Subspace methods for computational relighting

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

Research output: Chapter in Book/Report/Conference proceedingConference contribution


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.

Original languageEnglish (US)
Title of host publicationProceedings of SPIE-IS and T Electronic Imaging - Computational Imaging XI
StatePublished - 2013
EventComputational Imaging XI - Burlingame, CA, United States
Duration: Feb 5 2013Feb 7 2013

Publication series

NameProceedings of SPIE - The International Society for Optical Engineering
ISSN (Print)0277-786X


OtherComputational Imaging XI
Country/TerritoryUnited States
CityBurlingame, CA


  • convex optimization
  • inverse rendering
  • Lambertian surfaces
  • matrix factorization
  • reflectance function
  • relighting
  • singular value decomposition
  • spherical convolution
  • spherical harmonics

ASJC Scopus subject areas

  • Applied Mathematics
  • Computer Science Applications
  • Electrical and Electronic Engineering
  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


Dive into the research topics of 'Subspace methods for computational relighting'. Together they form a unique fingerprint.

Cite this