We prove that the set of all reflectance functions (the mapping from surface normals to intensities) produced by Lambertian objects under distant, isotropic lighting 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 non-negative lighting functions. Finally, we show a simple way to enforce non-negative lighting when the images of an object lie near a 4D linear space. Research conducted w...

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.

Image analysis and graphics synthesis can be achieved with learning techniques using directly image examples without physically-based, 3D models. We describe here novel techniques for the analysis and the synthesis of new grey-level (and color) images. With the first technique, ffl the mapping from novel images to a vector of "pose" and "expression" parameters can be learned from a small set of example images using a function approximation technique that we call an analysis network; ffl the inverse mapping from input "pose" and "expression" parameters to output grey-level images can be synthesized from a small set of example images and used to produce new images under real-time control using a similar learning network, called in this case a synthesis network. This technique relies on (i) using a correspondence algorithm that matches corresponding pixels among pairs of grey-level images and effectively "vectorizes" them, and (ii) exploiting a class of multidimensional interpolation n...

We study the recognition of surfaces made from different materials such as concrete, rug, marble or leather on the basis of their textural appearance. Such natural textures arise from spatial variation of two surface attributes: (1) reflectance and (2) surface normal. In this paper, we provide a unified model to address both these aspects of natural texture. The main idea is to construct a vocabulary of prototype tiny surface patches with associated local geometric and photometric properties. We call these 3D textons. Examples might be ridges, grooves, spots or stripes or combinations thereof. Associated with each texton is an appearance vector, which characterizes the local irradiance distribution, represented as a set of linear Gaussian derivative filter outputs, under different lighting and viewing conditions. Given a large collection of images of different materials, a clustering approach is used to acquire a small (on the order of 100) 3D texton vocabulary. Given a few (1 to 4) ...

In this paper we describe a holistic face recognition method based on subspace Linear Discriminant Analysis (LDA). The method consists of two steps: first we project the face image from the original vector space to a face subspace via Principal Component Analysis where the subspace dimension is carefully chosen, and then use LDA to obtain a linear classifier in the subspace. The criterion we use to choose the subspace dimension enables us to generate class-separable features via LDA. In addition, we employ a weighted distance metric guided by the LDA eigenvalues to improve the performance of the subspace LDA method. Finally, the improved performance of the subspace LDA approach is demonstrated through experiments using the FERET dataset for face recognition/verification, a large mugshot dataset for person verification, and the MPEG-7 dataset. 1 Partially supported by the Office of Naval Research under Grant N00014-95-1-0521. I. Introduction The problem of automatic face recognition...

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 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 isotropic and distant from the object but otherwise unconstrained. Lighting in each image may be an unknown and 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. 1.

Lambertian object

We derive algorithms for finding a nonnegative n-dimensional tensor factorization (n-NTF) which includes the non-negative matrix factorization (NMF) as a particular case when n = 2. We motivate the use of n-NTF in three areas of data analysis: (i) connection to latent class models in statistics, (ii) sparse image coding in computer vision, and (iii) model selection problems. We derive a ”direct ” positive-preserving gradient descent algorithm and an alternating scheme based on repeated multiple rank-1 problems. 1.

this paper, we focus on recognition and image rerendering under lighting condition variability of a class of objects, i.e., objects that belong to a general class, such as the class of faces. In other words, for the re-rendering task, given sample images of members of a class of objects and a single image of a new object of the class, we wish to render new images of the new object that simulate changing lighting conditions

We consider the problem of determining functions of an image of an object that are insensitive to illumination changes. We first show that for an object with Lambertian reflectance there are no discriminative functions that are invariant to illumination. This result leads us to adopt a probabilistic approach in which we analytically determine a probability distribution for the image gradient as a function of the surface's geometry and reflectance. Our distribution reveals that the direction of the image gradient is insensitive to changes in illumination direction. We verify this empirically by constructing a distribution for the image gradient from more than 20 million samples of gradients in a datab aseof 1,280 images of 20 inanimate objects taken under varying lighting condition. Using this distribution, we develop an illumination insensitive measure of image comparison and test it on the problem of face recognition.