Mr. Ha Q. Nguyen Profile

Ha Q. Nguyen

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Proceedings Article | 14 February 2013 Paper

Subspace methods for computational relighting

Ha Nguyen, Siying Liu, Minh Do

Proceedings Volume 8657, 865703 (2013) https://doi.org/10.1117/12.2011522

KEYWORDS: Spherical lenses, Light sources and illumination, Reflectivity, Convolution, 3D modeling, Signal to noise ratio, Reflection, Matrices, Bidirectional reflectance transmission function, Light sources

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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.

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