Linear Depth Estimation from an Uncalibrated, Monocular Polarisation Image

  • William A. P. SmithEmail author
  • Ravi Ramamoorthi
  • Silvia Tozza
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9912)


We present a method for estimating surface height directly from a single polarisation image simply by solving a large, sparse system of linear equations. To do so, we show how to express polarisation constraints as equations that are linear in the unknown depth. The ambiguity in the surface normal azimuth angle is resolved globally when the optimal surface height is reconstructed. Our method is applicable to objects with uniform albedo exhibiting diffuse and specular reflectance. We extend it to an uncalibrated scenario by demonstrating that the illumination (point source or first/second order spherical harmonics) can be estimated from the polarisation image, up to a binary convex/concave ambiguity. We believe that our method is the first monocular, passive shape-from-x technique that enables well-posed depth estimation with only a single, uncalibrated illumination condition. We present results on glossy objects, including in uncontrolled, outdoor illumination.


Polarisation Shape-from-x Bas-relief ambiguity 



This work was undertaken while W. Smith was a visiting scholar at UCSD, supported by EPSRC Overseas Travel Grant EP/N028481/1. S. Tozza was supported by Gruppo Nazionale per il Calcolo Scientifico (GNCS-INdAM). This work was supported in part by ONR grant N00014-15-1-2013 and the UC San Diego Center for Visual Computing. We thank Zak Murez for assistance with data collection.

Supplementary material

419983_1_En_7_MOESM1_ESM.pdf (6.8 mb)
Supplementary material 1 (pdf 6991 KB)


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Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  • William A. P. Smith
    • 1
    Email author
  • Ravi Ramamoorthi
    • 2
  • Silvia Tozza
    • 3
  1. 1.University of YorkYorkUK
  2. 2.UC San DiegoSan DiegoUSA
  3. 3.Sapienza - Università di RomaRomeItaly

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