Showing papers on "Three-dimensional face recognition published in 2008"
01 Oct 2008
TL;DR: The database contains labeled face photographs spanning the range of conditions typically encountered in everyday life, and exhibits “natural” variability in factors such as pose, lighting, race, accessories, occlusions, and background.
Abstract: Most face databases have been created under controlled conditions to facilitate the study of specific parameters on the face recognition problem. These parameters include such variables as position, pose, lighting, background, camera quality, and gender. While there are many applications for face recognition technology in which one can control the parameters of image acquisition, there are also many applications in which the practitioner has little or no control over such parameters. This database, Labeled Faces in the Wild, is provided as an aid in studying the latter, unconstrained, recognition problem. The database contains labeled face photographs spanning the range of conditions typically encountered in everyday life. The database exhibits “natural” variability in factors such as pose, lighting, race, accessories, occlusions, and background. In addition to describing the details of the database, we provide specific experimental paradigms for which the database is suitable. This is done in an effort to make research performed with the database as consistent and comparable as possible. We provide baseline results, including results of a state of the art face recognition system combined with a face alignment system. To facilitate experimentation on the database, we provide several parallel databases, including an aligned version.
5,742 citations
Proceedings Article•
[...]
TL;DR: The CMU Multi-PIE database as mentioned in this paper contains 337 subjects, imaged under 15 view points and 19 illumination conditions in up to four recording sessions, with a limited number of subjects, a single recording session and only few expressions captured.
Abstract: A close relationship exists between the advancement of face recognition algorithms and the availability of face databases varying factors that affect facial appearance in a controlled manner. The CMU PIE database has been very influential in advancing research in face recognition across pose and illumination. Despite its success the PIE database has several shortcomings: a limited number of subjects, a single recording session and only few expressions captured. To address these issues we collected the CMU Multi-PIE database. It contains 337 subjects, imaged under 15 view points and 19 illumination conditions in up to four recording sessions. In this paper we introduce the database and describe the recording procedure. We furthermore present results from baseline experiments using PCA and LDA classifiers to highlight similarities and differences between PIE and Multi-PIE.
1,181 citations
01 Sep 2008
TL;DR: This paper presents a newly created high-resolution 3D dynamic facial expression database, which is made available to the scientific research community and has been validated through the authors' facial expression recognition experiment using an HMM based 3D spatio-temporal facial descriptor.
Abstract: Face information processing relies on the quality of data resource From the data modality point of view, a face database can be 2D or 3D, and static or dynamic From the task point of view, the data can be used for research of computer based automatic face recognition, face expression recognition, face detection, or cognitive and psychological investigation With the advancement of 3D imaging technologies, 3D dynamic facial sequences (called 4D data) have been used for face information analysis In this paper, we focus on the modality of 3D dynamic data for the task of facial expression recognition We present a newly created high-resolution 3D dynamic facial expression database, which is made available to the scientific research community The database contains 606 3D facial expression sequences captured from 101 subjects of various ethnic backgrounds The database has been validated through our facial expression recognition experiment using an HMM based 3D spatio-temporal facial descriptor It is expected that such a database shall be used to facilitate the facial expression analysis from a static 3D space to a dynamic 3D space, with a goal of scrutinizing facial behavior at a higher level of detail in a real 3D spatio-temporal domain
537 citations
23 Jun 2008
TL;DR: This work proposes a new procedure for recognition of low-resolution faces, when there is a high-resolution training set available, and shows that recognition of faces of as low as 6 times 6 pixel size is considerably improved compared to matching using a super-resolution reconstruction followed by classification, and to matching with a low- resolution training set.
Abstract: Face recognition degrades when faces are of very low resolution since many details about the difference between one person and another can only be captured in images of sufficient resolution. In this work, we propose a new procedure for recognition of low-resolution faces, when there is a high-resolution training set available. Most previous super-resolution approaches are aimed at reconstruction, with recognition only as an after-thought. In contrast, in the proposed method, face features, as they would be extracted for a face recognition algorithm (e.g., eigenfaces, Fisher-faces, etc.), are included in a super-resolution method as prior information. This approach simultaneously provides measures of fit of the super-resolution result, from both reconstruction and recognition perspectives. This is different from the conventional paradigms of matching in a low-resolution domain, or, alternatively, applying a super-resolution algorithm to a low-resolution face and then classifying the super-resolution result. We show, for example, that recognition of faces of as low as 6 times 6 pixel size is considerably improved compared to matching using a super-resolution reconstruction followed by classification, and to matching with a low-resolution training set.
272 citations
TL;DR: A new face recognition algorithm based on the well-known EBGM which replaces Gabor features by HOG descriptors is presented which shows a better performance compared to other face recognition approaches using public available databases.
229 citations
01 Sep 2008
TL;DR: An expression-invariant method for face recognition by fitting an identity/expression separated 3D Morphable Model to shape data that greatly improves recognition and retrieval rates in the uncooperative setting, while achieving recognition rates on par with the best recognition algorithms in the face recognition great vendor test.
Abstract: We describe an expression-invariant method for face recognition by fitting an identity/expression separated 3D Morphable Model to shape data. The expression model greatly improves recognition and retrieval rates in the uncooperative setting, while achieving recognition rates on par with the best recognition algorithms in the face recognition great vendor test. The fitting is performed with a robust nonrigid ICP algorithm. It is able to perform face recognition in a fully automated scenario and on noisy data. The system was evaluated on two datasets, one with a high noise level and strong expressions, and the standard UND range scan database, showing that while expression invariance increases recognition and retrieval performance for the expression dataset, it does not decrease performance on the neutral dataset. The high recognition rates are achieved even with a purely shape based method, without taking image data into account.
221 citations
TL;DR: The application of Gabor filter based feature extraction in combination with learning vector quantization (LVQ) for recognition of seven different facial expressions from still pictures of the human face proves the feasibility of computer vision based facial expression recognition for practical applications like surveillance and human computer interaction.
214 citations
TL;DR: An elastically deformable model algorithm that establishes correspondence among a set of faces is proposed first and then bilinear models that decouple the identity and facial expression factors are constructed, enabling face recognition invariant to facial expressions and facialexpression recognition with unknown identity.
Abstract: In this paper, we explore bilinear models for jointly addressing 3D face and facial expression recognition. An elastically deformable model algorithm that establishes correspondence among a set of faces is proposed first and then bilinear models that decouple the identity and facial expression factors are constructed. Fitting these models to unknown faces enables us to perform face recognition invariant to facial expressions and facial expression recognition with unknown identity. A quantitative evaluation of the proposed technique is conducted on the publicly available BU-3DFE face database in comparison with our previous work on face recognition and other state-of-the-art algorithms for facial expression recognition. Experimental results demonstrate an overall 90.5% facial expression recognition rate and an 86% rank-1 face recognition rate.
187 citations
01 Dec 2008
TL;DR: A real-time liveness detection approach is presented against photograph spoofing in a non-intrusive manner for face recognition, which does not require any additional hardware except for a generic webcamera.
Abstract: Biometrics is an emerging technology that enables uniquely recognizing humans based upon one or more intrinsic physiological or behavioral characteristics, such as faces, fingerprints, irises, voices (Ross et al., 2006). However, spoofing attack (or copy attack) is still a fatal threat for biometric authentication systems (Schukers, 2002). Liveness detection, which aims at recognition of human physiological activities as the liveness indicator to prevent spoofing attack, is becoming a very active topic in field of fingerprint recognition and iris recognition (Schuckers, 2002; Bigun et al., 2004; Parthasaradhi et al., 2005; Antonelli et al., 2006). In face recognition community, although numerous recognition approaches have been presented, the effort on anti-spoofing is still very limited (Zhao et al., 2003). The most common faking way is to use a facial photograph of a valid user to spoof face recognition systems. Nowadays, video of a valid user can also be easily captured by needle camera for spoofing. Therefore anti-spoof problem should be well solved before face recognition could be widely applied in our life. Most of the current face recognition works with excellent performance, are based on intensity images and equipped with a generic camera. Thus, an anti-spoofing method without additional device will be preferable, since it could be easily integrated into the existing face recognition systems. In Section 2, we give a brief review of spoofing ways in face recognition and some related work. The potential clues will be also presented and commented. In Section 3, a real-time liveness detection approach is presented against photograph spoofing in a non-intrusive manner for face recognition, which does not require any additional hardware except for a generic webcamera. In Section 4, databases are introduced for eyeblink-based anti-spoofing. Section 5 presents an extensive set of experiments to show effectiveness of our approach. Discussions are in Section 6.
178 citations
TL;DR: Experimental results show that the method of combining 2D-LDA (Linear Discriminant Analysis) and SVM (Support Vector Machine) outperforms others and takes only 0.0357 second to process one image of size 256 × 256.
Abstract: Facial expression provides an important behavioral measure for studies of emotion, cognitive processes, and social interaction. Facial expression recognition has recently become a promising research area. Its applications include human-computer interfaces, human emotion analysis, and medical care and cure. In this paper, we investigate various feature representation and expression classification schemes to recognize seven different facial expressions, such as happy, neutral, angry, disgust, sad, fear and surprise, in the JAFFE database. Experimental results show that the method of combining 2D-LDA (Linear Discriminant Analysis) and SVM (Support Vector Machine) outperforms others. The recognition rate of this method is 95.71% by using leave-one-out strategy and 94.13% by using cross-validation strategy. It takes only 0.0357 second to process one image of size 256 × 256.
160 citations
TL;DR: A recursive error back-projection method to compensate for residual errors, and a region-based reconstruction method to preserve characteristics of local facial regions to create an extended morphable face model.
Abstract: This paper proposes a face hallucination method for the reconstruction of high-resolution facial images from single-frame, low-resolution facial images. The proposed method has been derived from example-based hallucination methods and morphable face models. First, we propose a recursive error back-projection method to compensate for residual errors, and a region-based reconstruction method to preserve characteristics of local facial regions. Then, we define an extended morphable face model, in which an extended face is composed of the interpolated high-resolution face from a given low-resolution face, and its original high-resolution equivalent. Then, the extended face is separated into an extended shape and an extended texture. We performed various hallucination experiments using the MPI, XM2VTS, and KF databases, compared the reconstruction errors, structural similarity index, and recognition rates, and showed the effects of face detection errors and shape estimation errors. The encouraging results demonstrate that the proposed methods can improve the performance of face recognition systems. Especially the proposed method can enhance the resolution of single-frame, low-resolution facial images.
01 Sep 2008
TL;DR: This work builds on the method of to create a prototype access control system, capable of handling variations in illumination and expression, as well as significant occlusion or disguise, and gaining a better understanding strengths and limitations of sparse representation as a tool for robust recognition.
Abstract: This work builds on the method of to create a prototype access control system, capable of handling variations in illumination and expression, as well as significant occlusion or disguise. Our demonstration will allow participants to interact with the algorithm, gaining a better understanding strengths and limitations of sparse representation as a tool for robust recognition.
TL;DR: This work modeled human familiarity by using image averaging to derive stable face representations from naturally varying photographs, increasing the accuracy of an industry standard face-recognition algorithm from 54% to 100%, bringing the robust performance of a familiar human to an automated system.
Abstract: Accurate face recognition is critical for many security applications. Current automatic face-recognition systems are defeated by natural changes in lighting and pose, which often affect face images more profoundly than changes in identity. The only system that can reliably cope with such variability is a human observer who is familiar with the faces concerned. We modeled human familiarity by using image averaging to derive stable face representations from naturally varying photographs. This simple procedure increased the accuracy of an industry standard face-recognition algorithm from 54% to 100%, bringing the robust performance of a familiar human to an automated system.
TL;DR: It is concluded that the most suitable algorithms for achieving illumination compensation and normalization in eigenspace-based face recognition are SQI and the modified LBP transform.
23 Jun 2008
TL;DR: A novel alignment strategy is proposed which is referred to as ldquostack flowrdquo that discovers viewpoint induced spatial deformities undergone by a face at the patch level and can view the spatial deformation of a patch as the correspondence of that patch between two viewpoints.
Abstract: Variation due to viewpoint is one of the key challenges that stand in the way of a complete solution to the face recognition problem. It is easy to note that local regions of the face change differently in appearance as the viewpoint varies. Recently, patch-based approaches, such as those of Kanade and Yamada, have taken advantage of this effect resulting in improved viewpoint invariant face recognition. In this paper we propose a data-driven extension to their approach, in which we not only model how a face patch varies in appearance, but also how it deforms spatially as the viewpoint varies. We propose a novel alignment strategy which we refer to as ldquostack flowrdquo that discovers viewpoint induced spatial deformities undergone by a face at the patch level. One can then view the spatial deformation of a patch as the correspondence of that patch between two viewpoints. We present improved identification and verification results to demonstrate the utility of our technique.
01 Sep 2008
TL;DR: This paper performs person and gender independent facial expression recognition based on properties of the line segments connecting certain 3D facial feature points, which comprises a set of 96 distinguishing features for recognizing six universal facial expressions.
Abstract: The 3D facial geometry contains ample information about human facial expressions. Such information is invariant to pose and lighting conditions, which have imposed serious hurdles on many 2D facial analysis problems. In this paper, we perform person and gender independent facial expression recognition based on properties of the line segments connecting certain 3D facial feature points. The normalized distances and slopes of these line segments comprise a set of 96 distinguishing features for recognizing six universal facial expressions, namely anger, disgust, fear, happiness, sadness, and surprise. Using a multi-class support vector machine (SVM) classifier, an 87.1% average recognition rate is achieved on the publicly available 3D facial expression database BU-3DFE. The highest average recognition rate obtained in our experiments is 99.2% for the recognition of surprise. Our result outperforms the result reported in the prior work, which uses elaborately extracted primitive facial surface features and an LDA classifier and which yields an average recognition rate of 83.6% on the same database.
08 Dec 2008
TL;DR: A new 3D face registration and recognition method based on local facial regions based on average regional models (ARMs) that is able to provide better accuracy in the presence of expression variations and facial occlusions is proposed.
Abstract: Facial expression variations and occlusions complicate the task of identifying persons from their 3D facial scans. We propose a new 3D face registration and recognition method based on local facial regions that is able to provide better accuracy in the presence of expression variations and facial occlusions. Proposed fast and flexible alignment method uses average regional models (ARMs), where local correspondences are inferred by the iterative closest point (ICP) algorithm. Dissimilarity scores obtained from local regional matchers are fused to robustly identify probe subjects. In this work, a multi-expression 3D face database, Bosphorus 3D face database, that contains significant amount of different expression types and realistic facial occlusion is used for identification experiments. The experimental results on this challenging database demonstrate that the proposed system improves the performance of the standard ICP-based holistic approach (71.39%) by obtaining 95.87% identification rate in the case of expression variations. When facial occlusions are present, the performance gain is even better. Identification rate improves from 47.05% to 94.12%.
01 Sep 2008
TL;DR: Overall LBP with overlapping gives the best performance (92.9% recognition rate on the Cohn-Kanade database), while maintaining a compact feature vector and best robustness against face registration errors.
Abstract: In this paper, we extensively investigate local features based facial expression recognition with face registration errors, which has never been addressed before. Our contributions are three fold. Firstly, we propose and experimentally study the histogram of oriented gradients (HOG) descriptors for facial representation. Secondly, we present facial representations based on local binary patterns (LBP) and local ternary patterns (LTP) extracted from overlapping local regions. Thirdly, we quantitatively study the impact of face registration errors on facial expression recognition using different facial representations. Overall LBP with overlapping gives the best performance (92.9% recognition rate on the Cohn-Kanade database), while maintaining a compact feature vector and best robustness against face registration errors.
01 Sep 2008
TL;DR: An automatic aging simulation technique that can assist any existing face recognition engine for aging-invariant face recognition and improves the rank-1 matching accuracy on FG-NET database from 28.0% to 37.8%, on average.
Abstract: The variation caused by aging has not received adequate attention compared with pose, lighting, and expression variations. Aging is a complex process that affects both the 3D shape of the face and its texture (e.g., wrinkles). While the facial age modeling has been widely studied in computer graphics community, only a few studies have been reported in computer vision literature on age-invariant face recognition. We propose an automatic aging simulation technique that can assist any existing face recognition engine for aging-invariant face recognition. We learn the aging patterns of shape and the corresponding texture in 3D domain by adapting a 3D morphable model to the 2D aging database (public domain FG-NET). At recognition time, each probe and all gallery images are modified to compensate for the age-induced variation using an intermediate 3D model deformation and a texture modification, prior to matching. The proposed approach is evaluated on a set of age-separated probe and gallery data using a state-of-the-art commercial face recognition engine, FaceVACS. Use of 3D aging model improves the rank-1 matching accuracy on FG-NET database from 28.0% to 37.8%, on average.
01 Dec 2008
TL;DR: The extensive recognition experiments suggests that the non-frontal-view facial expression classification can outperform frontal- view facial expression recognition, given the manually labeled facial key points.
Abstract: The existing methods of facial expression recognition are typically based on the near-frontal face data. The analysis of non-frontal-view facial expression is a largely unexplored research. The accessibility to a recent 3D facial expression database (BU-3DFE database) motivates us to explore an interesting question: whether non-frontal-view facial expression analysis can achieve the same as or better performance than the existing frontal-view facial expression method. Our extensive recognition experiments on data of 100 subjects with 5 yaw rotation view angles suggests that the non-frontal-view facial expression classification can outperform frontal-view facial expression recognition, given the manually labeled facial key points.
TL;DR: A hybrid-boost learning algorithm for multi-pose face detection and facial expression recognition based on the Harr-like (local) features and Gabor (global) features to speed-up the detection process.
07 Jul 2008
TL;DR: The evaluation showed that worst-case eye localization errors have a big impact on face matching performance, and under a minimum required accuracy, eye localization can boost performance of naive face matchers, and eye localization allows for more efficient face matching without degrading performance.
Abstract: In this paper we address the influence of eye localization accuracy on face matching performance in the case of low resolution image and video content. By means of a broad experimental evaluation involving several base-line eye localizers and face matching algorithms we investigated to which extent and under what conditions the eye localization accuracy will benefit the face matching performance, both in terms of effectiveness and efficiency. Our evaluation showed that (1) worst-case eye localization errors have a big impact on face matching performance, (2) in respect to that and under a minimum required accuracy, eye localization can boost performance of naive face matchers, (3) eye localization allows for more efficient face matching without degrading performance.
01 Sep 2008
TL;DR: This paper proposes a learning based 2D-3D face matching method using the CCA to learn the mapping between 2D face image and 3D face data, and a patch based strategy is proposed to boost the accuracy of matching.
Abstract: In recent years, 3D face recognition has obtained much attention. Using 2D face image as probe and 3D face data as gallery is an alternative method to deal with computation complexity, expensive equipment and fussy pretreatment in 3D face recognition systems. In this paper we propose a learning based 2D-3D face matching method using the CCA to learn the mapping between 2D face image and 3D face data. This method makes it possible to match the on-site 2D face image with enrolled 3D face data. Our 2D-3D face matching method decreased the computation complexity drastically compared to the conventional 3D-3D face matching while keeping relative high recognition rate. Furthermore, to simplify the mapping between 2D face image and 3D face data, a patch based strategy is proposed to boost the accuracy of matching. And the kernel method is also evaluated to reveal the non-linear relationship. The experiment results show that CCA based method has good performance and patch based method has significant improvement compared to the holistic method.
23 Dec 2008
TL;DR: It is shown that it is possible to boost the identification accuracy by focusing on the rigid facial regions and by fusing complementary information coming from shape and texture modalities.
Abstract: This paper presents an evaluation of several 3D face recognizers on the Bosphorus database which was gathered for studies on expression and pose invariant face analysis. We provide identification results of three 3D face recognition algorithms, namely generic face template based ICP approach, one-to-all ICP approach, and depth image-based Principal Component Analysis (PCA) method. All of these techniques treat faces globally and are usually accepted as baseline approaches. In addition, 2D texture classifiers are also incorporated in a fusion setting. Experimental results reveal that even though global shape classifiers achieve almost perfect identification in neutral-to-neutral comparisons, they are sub-optimal under extreme expression variations. We show that it is possible to boost the identification accuracy by focusing on the rigid facial regions and by fusing complementary information coming from shape and texture modalities.
TL;DR: The encouraging experimental results demonstrated that the proposed approach by using frontal and side-view images is a feasible and effective solution to recognizing rotated faces, which can lead to a better and practical use of existing forensic databases in computerized human face-recognition applications.
Abstract: Mug shot photography has been used to identify criminals by the police for more than a century. However, the common scenario of face recognition using frontal and side-view mug shots as gallery remains largely uninvestigated in computerized face recognition across pose. This paper presents a novel appearance-based approach using frontal and sideface images to handle pose variations in face recognition, which has great potential in forensic and security applications involving police mugshot databases. Virtual views in different poses are generated in two steps: 1) shape modelling and 2) texture synthesis. In the shape modelling step, a multilevel variation minimization approach is applied to generate personalized 3-D face shapes. In the texture synthesis step, face surface properties are analyzed and virtual views in arbitrary viewing conditions are rendered, taking diffuse and specular reflections into account. Appearance-based face recognition is performed with the augmentation of synthesized virtual views covering possible viewing angles to recognize probe views in arbitrary conditions. The encouraging experimental results demonstrated that the proposed approach by using frontal and side-view images is a feasible and effective solution to recognizing rotated faces, which can lead to a better and practical use of existing forensic databases in computerized human face-recognition applications.
TL;DR: Overall, the paper describes how an abstract feature-based model can reconcile a range of results in the face recognition literature and, in turn, lessen currently perceived differences between the representation of faces and other objects.
Abstract: Humans typically have a remarkable memory for faces. Nonetheless, in some cases they can be fooled. Experiments described in this paper provide new evidence for an effect in which observers falsely “recognize” a face that they have never seen before. The face is a chimera (prototype) built from parts extracted from previously viewed faces. It is known that faces of this kind can be confused with truly familiar faces, a result referred to as the prototype effect. However, recent studies have failed to find evidence for a full effect, one in which the prototype is regarded not only as familiar, but as more familiar than faces which have been seen before. This study sought to reinvestigate the effect. In a pair of experiments, evidence is reported for the full effect based on both an old/new discrimination task and a familiarity ranking task. The results are shown to be consistent with a recognition model in which faces are represented as combinations of reusable, abstract features. In a final experiment, novel predictions of the model are verified by comparing the size of the prototype effect for upright and upside-down faces. Despite the fundamentally piecewise nature of the model, an explanation is provided as to how it can also account for the sensitivity of observers to configural and holistic cues. This discussion is backed up with the use of an unsupervised network model. Overall, the paper describes how an abstract feature-based model can reconcile a range of results in the face recognition literature and, in turn, lessen currently perceived differences between the representation of faces and other objects.
TL;DR: Combining these multi-feature subspace components into a unified surface subspace, this paper creates a three-dimensional face recognition system producing significantly lower error rates than individual surface feature map systems tested on the same data.
01 Dec 2008
TL;DR: Two novel contributions of this paper are: scaling of RMS contrast, and contribution of morphing as an advancement of image recognition perfection.
Abstract: Gabor based face representation has achieved enormous success in face recognition. This paper addresses a novel algorithm for face recognition using neural networks trained by Gabor features. The system is commences on convolving some morphed images of particular face with a series of Gabor filter co-efficient at different scales and orientations. Two novel contributions of this paper are: scaling of RMS contrast, and contribution of morphing as an advancement of image recognition perfection. The neural network employed for face recognition is based on the multy layer perceptron (MLP) architecture with back-propegation algorithm and incorporates the convolution filter response of Gabor jet. The effectiveness of the algorithm has been justified over a morphed facial image database with images captured in different illumination conditions.
14 Oct 2008
TL;DR: A novel method for modeling a human head as a simple 3D ellipsoid model is proposed and also, 3D head tracking and pose estimation methods using the proposedEllipsoidal model are presented.
Abstract: A human face provides a variety of different communicative functions such as identification, the perception of emotional expression, and lip-reading. For these reasons, many applications in robotics require tracking and recognizing a human face. A novel face recognition system should be able to deal with various changes in face images, such as pose, illumination, and expression, among which pose variation is the most difficult one to deal with. Therefore, face registration (alignment) is the key of robust face recognition. If we can register face images into frontal views, the recognition task would be much easier. To align a face image into a canonical frontal view, we need to know the pose information of a human head. Therefore, in this paper, we propose a novel method for modeling a human head as a simple 3D ellipsoid. And also, we present 3D head tracking and pose estimation methods using the proposed ellipsoidal model. After recovering full motion of the head, we can register face images with pose variations into stabilized view images which are suitable for frontal face recognition. By doing so, simple and efficient frontal face recognition can be easily carried out in the stabilized texture map space instead of the original input image space. To evaluate the feasibility of the proposed approach using a simple ellipsoid model, 3D head tracking experiments are carried out on 45 image sequences with ground truth from Boston University, and several face recognition experiments are conducted on our laboratory database and the Yale Face Database B by using subspace-based face recognition methods such as PCA, PCA+LAD, and DCV.