Face Relighting from a Single Image under Arbitrary Unknown Lighting Conditions

In this paper, we present a new method to modify the appearance of a face image by manipulating the illumination condition, when the face geometry and albedo information is unknown. This problem is particularly difficult when there is only a single image of the subject available. Recent research demonstrates that the set of images of a convex Lambertian object obtained under a wide variety of lighting conditions can be approximated accurately by a low-dimensional linear subspace using a spherical harmonic representation. Moreover, morphable models are statistical ensembles of facial properties such as shape and texture. In this paper, we integrate spherical harmonics into the morphable model framework by proposing a 3D spherical harmonic basis morphable model (SHBMM). The proposed method can represent a face under arbitrary unknown lighting and pose simply by three low-dimensional vectors, i.e., shape parameters, spherical harmonic basis parameters, and illumination coefficients, which are called the SHBMM parameters. However, when the image was taken under an extreme lighting condition, the approximation error can be large, thus making it difficult to recover albedo information. In order to address this problem, we propose a subregion-based framework that uses a Markov random field to model the statistical distribution and spatial coherence of face texture, which makes our approach not only robust to extreme lighting conditions, but also insensitive to partial occlusions. The performance of our framework is demonstrated through various experimental results, including the improved rates for face recognition under extreme lighting conditions.     

任意光照下人脸图像的低维光照空间表示

本文提出一种不同光照条件下人脸图像的低维光照空间表示方法.这种低维光照空间表示不仅能够由输入图像估计其光照参数,而且能够由给定的光照条件生成虚拟的人脸图像.利用主成分分析和最近邻聚类方法得到9个基本点光源的位置,这9个基本点光源可以近似人脸识别应用中几乎所有的光照条件.在这9个基本光源照射下的9幅人脸基图像构成了低维人脸光照空间,它可以表示不同光照条件下的人脸图像,结合光照比图像方法,可以生成不同光照下的虚拟人脸图像.本文提出的低维光照空间的最大优点是利用某个人脸的图像建立的光照空间,可以用于不同的人脸.图像重构和不同光照下的人脸识别实验说明了本文算法的有效性.     

Illumination invariant face recognition

The appearance of a face will vary drastically when the illumination changes. Variations in lighting conditions make face recognition an even more challenging and difficult task. In this paper, we propose a novel approach to handle the illumination problem. Our method can restore a face image captured under arbitrary lighting conditions to one with frontal illumination by using a ratio-image between the face image and a reference face image, both of which are blurred by a Gaussian filter. An iterative algorithm is then used to update the reference image, which is reconstructed from the restored image by means of principal component analysis (PCA), in order to obtain a visually better restored image. Image processing techniques are also used to improve the quality of the restored image. To evaluate the performance of our algorithm, restored images with frontal illumination are used for face recognition by means of PCA. Experimental results demonstrate that face recognition using our method can achieve a higher recognition rate based on the Yale B database and the Yale database. Our algorithm has several advantages over other previous algorithms: (1) it does not need to estimate the face surface normals and the light source directions, (2) it does not need many images captured under different lighting conditions for each person, nor a set of bootstrap images that includes many images with different illuminations, and (3) it does not need to detect accurate positions of some facial feature points or to warp the image for alignment, etc.     

Acquiring linear subspaces for face recognition under variable lighting

Previous work has demonstrated that the image variation of many objects (human faces in particular) under variable lighting can be effectively modeled by low-dimensional linear spaces, even when there are multiple light sources and shadowing. Basis images spanning this space are usually obtained in one of three ways: a large set of images of the object under different lighting conditions is acquired, and principal component analysis (PCA) is used to estimate a subspace. Alternatively, synthetic images are rendered from a 3D model (perhaps reconstructed from images) under point sources and, again, PCA is used to estimate a subspace. Finally, images rendered from a 3D model under diffuse lighting based on spherical harmonics are directly used as basis images. In this paper, we show how to arrange physical lighting so that the acquired images of each object can be directly used as the basis vectors of a low-dimensional linear space and that this subspace is close to those acquired by the other methods. More specifically, there exist configurations of k point light source directions, with k typically ranging from 5 to 9, such that, by taking k images of an object under these single sources, the resulting subspace is an effective representation for recognition under a wide range of lighting conditions. Since the subspace is generated directly from real images, potentially complex and/or brittle intermediate steps such as 3D reconstruction can be completely avoided; nor is it necessary to acquire large numbers of training images or to physically construct complex diffuse (harmonic) light fields. We validate the use of subspaces constructed in this fashion within the context of face recognition.     

Face relighting using discriminative 2D spherical spaces for face recognition

As part of the face recognition task in a robust security system, we propose a novel approach for the illumination recovery of faces with cast shadows and specularities. Given a single 2D face image, we relight the face object by extracting the nine spherical harmonic bases and the face spherical illumination coefficients by using the face spherical spaces properties. First, an illumination training database is generated by computing the properties of the spherical spaces out of face albedo and normal values estimated from 2D training images. The training database is then discriminately divided into two directions in terms of the illumination quality and light direction of each image. Based on the generated multi-level illumination discriminative training space, we analyze the target face pixels and compare them with the appropriate training subspace using pre-generated tiles. When designing the framework, practical real-time processing speed and small image size were considered. In contrast to other approaches, our technique requires neither 3D face models nor restricted illumination conditions for the training process. Furthermore, the proposed approach uses one single face image to estimate the face albedo and face spherical spaces. In this work, we also provide the results of a series of experiments performed on publicly available databases to show the significant improvements in the face recognition rates.     

基于球面谐波基图像的任意光照下的人脸识别

提出了一种基于球面谐波基图像的光照补偿算法,用以在任意光照条件下进行人脸识别.算法分两步进行：光照估计和光照补偿.基于人脸形状大致相同和每个人脸的反射率基本相等的假设,首先估计了输入人脸图像光照的9个低频谐波系数.根据光照估计的结果,提出了两种光照补偿方法：纹理图像和差图像.纹理图像为输入图像与其光照辐照图之商,与输入图像的光照条件无关.差图像为输入图像与平均人脸在相同光照下的图像之差,通过减去平均人脸在相同光照下的图像,减弱了光照的影响.在CMU-PIE人脸库和Yale B人脸库上的实验表明,通过光照补偿,不同光照下人脸图像识别率有了很大提高.     

Face recognition under arbitrary illumination using illuminated exemplars

Recently, the importance of face recognition has been increasingly emphasized since popular CCD cameras are distributed to various applications. However, facial images are dramatically changed by lighting variations, so that facial appearance changes caused serious performance degradation in face recognition. Many researchers have tried to overcome these illumination problems using diverse approaches, which have required a multiple registered images per person or the prior knowledge of lighting conditions. In this paper, we propose a new method for face recognition under arbitrary lighting conditions, given only a single registered image and training data under unknown illuminations. Our proposed method is based on the illuminated exemplars which are synthesized from photometric stereo images of training data. The linear combination of illuminated exemplars can represent the new face and the weighted coefficients of those illuminated exemplars are used as identity signature. We make experiments for verifying our approach and compare it with two traditional approaches. As a result, higher recognition rates are reported in these experiments using the illumination subset of Max-Planck Institute face database and Korean face database.     

From few to many: illumination cone models for face recognitionunder variable lighting and pose

We present a generative appearance-based method for recognizing human faces under variation in lighting and viewpoint. Our method exploits the fact that the set of images of an object in fixed pose, but under all possible illumination conditions, is a convex cone in the space of images. Using a small number of training images of each face taken with different lighting directions, the shape and albedo of the face can be reconstructed. In turn, this reconstruction serves as a generative model that can be used to render (or synthesize) images of the face under novel poses and illumination conditions. The pose space is then sampled and, for each pose, the corresponding illumination cone is approximated by a low-dimensional linear subspace whose basis vectors are estimated using the generative model. Our recognition algorithm assigns to a test image the identity of the closest approximated illumination cone. Test results show that the method performs almost without error, except on the most extreme lighting directions     

Face recognition under varying illumination based on a 2D face shape model

This paper proposes a novel illumination compensation algorithm, which can compensate for the uneven illuminations on human faces and reconstruct face images in normal lighting conditions. A simple yet effective local contrast enhancement method, namely block-based histogram equalization (BHE), is first proposed. The resulting image processed using BHE is then compared with the original face image processed using histogram equalization (HE) to estimate the category of its light source. In our scheme, we divide the light source for a human face into 65 categories. Based on the category identified, a corresponding lighting compensation model is used to reconstruct an image that will visually be under normal illumination. In order to eliminate the influence of uneven illumination while retaining the shape information about a human face, a 2D face shape model is used. Experimental results show that, with the use of principal component analysis for face recognition, the recognition rate can be improved by 53.3% to 62.6% when our proposed algorithm for lighting compensation is used.     

Face recognition under varying illumination

To eliminate the effects of illumination variation, the conventional approaches firstly produce a compensation-based face image under standard illumination from the input image and then match the image with the face templates in a database. This method is not inapplicable to the input image with large illumination variation. Therefore, a novel method for varying illumination conditions is proposed. Firstly, the quotient image method is improved. Then, the nine basis images of each subject are generated by the improved quotient image method. Thirdly, one new image of each subject under the same lighting conditions with an input image is synthesized by the corresponding basis images. Finally, the synthetic images and the input image are projected to PCA plane to fulfill the recognition task. The experimental results show that the proposed approach can eliminate the effects of illumination variation and have a high recognition rate in the illumination conditions with remarkable changes.     

Lambertian reflectance and linear subspaces

We prove that the set of all Lambertian reflectance functions (the mapping from surface normals to intensities) obtained with arbitrary distant light sources lies close to a 9D linear subspace. This implies that, in general, the set of images of a convex Lambertian object obtained under a wide variety of lighting conditions can be approximated accurately by a low-dimensional linear subspace, explaining prior empirical results. We also provide a simple analytic characterization of this linear space. We obtain these results by representing lighting using spherical harmonics and describing the effects of Lambertian materials as the analog of a convolution. These results allow us to construct algorithms for object recognition based on linear methods as well as algorithms that use convex optimization to enforce nonnegative lighting functions. We also show a simple way to enforce nonnegative lighting when the images of an object lie near a 4D linear space. We apply these algorithms to perform face recognition by finding the 3D model that best matches a 2D query image.     

Virtual illumination grid for correction of uncontrolled illumination in facial images

Face recognition under uncontrolled illumination conditions is still considered an unsolved problem. In order to correct for these illumination conditions, we propose a virtual illumination grid (VIG) approach to model the unknown illumination conditions. Furthermore, we use coupled subspace models of both the facial surface and albedo to estimate the face shape. In order to obtain a representation of the face under frontal illumination, we relight the estimated face shape. We show that the frontal illuminated facial images achieve better performance in face recognition. We have performed the challenging Experiment 4 of the FRGCv2 database, which compares uncontrolled probe images to controlled gallery images. Our illumination correction method results in considerably better recognition rates for a number of well-known face recognition methods. By fusing our global illumination correction method with a local illumination correction method, further improvements are achieved.     

A theory of frequency domain invariants: spherical harmonic identities for BRDF/lighting transfer and image consistency

This paper develops a theory of frequency domain invariants in computer vision. We derive novel identities using spherical harmonics, which are the angular frequency domain analog to common spatial domain invariants such as reflectance ratios. These invariants are derived from the spherical harmonic convolution framework for reflection from a curved surface. Our identities apply in a number of canonical cases, including single and multiple images of objects under the same and different lighting conditions. One important case we consider is two different glossy objects in two different lighting environments. For this case, we derive a novel identity, independent of the specific lighting configurations or BRDFs, that allows us to directly estimate the fourth image if the other three are available. The identity can also be used as an invariant to detecttampering in the images.While this paper is primarily theoretical, it has the potential to lay the mathematical foundations for two important practical applications. First, we can develop more general algorithms for inverse rendering problems, which can directly relight and change material properties by transferring the BRDF or lighting from another object or illumination. Second, we can check the consistency of an image, to detect tampering or image splicing.     

可变光照条件下的人脸图像识别

对于人脸图像识别中光照变化的影响,传统的解决方法是对待识别图像进行光照补偿,先使它成为标准光照条件下的图像,然后和模板图像匹配来进行识别。为了提高在光照条件大范围变化时,人脸图像的识别率,提出了一种新的可变光照条件下的人脸图像识别方法。该方法首先利用在9个基本光照方向下分别获得的9幅图像来构成人脸光照特征空间,再通过这个光照特征空间,将图像库中的人脸图像变换成与待识别图像具有相同光照条件的图像,并将其作为模板图像;然后利用特征脸方法进行识别。实验结果表明,这种方法不仅能够有效地解决人脸识别中由于光照变化影响所造成的识别率下降的问题,而且对于光照条件大范围变化的情况,也可以得到比较高的正确识别率。     

基于样例学习的任意光照下的人脸3D重建方法

待匹配的人脸图像与数据库中的原型图像之间的光照差异是自动人脸识别的主要瓶颈问题之一。提出了一种基于样例学习方式的3D人脸形状重建方法,既可以生成任意光照条件下的数据库中人脸图像,也可以对待识别图像进行重新光照,合成无阴影的图像。该方法在建立人脸数据库时利用光度立体技术分离人脸图像的纹理和形状信息,并用多面体模型在最小二乘意义下恢复其3D信息并更新法向量场以克服阴影误差,从而可以利用计算机图形学的方法合成任意光照条件下和小角度姿态改变时的人脸图像;在识别时采用数据库中3D数据的线性组合形式对输入图像建模,以估计其3D信息,从而可以重新照明。在YaleB人脸数据库上的实验表明,在建立3D人脸数据库后,该方法可以快速恢复输入单幅图像中人脸的3D信息,并生成任意光照条件的该人脸图像。     

Total variation models for variable lighting face recognition

In this paper, we present the logarithmic total variation (LTV) model for face recognition under varying illumination, including natural lighting conditions, where we rarely know the strength, direction, or number of light sources. The proposed LTV model has the ability to factorize a single face image and obtain the illumination invariant facial structure, which is then used for face recognition. Our model is inspired by the SQI model but has better edge-preserving ability and simpler parameter selection. The merit of this model is that neither does it require any lighting assumption nor does it need any training. The LTV model reaches very high recognition rates in the tests using both Yale and CMU PIE face databases as well as a face database containing 765 subjects under outdoor lighting conditions.     

Local histogram specification for face recognition under varying lighting conditions

High frequency illumination and low frequency face features bring difficulties for most of the state-of-the-art face image preprocessors. In this paper, we propose two methods based on Local Histogram Specification (LHS) to preprocess face images under varying lighting conditions. The proposed methods are able to significantly remove both the low and high frequency parts of illumination on face images, as well as enhance face features lying in the low frequency part. Specifically, we first apply a high-pass filter on a face image to filter the low frequency illumination. Then, local histograms and local histogram statistics are learned from normal lighting images. In our first method, LHS is applied on the entire image. By contrast, in the second method, the regions contain high frequency illumination and weak face features on a face image are identified by local histogram statistics, before LHS is applied on these regions to eliminate high frequency illumination and enhance weak face features. Experimental results on the CMU PIE, Extended Yale B and CAS-PEAL-R1 databases demonstrate the effectiveness and efficiency of our methods.     

Efficient Relighting of RBF-Based Illumination Adjustable Images

An illumination adjustable image (IAI) contains a large number of prerecorded images under various light directions. Relighting a scene under complicated lighting conditions can be achieved from the IAI. Using the radial basis function (RBF) approach to represent an IAI is proven to be more efficient than using the spherical harmonic approach. However, to represent high-frequency lighting effects, we need to use many RBFs. Hence, the relighting speed could be very slow. This brief investigates a partial reconstruction scheme for relighting an IAI based on the locality of RBFs. Compared with the conventional RBF and spherical harmonics (SH) approaches, the proposed scheme has a much faster relighting speed under the similar distortion performance.      

Homomorphic filtering based illumination normalization method for face recognition

The appearance of a face image is severely affected by illumination conditions that will hinder the automatic face recognition process. To recognize faces under varying lighting conditions, a homomorphic filtering-based illumination normalization method is proposed in this paper. In this work, the effect of illumination is effectively reduced by a modified implementation of homomorphic filtering whose key component is a Difference of Gaussian (DoG) filter, and the contrast is enhanced by histogram equalization. The resulted face image is not only reduced illumination effect but also preserved edges and details that will facilitate the further face recognition task. Among others, our method has the following advantages: (1) neither does it need any prior information of 3D shape or light sources, nor many training samples thus can be directly applied to single training image per person condition; and (2) it is simple and computationally fast because there are mature and fast algorithms for the Fourier transform used in homomorphic filter. The Eigenfaces method is chosen to recognize the normalized face images. Experimental results on the Yale face database B and the CMU PIE face database demonstrate the significant performance improvement of the proposed method in the face recognition system for the face images with large illumination variations.