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Height-from-Polarisation with Unknown Lighting or Albedo

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Publication details

JournalIEEE Transactions on Pattern Analysis and Machine Intelligence
DateAccepted/In press - 26 Aug 2018
DateE-pub ahead of print - 6 Sep 2018
DatePublished (current) - 1 Dec 2019
Issue number12
Number of pages14
Pages (from-to)2875 - 2888
Early online date6/09/18
Original languageEnglish


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 height. The local ambiguity in the surface normal azimuth angle is resolved globally when the optimal surface height is reconstructed. Our method is applicable to dielectric objects exhibiting diffuse and specular reflectance, though lighting and albedo must be known. We relax this requirement by showing that either spatially varying albedo or illumination can be estimated from the polarisation image alone using nonlinear methods. In the case of illumination, the estimate can only be made up to a binary ambiguity which we show is a generalised Bas-relief transformation corresponding to the convex/concave ambiguity. We believe that our method is the first passive, monocular shape-from-x technique that enables well-posed height estimation with only a single, uncalibrated illumination condition. We present results on real world data, including in uncontrolled, outdoor illumination.

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    Research areas

  • Azimuth, Bas-relief ambiguity, Estimation, Light sources, Lighting, Refractive index, Shape, Surface reconstruction, albedo estimation, illumination estimation, polarisation, shape-from-x


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