propose Federated Face Presentation Attack Detection (FedPAD) framework. FedPAD simulta…
Face signatures, including size, shape, texture, skin tone, eye color, appearance, and scars/marks, are widely used as discriminative, biometric information for access control. Despite recent advancements in facial recognition systems, presentation attacks on facial recognition systems have become increasingly sophisticated. The ability to detect presentation attacks or spoofing attempts is a pressing concern for the integrity, security, and trust of facial recognition systems. Multi-spectral imaging has been previously introduced as a way to improve presentation attack detection by utilizing …
Face presentation attack detection (PAD) is an essential measure to protect face recognition systems from being spoofed by malicious users and has attracted great attention from both academia and industry. Although most of the existing methods can achieve desired performance to some extent, the generalization issue of face presentation attack detection under cross-domain settings (e.g., the setting of unseen attacks and varying illumination) remains to be solved. In this paper, we propose a novel framework based on asymmetric modality translation for face presentation attack detection in bi-mo…
The one-class anomaly detection approach has previously been found to be effective in face presentation attack detection, especially in an \textit{unseen} attack scenario, where the system is exposed to novel types of attacks. This work follows the same anomaly-based formulation of the problem and analyses the merits of deploying \textit{client-specific} information for face spoofing detection. We propose training one-class client-specific classifiers (both generative and discriminative) using representations obtained from pre-trained deep convolutional neural networks. Next, based on subject-…
University of Chinese Academy of Sciences(中国科学院大学);Peng Cheng Laboratory(鹏城实验室)
Face presentation attack detection (PAD) has been an urgent problem to be solved in the face recognition systems. Conventional approaches usually assume the testing and training are within the same domain; as a result, they may not generalize well into unseen scenarios because the representations learned for PAD may overfit to the subjects in the training set. In light of this, we propose an efficient disentangled representation learning for cross-domain face PAD. Our approach consists of disentangled representation learning (DR-Net) and multi-domain learning (MD-Net). DR-Net learns a pair of …
Institute of Artificial Intelligence and Robotics for Society(人工智能与数字经济广东省实验室(深圳));Norwegian University of Science and Technology(挪威科技大学);Shenzhen University(深圳大学);King Abdullah University of Science and Technology(阿卜杜拉国王科技大学)
The robustness and generalization ability of Presentation Attack Detection (PAD) methods is critical to ensure the security of Face Recognition Systems (FRSs). However, in a real scenario, Presentation Attacks (PAs) are various and it is hard to predict the Presentation Attack Instrument (PAI) species that will be used by the attacker. Existing PAD methods are highly dependent on the limited training set and cannot generalize well to unknown PAI species. Unlike this specific PAD task, other face related tasks trained by huge amount of real faces (e.g. face recognition and attribute editing) ca…
GRADIANT;University of Vigo(维戈大学);University of Alcalá(阿尔卡拉大学)
Over the past few years, Presentation Attack Detection (PAD) has become a fundamental part of facial recognition systems. Although much effort has been devoted to anti-spoofing research, generalization in real scenarios remains a challenge. In this paper we present a new open-source evaluation framework to study the generalization capacity of face PAD methods, coined here as face-GPAD. This framework facilitates the creation of new protocols focused on the generalization problem establishing fair procedures of evaluation and comparison between PAD solutions. We also introduce a large aggregate…
Hong Kong Baptist University(香港浸会大学);Johns Hopkins University(约翰斯·霍普金斯大学)
Face presentation attack detection (fPAD) plays a critical role in the modern face recognition pipeline. The generalization ability of face presentation attack detection models to unseen attacks has become a key issue for real-world deployment, which can be improved when models are trained with face images from different input distributions and different types of spoof attacks. In reality, due to legal and privacy issues, training data (both real face images and spoof images) are not allowed to be directly shared between different data sources. In this paper, to circumvent this challenge, we p…
Wuhan University(武汉大学);West Virginia University(西弗吉尼亚大学)
We have witnessed rapid advances in both face presentation attack models and presentation attack detection (PAD) in recent years. Compared to widely studied 2D face presentation attacks (e.g. printed photos and video replays), 3D face presentation attacks are more challenging because face recognition systems (FRS) is more easily confused by the 3D characteristics of materials similar to real faces. Existing 3D face spoofing databases, mostly based on 3D facial masks, are restricted to small data size and suffer from poor authenticity due to the difficulty and expense of mask production. In thi…
Hong Kong Baptist University(香港浸会大学);AWS AI Labs(AWS人工智能实验室);Johns Hopkins University(约翰斯·霍普金斯大学)
Face presentation attack detection plays a critical role in the modern face recognition pipeline. A face presentation attack detection model with good generalization can be obtained when it is trained with face images from different input distributions and different types of spoof attacks. In reality, training data (both real face images and spoof images) are not directly shared between data owners due to legal and privacy issues. In this paper, with the motivation of circumventing this challenge, we propose a Federated Face Presentation Attack Detection (FedPAD) framework that simultaneously …
Federal Institute of São Paulo (IFSP)(圣保罗联邦理工学院);University of Campinas (UNICAMP)(坎皮纳斯大学)
Nowadays, the adoption of face recognition for biometric authentication systems is usual, mainly because this is one of the most accessible biometric modalities. Techniques that rely on trespassing these kind of systems by using a forged biometric sample, such as a printed paper or a recorded video of a genuine access, are known as presentation attacks, but may be also referred in the literature as face spoofing. Presentation attack detection is a crucial step for preventing this kind of unauthorized accesses into restricted areas and/or devices. In this paper, we propose a novel approach whic…
Universidad Autonoma de Madrid(马德里自治大学);European Commission - DG Joint Research Centre(欧盟委员会联合研究中心)
The main scope of this chapter is to serve as an introduction to face presentation attack detection, including key resources and advances in the field in the last few years. The next pages present the different presentation attacks that a face recognition system can confront, in which an attacker presents to the sensor, mainly a camera, a Presentation Attack Instrument (PAI), that is generally a photograph, a video, or a mask, to try to impersonate a genuine user. First, we make an introduction of the current status of face recognition, its level of deployment, and its challenges. In addition,…
3D mask face presentation attack detection (PAD) plays a vital role in securing face recognition systems from emergent 3D mask attacks. Recently, remote photoplethysmography (rPPG) has been developed as an intrinsic liveness clue for 3D mask PAD without relying on the mask appearance. However, the rPPG features for 3D mask PAD are still needed expert knowledge to design manually, which limits its further progress in the deep learning and big data era. In this letter, we propose a pure rPPG transformer (TransRPPG) framework for learning intrinsic liveness representation efficiently. At first, r…
Face recognition is a mainstream biometric authentication method. However, vulnerability to presentation attacks (a.k.a spoofing) limits its usability in unsupervised applications. Even though there are many methods available for tackling presentation attacks (PA), most of them fail to detect sophisticated attacks such as silicone masks. As the quality of presentation attack instruments improves over time, achieving reliable PA detection with visual spectra alone remains very challenging. We argue that analysis in multiple channels might help to address this issue. In this context, we propose …
Center for Machine Vision and Signal Analysis(机器视觉与信号分析中心);University of Oulu(奥卢大学)
Face presentation attack detection (PAD) plays an important role in defending face recognition systems against presentation attacks. The success of PAD largely relies on supervised learning that requires a huge number of labeled data, which is especially challenging for videos and often requires expert knowledge. To avoid the costly collection of labeled data, this paper presents a novel method for self-supervised video representation learning via motion prediction. To achieve this, we exploit the temporal consistency based on three RGB frames which are acquired at three different times in the…
Fraunhofer Institute for Computer Graphics Research IGD(弗劳恩霍夫计算机图形研究所);TU Darmstadt(达姆施塔特工业大学)
Wearing a mask has proven to be one of the most effective ways to prevent the transmission of SARS-CoV-2 coronavirus. However, wearing a mask poses challenges for different face recognition tasks and raises concerns about the performance of masked face presentation detection (PAD). The main issues facing the mask face PAD are the wrongly classified bona fide masked faces and the wrongly classified partial attacks (covered by real masks). This work addresses these issues by proposing a method that considers partial attack labels to supervise the PAD model training, as well as regional weighted …
Graduate University for Advanced Studies, SOKENDAI(综合研究大学院大学);Idiap Research Institute(Idiap研究所);National Institute of Informatics(国立情报学研究所);SOKENDAI(综合研究大学院大学);University of Tokyo(东京大学)
Face authentication is now widely used, especially on mobile devices, rather than authentication using a personal identification number or an unlock pattern, due to its convenience. It has thus become a tempting target for attackers using a presentation attack. Traditional presentation attacks use facial images or videos of the victim. Previous work has proven the existence of master faces, i.e., faces that match multiple enrolled templates in face recognition systems, and their existence extends the ability of presentation attacks. In this paper, we perform an extensive study on latent variab…
Anomaly detection-based spoof attack detection is a recent development in face Presentation Attack Detection (fPAD), where a spoof detector is learned using only non-attacked images of users. These detectors are of practical importance as they are shown to generalize well to new attack types. In this paper, we present a deep-learning solution for anomaly detection-based spoof attack detection where both classifier and feature representations are learned together end-to-end. First, we introduce a pseudo-negative class during training in the absence of attacked images. The pseudo-negative class …
Face recognition has evolved as a prominent biometric authentication modality. However, vulnerability to presentation attacks curtails its reliable deployment. Automatic detection of presentation attacks is essential for secure use of face recognition technology in unattended scenarios. In this work, we introduce a Convolutional Neural Network (CNN) based framework for presentation attack detection, with deep pixel-wise supervision. The framework uses only frame level information making it suitable for deployment in smart devices with minimal computational and time overhead. We demonstrate the…
The vulnerability against presentation attacks is a crucial problem undermining the wide-deployment of face recognition systems. Though presentation attack detection (PAD) systems try to address this problem, the lack of generalization and robustness continues to be a major concern. Several works have shown that using multi-channel PAD systems could alleviate this vulnerability and result in more robust systems. However, there is a wide selection of channels available for a PAD system such as RGB, Near Infrared, Shortwave Infrared, Depth, and Thermal sensors. Having a lot of sensors increases …
MUST(澳门科技大学);Mininglamp Academy of Sciences, Mininglamp Technology(明略科技集团明略科学院);NLPR, CASIA, UCAS(中国科学院自动化研究所模式识别国家重点实验室,中国科学院大学);CVC, UB(巴塞罗那大学计算机视觉中心);Baidu Research(百度研究院);Westlake University(西湖大学);University of Oulu(奥卢大学)
Face presentation attack detection (PAD) is essential to secure face recognition systems primarily from high-fidelity mask attacks. Most existing 3D mask PAD benchmarks suffer from several drawbacks: 1) a limited number of mask identities, types of sensors, and a total number of videos; 2) low-fidelity quality of facial masks. Basic deep models and remote photoplethysmography (rPPG) methods achieved acceptable performance on these benchmarks but still far from the needs of practical scenarios. To bridge the gap to real-world applications, we introduce a largescale High-Fidelity Mask dataset, n…
La Rochelle University(拉罗谢尔大学);Hanoi University of Science and Technology(河内科技大学)
The widespread deployment of face recognition-based biometric systems has made face Presentation Attack Detection (face anti-spoofing) an increasingly critical issue. This survey thoroughly investigates the face Presentation Attack Detection (PAD) methods, that only require RGB cameras of generic consumer devices, over the past two decades. We present an attack scenario-oriented typology of the existing face PAD methods and we provide a review of over 50 of the most recent face PAD methods and their related issues. We adopt a comprehensive presentation of the methods that have most influenced …
Fraunhofer Institute for Computer Graphics Research IGD(弗劳恩霍夫计算机图形研究所);TU Darmstadt(达姆施塔特工业大学)
With the increased deployment of face recognition systems in our daily lives, face presentation attack detection (PAD) is attracting much attention and playing a key role in securing face recognition systems. Despite the great performance achieved by the hand-crafted and deep-learning-based methods in intra-dataset evaluations, the performance drops when dealing with unseen scenarios. In this work, we propose a dual-stream convolution neural networks (CNNs) framework. One stream adapts four learnable frequency filters to learn features in the frequency domain, which are less influenced by vari…
Identity authentication is the process of verifying one's identity. There are several identity authentication methods, among which biometric authentication is of utmost importance. Facial recognition is a sort of biometric authentication with various applications, such as unlocking mobile phones and accessing bank accounts. However, presentation attacks pose the greatest threat to facial recognition. A presentation attack is an attempt to present a non-live face, such as a photo, video, mask, and makeup, to the camera. Presentation attack detection is a countermeasure that attempts to identify…
The non-intrusive nature and high accuracy of face recognition algorithms have led to their successful deployment across multiple applications ranging from border access to mobile unlocking and digital payments. However, their vulnerability against sophisticated and cost-effective presentation attack mediums raises essential questions regarding its reliability. In the literature, several presentation attack detection algorithms are presented; however, they are still far behind from reality. The major problem with existing work is the generalizability against multiple attacks both in the seen a…
Wuhan University(武汉大学);West Virginia University(西弗吉尼亚大学)
We have witnessed rapid advances in both face presentation attack models and presentation attack detection (PAD) in recent years. When compared with widely studied 2D face presentation attacks, 3D face spoofing attacks are more challenging because face recognition systems are more easily confused by the 3D characteristics of materials similar to real faces. In this work, we tackle the problem of detecting these realistic 3D face presentation attacks, and propose a novel anti-spoofing method from the perspective of fine-grained classification. Our method, based on factorized bilinear coding of …
MUST(澳门科技大学);Mininglamp Academy of Sciences, Mininglamp Technology(明略科技研究院,明略科技);University of Oulu(奥卢大学);NLPR, CASIA(中国科学院自动化研究所模式识别国家重点实验室);SAI, UCAS(中国科学院大学人工智能学院);ChaLearn;CVC, UB(巴塞罗那大学计算机视觉中心);INAOE(国家天体物理、光学和电子学研究所);CINVESTAV(研究与高级研究中心);CAIR, HKISI, CAS(中国科学院香港创新研究院人工智能与机器人创新中心);Baidu Research(百度研究院)
The threat of 3D masks to face recognition systems is increasingly serious and has been widely concerned by researchers. To facilitate the study of the algorithms, a large-scale High-Fidelity Mask dataset, namely CASIA-SURF HiFiMask (briefly HiFiMask) has been collected. Specifically, it consists of a total amount of 54, 600 videos which are recorded from 75 subjects with 225 realistic masks under 7 new kinds of sensors. Based on this dataset and Protocol 3 which evaluates both the discrimination and generalization ability of the algorithm under the open set scenarios, we organized a 3D High-F…
Surveillance Face Presentation Attack Detection Challenge
University of Chinese Academy of Sciences(中国科学院大学);Institute of Automation, Chinese Academy of Sciences(中国科学院自动化研究所);Universitat de Barcelona(巴塞罗那大学);Computer Vision Center(计算机视觉中心);Instituto Nacional de Astrofísica, Óptica y Electrónica(国家天体物理、光学与电子研究所);CAS(中国科学院)
University of Colorado at Colorado Springs(科罗拉多大学科罗拉多斯普林斯分校)
For applications such as airport border control, biometric technologies that can process many capture subjects quickly, efficiently, with weak supervision, and with minimal discomfort are desirable. Facial recognition is particularly appealing because it is minimally invasive yet offers relatively good recognition performance. Unfortunately, the combination of weak supervision and minimal invasiveness makes even highly accurate facial recognition systems susceptible to spoofing via presentation attacks. Thus, there is great demand for an effective and low cost system capable of rejecting such …
We present a multi-purpose algorithm for simultaneous face detection, face alignment, pose estimation, gender recognition, smile detection, age estimation and face recognition using a single deep convolutional neural network (CNN). The proposed method employs a multi-task learning framework that regularizes the shared parameters of CNN and builds a synergy among different domains and tasks. Extensive experiments show that the network has a better understanding of face and achieves state-of-the-art result for most of these tasks.
In recent years, the popularity of fingerprint-based biometric authentication systems significantly increased. However, together with many advantages, biometric systems are still vulnerable to presentation attacks (PAs). In particular, this applies for unsupervised applications, where new attacks unknown to the system operator may occur. Therefore, presentation attack detection (PAD) methods are used to determine whether samples stem from a bona fide subject or from a presentation attack instrument (PAI). In this context, most works are dedicated to solve PAD as a two-class classification prob…
University of La Rochelle(拉罗谢尔大学);RIKEN(理化学研究所);University of Toulouse(图卢兹大学)
This paper proposes a holistic multi-task Convolutional Neural Networks (CNNs) with the dynamic weights of the tasks,namely FaceLiveNet+, for face authentication. FaceLiveNet+ can employ face verification and facial expression recognition as a solution of liveness control simultaneously. Comparing to the single-task learning, the proposed multi-task learning can better capture the feature representation for all of the tasks. The experimental results show the superiority of the multi-task learning to the single-task learning for both the face verification task and facial expression recognition …
Face recognition has been an active research area in the past few decades. In general, face recognition can be very challenging due to variations in viewpoint, illumination, facial expression, etc. Therefore it is essential to extract features which are invariant to some or all of these variations. Here a new image representation, called scattering transform/network, has been used to extract features from faces. The scattering transform is a kind of convolutional network which provides a powerful multi-layer representation for signals. After extraction of scattering features, PCA is applied to…
In this paper we describe a solution to our entry for the emotion recognition challenge EmotiW 2017. We propose an ensemble of several models, which capture spatial and audio features from videos. Spatial features are captured by convolutional neural networks, pretrained on large face recognition datasets. We show that usage of strong industry-level face recognition networks increases the accuracy of emotion recognition. Using our ensemble we improve on the previous best result on the test set by about 1 %, achieving a 60.03 % classification accuracy without any use of visual temporal informat…
University of Hertfordshire(赫特福德大学);IDscan Biometrics(IDscan生物识别技术公司)
Despite the recent success of convolutional neural networks for computer vision applications, unconstrained face recognition remains a challenge. In this work, we make two contributions to the field. Firstly, we consider the problem of face recognition with partial occlusions and show how current approaches might suffer significant performance degradation when dealing with this kind of face images. We propose a simple method to find out which parts of the human face are more important to achieve a high recognition rate, and use that information during training to force a convolutional neural n…
Sfax University(斯法克斯大学);Digital Research Center of Sfax(斯法克斯数字研究中心)
This paper focuses on designing data-driven models to learn a discriminant representation space for face recognition using RGB-D data. Unlike hand-crafted representations, learned models can extract and organize the discriminant information from the data, and can automatically adapt to build new compute vision applications faster. We proposed an effective way to train Convolutional Neural Networks to learn face patch discriminant features. The proposed solution was tested and validated on state-of-the-art RGB-D datasets and showed competitive and promising results relatively to standard hand-c…
Convolutional neural networks (CNNs) give state of the art performance in many pattern recognition problems but can be fooled by carefully crafted patterns of noise. We report that CNN face recognition systems also make surprising "errors". We tested six commercial face recognition CNNs and found that they outperform typical human participants on standard face matching tasks. However, they also declare matches that humans would not, where one image from the pair has been transformed to look a different sex or race. This is not due to poor performance; the best CNNs perform almost perfectly on …
University of Electronic Science and Technology of China(电子科技大学);National University of Singapore(新加坡国立大学);National University of Defense Technology(国防科技大学)
Face anti-spoofing (a.k.a presentation attack detection) has drawn growing attention due to the high-security demand in face authentication systems. Existing CNN-based approaches usually well recognize the spoofing faces when training and testing spoofing samples display similar patterns, but their performance would drop drastically on testing spoofing faces of unseen scenes. In this paper, we try to boost the generalizability and applicability of these methods by designing a CNN model with two major novelties. First, we propose a simple yet effective Total Pairwise Confusion (TPC) loss for CN…
Artist, year and style classification of fine-art paintings are generally achieved using standard image classification methods, image segmentation, or more recently, convolutional neural networks (CNNs). This works aims to use newly developed face recognition methods such as FaceNet that use CNNs to cluster fine-art paintings using the extracted faces in the paintings, which are found abundantly. A dataset consisting of over 80,000 paintings from over 1000 artists is chosen, and three separate face recognition and clustering tasks are performed. The produced clusters are analyzed by the file n…
Over the last five years, methods based on Deep Convolutional Neural Networks (DCNNs) have shown impressive performance improvements for object detection and recognition problems. This has been made possible due to the availability of large annotated datasets, a better understanding of the non-linear mapping between input images and class labels as well as the affordability of GPUs. In this paper, we present the design details of a deep learning system for unconstrained face recognition, including modules for face detection, association, alignment and face verification. The quantitative perfor…