Subspace methods for computational relighting

Ha Q. Nguyen; Siying Liu; Minh N. Do

doi:10.1117/12.2011522

14 February 2013 Subspace methods for computational relighting

Ha Q. Nguyen, Siying Liu, Minh N. Do

Proceedings Volume 8657, Computational Imaging XI; 865703 (2013) https://doi.org/10.1117/12.2011522
Event: IS&T/SPIE Electronic Imaging, 2013, Burlingame, California, United States

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.

Citation Download Citation

Ha Q. Nguyen, Siying Liu, and Minh N. Do "Subspace methods for computational relighting", Proc. SPIE 8657, Computational Imaging XI, 865703 (14 February 2013); https://doi.org/10.1117/12.2011522

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