@inproceedings{49447d99cd7d4b84aef096ac8ca410f9,

title = "Subspace methods for computational relighting",

abstract = "We propose a vector space approach for relighting a Lambertian convex object with distant light source, whose crucial task is the decomposition of the reflectance function into albedos (or reflection coefficients) and lightings based on a set of images of the same object and its 3-D model. Making use of the fact that reflectance functions are well approximated by a low-dimensional linear subspace spanned by the first few spherical harmonics, this inverse problem can be formulated as a matrix factorization, in which the basis of the subspace is encoded in the spherical harmonic matrix S. A necessary and sufficient condition on S for unique factorization is derived with an introduction to a new notion of matrix rank called nonseparable full rank. An SVD-based algorithm for exact factorization in the noiseless case is introduced. In the presence of noise, the algorithm is slightly modified by incorporating the positivity of albedos into a convex optimization problem. Implementations of the proposed algorithms are done on a set of synthetic data.",

keywords = "convex optimization, inverse rendering, Lambertian surfaces, matrix factorization, reflectance function, relighting, singular value decomposition, spherical convolution, spherical harmonics",

author = "Nguyen, {Ha Q.} and Siying Liu and Do, {Minh N.}",

year = "2013",

doi = "10.1117/12.2011522",

language = "English (US)",

isbn = "9780819494306",

series = "Proceedings of SPIE - The International Society for Optical Engineering",

booktitle = "Proceedings of SPIE-IS and T Electronic Imaging - Computational Imaging XI",

note = "Computational Imaging XI ; Conference date: 05-02-2013 Through 07-02-2013",

}