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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 recent 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.
Index Terms- Face recognition, spherical harmonics illumination representation, 3D face morphable models, illumination invariance.

D. Samaras and L. Zhang, "Face Recognition from a Single Training Image under Arbitrary Unknown Lighting Using Spherical Harmonics," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 28, no. , pp. 351-363, 2006.
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