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Understanding and modifying the effects of arbitrary illumination on human faces in a realistic manner is a challenging problem both for face synthesis and recognition. 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 spherical harmonics representation. 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) and demonstrate that any face under arbitrary unknown lighting can be simply represented by three low-dimensional vectors: shape parameters, spherical harmonic basis parameters and illumination coefficients. We show that, with our SHBMM, given one single image under arbitrary unknown lighting, we can remove the illumination effects from the image (face "delighting") and synthesize new images under different illumination conditions (face "re-lighting"). Furthermore, we demonstrate that cast shadows can be detected and subsequently removed by using the image error between the input image and the corresponding rendered image. We also propose two illumination invariant face recognition methods based on the recovered SHBMM parameters and the de-lit images respectively. Experimental results show that using only a single image of a face under unknown lighting, we can achieve high recognition rates and generate photorealistic images of the face under a wide range of illumination conditions, including multiple sources of illumination.