Face recognition from a single training image under arbitrary unknown lighting using spherical harmonics

In this paper, we propose two novel methods for face recognition under arbitrary unknown lighting by using spherical harmonics illumination representation, which require only one training image per subject and no 3D shape information. Our methods are based on the result which demonstrated 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. We provide two methods to estimate the spherical harmonic basis images spanning this space from just one image. Our first method builds the statistical model based on a collection of 2D basis images. We demonstrate that, by using the learned statistics, we can estimate the spherical harmonic basis images from just one image taken under arbitrary illumination conditions if there is no pose variation. Compared to the first method, the second method builds the statistical models directly in 3D spaces by combining the spherical harmonic illumination representation and a 3D morphable model of human faces to recover basis images from images across both poses and illuminations. After estimating the basis images, we use the same recognition scheme for both methods: we recognize the face for which there exists a weighted combination of basis images that is the closest to the test face image. We provide a series of experiments that achieve high recognition rates, under a wide range of illumination conditions, including multiple sources of illumination. Our methods achieve comparable levels of accuracy with methods that have much more onerous training data requirements. Comparison of the two methods is also provided.     

Reconstructing 3D Shape,Albedo and Illumination from a Single Face Image

The morphable model has been employed to efficiently describe 3D face shape and the associated albedo with a reduced set of basis vectors. The spherical harmonics (SH) model provides a compact basis to well approximate the image appearance of a Lambertian object under different illumination conditions. Recently, the SH and morphable models have been integrated for 3D face shape reconstruction. However, the reconstructed 3D shape is either inconsistent with the SH bases or obtained just from landmarks only. In this work, we propose a geometrically consistent algorithm to reconstruct the 3D face shape and the associated albedo from a single face image iteratively by combining the morphable model and the SH model. The reconstructed 3D face geometry can uniquely determine the SH bases, therefore the optimal 3D face model can be obtained by minimizing the error between the input face image and a linear combination of the associated SH bases. In this way, we are able to preserve the consistency between the 3D geometry and the SH model, thus refining the 3D shape reconstruction recursively. Furthermore, we present a novel approach to recover the illumination condition from the estimated weighting vector for the SH bases in a constrained optimization formulation independent of the 3D geometry. Experimental results show the effectiveness and accuracy of the proposed face reconstruction and illumination estimation algorithm under different face poses and multiple‐light‐source illumination conditions.     

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     

超球流形约束下的3DMM分步全局优化

通过综合运用人脸空间的超球流形约束、基于梯度的启发式全局优化、光照的球面谐波描述以及凸包可见点集的直接消隐方法,提出一种三维可形变模型的图像匹配方法.首先通过形状超球流形约束下的全局优化算法求解摄像机参数和形状参数,然后使用以上参数和凸包点集的直接消隐方法确定物像点对应关系,最后根据物像点对应关系由反射率超球流形约束下的全局优化算法求解光照参数和反射率参数.定量的对比实验结果表明,该方法无需借助分区域拟合、人为估计参数值、层次匹配策略或复杂的特征组合,即可由单幅图像恢复三维可形变模型(3DMM)的全部参数.     

A lighting robust fitting approach of 3D morphable model for face reconstruction

Three-dimensional morphable model (3DMM) is a powerful tool for recovering 3D shape and texture from a single facial image. The success of 3DMM relies on two things: an effective optimization strategy and a realistic approach to synthesizing face images. However, most previous methods have focused on developing an optimization strategy under Phong’s synthesis approach. In this paper, we adopt a more realistic synthesis technique that fully considers illumination and reflectance in the 3DMM fitting process. Using the sphere harmonic illumination model (SHIM), our new synthesis approach can account for more lighting factors than Phong’s model. Spatially varying specular reflectance is also introduced into the synthesis process. Under SHIM, the cost function is nearly linear for all parameters, which simplifies the optimization. We apply our new optimization algorithm to determine the shape and texture parameters simultaneously. The accuracy of the recovered shape and texture can be improved significantly by considering the spatially varying specular reflectance. Hence, our algorithm produces an enhanced shape and texture compared with previous SHIM-based methods that recover shape from feature points. Although we use just a single input image in a profile pose, our approach gives plausible results. Experiments on a well-known image database show that, compared to state-of-the-art methods based on Phong’s model, the proposed approach enhances the robustness of the 3DMM fitting results under extreme lighting and profile pose.     

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.     

Driving 3D morphable models using shading cues

In this paper we show how surface orientation information inferred using shape-from-shading can be used to aid the process of fitting a 3D morphable model to an image of a face. We consider the problem of model dominance and show how shading constraints can be used to refine morphable model shape estimates, offering the possibility of exceeding the maximum possible accuracy of the model. We use this observation to motivate an optimisation scheme based on surface normal error. This ensures the fullest possible use of the information conveyed by the shading in an image. Moreover, our framework allows estimation of per-vertex albedo and bump maps which are not constrained to lie within the span of the model. This means the recovered model is capable of describing shape and reflectance phenomena not present in the training set. We show reconstruction and synthesis results and demonstrate that the shape and albedo estimates can be used for illumination insensitive recognition using only a single gallery image.     

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。     

Face recognition based on fitting a 3D morphable model

This paper presents a method for face recognition across variations in pose, ranging from frontal to profile views, and across a wide range of illuminations, including cast shadows and specular reflections. To account for these variations, the algorithm simulates the process of image formation in 3D space, using computer graphics, and it estimates 3D shape and texture of faces from single images. The estimate is achieved by fitting a statistical, morphable model of 3D faces to images. The model is learned from a set of textured 3D scans of heads. We describe the construction of the morphable model, an algorithm to fit the model to images, and a framework for face identification. In this framework, faces are represented by model parameters for 3D shape and texture. We present results obtained with 4,488 images from the publicly available CMU-PIE database and 1,940 images from the FERET database.     

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.     

Robust Estimation of Albedo for Illumination-Invariant Matching and Shape Recovery

We present a nonstationary stochastic filtering framework for the task of albedo estimation from a single image. There are several approaches in the literature for albedo estimation, but few include the errors in estimates of surface normals and light source direction to improve the albedo estimate. The proposed approach effectively utilizes the error statistics of surface normals and illumination direction for robust estimation of albedo, for images illuminated by single and multiple light sources. The albedo estimate obtained is subsequently used to generate albedo-free normalized images for recovering the shape of an object. Traditional Shape-from-Shading (SFS) approaches often assume constant/piecewise constant albedo and known light source direction to recover the underlying shape. Using the estimated albedo, the general problem of estimating the shape of an object with varying albedo map and unknown illumination source is reduced to one that can be handled by traditional SFS approaches. Experimental results are provided to show the effectiveness of the approach and its application to illumination-invariant matching and shape recovery. The estimated albedo maps are compared with the ground truth. The maps are used as illumination-invariant signatures for the task of face recognition across illumination variations. The recognition results obtained compare well with the current state-of-the-art approaches. Impressive shape recovery results are obtained using images downloaded from the Web with little control over imaging conditions. The recovered shapes are also used to synthesize novel views under novel illumination conditions.     

基于改进三维形变模型的三维人脸重建和密集人脸对齐方法

针对现在广泛使用的三维形变模型表达能力不够，导致重建出的三维人脸模型泛化性能不佳的问题，提出了一种在姿态、表情和光照未知的条件下的基于单张人脸图片的三维人脸重建和密集人脸对齐的新方法。首先，通过卷积神经网络对现有的三维形变模型进行改进，以提高三维人脸模型的表达能力；然后，基于人脸光滑性和图像相似性，在特征点和像素层面提出新的损失函数，并使用弱监督学习训练卷积神经网络模型；最后，通过训练出的网络模型进行三维人脸重建和密集人脸对齐。实验结果表明，对于三维人脸重建任务，所提模型在AFLW2000-3D上实现了2.25的归一化平均误差；对于密集人脸对齐任务，所提模型在AFLW2000-3D和AFLW-LFPA上分别实现了3.80和3.34的归一化平均误差。与原始使用三维形变模型的方法相比，所提模型在三维人脸重建和密集人脸对齐上的归一化平均误差分别降低了7.4%和7.8%。针对不同光照环境以及角度的人脸图片，该网络模型的重建准确，鲁棒性好，且具有较高的三维人脸重建和密集人脸对齐质量。     

基于改进三维形变模型的三维人脸重建和密集人脸对齐方法

针对现在广泛使用的三维形变模型表达能力不够,导致重建出的三维人脸模型泛化性能不佳的问题,提出了一种在姿态、表情和光照未知的条件下的基于单张人脸图片的三维人脸重建和密集人脸对齐的新方法。首先,通过卷积神经网络对现有的三维形变模型进行改进,以提高三维人脸模型的表达能力;然后,基于人脸光滑性和图像相似性,在特征点和像素层面提出新的损失函数,并使用弱监督学习训练卷积神经网络模型;最后,通过训练出的网络模型进行三维人脸重建和密集人脸对齐。实验结果表明,对于三维人脸重建任务,所提模型在AFLW2000-3D上实现了2.25的归一化平均误差;对于密集人脸对齐任务,所提模型在AFLW2000-3D和AFLW-LFPA上分别实现了3.80和3.34的归一化平均误差。与原始使用三维形变模型的方法相比,所提模型在三维人脸重建和密集人脸对齐上的归一化平均误差分别降低了7.4%和7.8%。针对不同光照环境以及角度的人脸图片,该网络模型的重建准确,鲁棒性好,且具有较高的三维人脸重建和密集人脸对齐质量。     

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.     

形状约束的三维人脸组件形变模型

传统的三维人脸形变模型是通过对大量的三维人脸数据进行学习,构建描述人脸三维形状和纹理的参数模型,通过模型优化完成对二维人脸图像的三维重构。但是,实际中大量的训练样本是很难获得的,这导致形变模型描述能力的不完善,制约了它的应用。如将整个人脸看成由若干个组件组合而成,则在样本数不变的情况下降低了描述空间的维数,提高了模型的描述能力。但是在重构人脸图像时必须解决组件间三维空间的重叠合并,并且随着组件数目的增加,模型参数也随之增加,所以对优化算法也提出了更高的要求。为了解决形变模型的这些困难,提出了一种全局模型和组件模型的折中算法,即在形状上保持全局约束而纹理上进行组件匹配,从而在算法性能和算法复杂度之间获得了一个有效的平衡。     

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.     

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.     

Occlusion-Aware 3D Morphable Models and an Illumination Prior for Face Image Analysis

Faces in natural images are often occluded by a variety of objects. We propose a fully automated, probabilistic and occlusion-aware 3D morphable face model adaptation framework following an analysis-by-synthesis setup. The key idea is to segment the image into regions explained by separate models. Our framework includes a 3D morphable face model, a prototype-based beard model and a simple model for occlusions and background regions. The segmentation and all the model parameters have to be inferred from the single target image. Face model adaptation and segmentation are solved jointly using an expectation–maximization-like procedure. During the E-step, we update the segmentation and in the M-step the face model parameters are updated. For face model adaptation we apply a stochastic sampling strategy based on the Metropolis–Hastings algorithm. For segmentation, we apply loopy belief propagation for inference in a Markov random field. Illumination estimation is critical for occlusion handling. Our combined segmentation and model adaptation needs a proper initialization of the illumination parameters. We propose a RANSAC-based robust illumination estimation technique. By applying this method to a large face image database we obtain a first empirical distribution of real-world illumination conditions. The obtained empirical distribution is made publicly available and can be used as prior in probabilistic frameworks, for regularization or to synthesize data for deep learning methods.     

Photometric Stereo with General,Unknown Lighting

Work on photometric stereo has shown how to recover the shape and reflectance properties of an object using multiple images taken with a fixed viewpoint and variable lighting conditions. This work has primarily relied on known lighting conditions or the presence of a single point source of light in each image. In this paper we show how to perform photometric stereo assuming that all lights in a scene are distant from the object but otherwise unconstrained. Lighting in each image may be an unknown and may include arbitrary combination of diffuse, point and extended sources. Our work is based on recent results showing that for Lambertian objects, general lighting conditions can be represented using low order spherical harmonics. Using this representation we can recover shape by performing a simple optimization in a low-dimensional space. We also analyze the shape ambiguities that arise in such a representation. We demonstrate our method by reconstructing the shape of objects from images obtained under a variety of lightings. We further compare the reconstructed shapes against shapes obtained with a laser scanner.