Abstract
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.
Highlights
WHEN unpolarised light is reflected by a surface it becomes partially polarised [1]
We evaluate our illumination, albedo and surface height estimation methods on both synthetic and real data
We have presented the first SfP technique in which polarisation constraints are expressed directly in terms of surface height
Summary
WHEN unpolarised light is reflected by a surface it becomes partially polarised [1]. This applies to both specular reflections [2] and diffuse reflections [3] caused by subsurface scattering. The angle and degree of polarisation of reflected light conveys information about the surface orientation and, provide a cue for shape recovery. There are a number of attractive properties to this ‘shapefrom-polarisation’ (SfP) cue. It requires only a single viewpoint and illumination condition, it is invariant to illumination direction and surface albedo and it provides information about both the zenith and azimuth angle of the surface normal. Shape estimates are dense (surface orientation information is available at every pixel so resolution is limited only by the sensor) and, since it does not rely on detecting or matching features, it is applicable to smooth, featureless surfaces
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