What Is the Set of Images of an Object Under All Possible Illumination Conditions?

The appearance of an object depends on both the viewpoint from which it is observed and the light sources by which it is illuminated. If the appearance of two objects is never identical for any pose or lighting conditions, then–in theory–the objects can always be distinguished or recognized. The question arises: What is the set of images of an object under all lighting conditions and pose? In this paper, we consider only the set of images of an object under variable illumination, including multiple, extended light sources and shadows. We prove that the set of n-pixel images of a convex object with a Lambertian reflectance function, illuminated by an arbitrary number of point light sources at infinity, forms a convex polyhedral cone in IRⁿ and that the dimension of this illumination cone equals the number of distinct surface normals. Furthermore, the illumination cone can be constructed from as few as three images. In addition, the set of n-pixel images of an object of any shape and with a more general reflectance function, seen under all possible illumination conditions, still forms a convex cone in IRⁿ. Extensions of these results to color images are presented. These results immediately suggest certain approaches to object recognition. Throughout, we present results demonstrating the illumination cone representation.

     

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.     

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.     

Automatic interpretation and coding of face images using flexiblemodels

Face images are difficult to interpret because they are highly variable. Sources of variability include individual appearance, 3D pose, facial expression, and lighting. We describe a compact parametrized model of facial appearance which takes into account all these sources of variability. The model represents both shape and gray-level appearance, and is created by performing a statistical analysis over a training set of face images. A robust multiresolution search algorithm is used to fit the model to faces in new images. This allows the main facial features to be located, and a set of shape, and gray-level appearance parameters to be recovered. A good approximation to a given face can be reconstructed using less than 100 of these parameters. This representation can be used for tasks such as image coding, person identification, 3D pose recovery, gender recognition, and expression recognition. Experimental results are presented for a database of 690 face images obtained under widely varying conditions of 3D pose, lighting, and facial expression. The system performs well on all the tasks listed above     

Matching 2.5D face scans to 3D models

The performance of face recognition systems that use two-dimensional images depends on factors such as lighting and subject's pose. We are developing a face recognition system that utilizes three-dimensional shape information to make the system more robust to arbitrary pose and lighting. For each subject, a 3D face model is constructed by integrating several 2.5D face scans which are captured from different views. 2.5D is a simplified 3D (x,y,z) surface representation that contains at most one depth value (z direction) for every point in the (x, y) plane. Two different modalities provided by the facial scan, namely, shape and texture, are utilized and integrated for face matching. The recognition engine consists of two components, surface matching and appearance-based matching. The surface matching component is based on a modified iterative closest point (ICP) algorithm. The candidate list from the gallery used for appearance matching is dynamically generated based on the output of the surface matching component, which reduces the complexity of the appearance-based matching stage. Three-dimensional models in the gallery are used to synthesize new appearance samples with pose and illumination variations and the synthesized face images are used in discriminant subspace analysis. The weighted sum rule is applied to combine the scores given by the two matching components. Experimental results are given for matching a database of 200 3D face models with 598 2.5D independent test scans acquired under different pose and some lighting and expression changes. These results show the feasibility of the proposed matching scheme.     

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.     

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.