Variational estimation of inhomogeneous specular reflectance and illumination from a single view

Kenji Hara, Ko Nishino

Research output: Contribution to journalReview articlepeer-review

8 Citations (Scopus)


Estimating the illumination and the reflectance properties of an object surface from a few images is an important but challenging problem. The problem becomes even more challenging if we wish to deal with real-world objects that naturally have spatially inhomogeneous reflectance. In this paper, we derive a novel method for estimating the spatially varying specular reflectance properties of a surface of known geometry as well as the illumination distribution of a scene from a specular-only image, for instance, recovered from two images captured with a polarizer to separate reflection components. Unlike previous work, we do not assume the illumination to be a single point light source. We model specular reflection with a spherical statistical distribution and encode its spatial variation with a radial basis function (RBF) network of their parameter values, which allows us to formulate the simultaneous estimation of spatially varying specular reflectance and illumination as a constrained optimization based on the I-divergence measure. To solve it, we derive a variational algorithm based on the expectation maximization principle. At the same time, we estimate optimal encoding of the specular reflectance properties by learning the number, centers, and widths of the RBF hidden units. We demonstrate the effectiveness of the method on images of synthetic and real-world objects.

Original languageEnglish
Pages (from-to)136-146
Number of pages11
JournalJournal of the Optical Society of America A: Optics and Image Science, and Vision
Issue number2
Publication statusPublished - Feb 2011

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Atomic and Molecular Physics, and Optics
  • Computer Vision and Pattern Recognition


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