Linear Depth Estimation from an Uncalibrated, Monocular Polarisation Image
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
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University of York, York, UK [email protected] 2 UC San Diego, San Diego, USA [email protected] Sapienza - Universit` a di Roma, Rome, Italy [email protected]
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 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. Keywords: Polarisation
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· Shape-from-x · Bas-relief ambiguity
Introduction
When unpolarised light is reflected by a surface it becomes partially polarised [1]. The degree to which the reflected light is polarised conveys information about the surface orientation and, therefore, provides a cue for shape recovery. There are a number of attractive properties to this ‘shape-from-polarisation’ (SfP) cue. It requires only a single viewpoint and illumination environment, it is invariant to illumination and surface albedo and it provides information about both the zenith and azimuth angle of the surface normal. Like photometric stereo, shape estimates are dense (the surface normal is estimated 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. Electronic supplementary material The online version of this chapter (doi:10. 1007/978-3-319-46484-8 7) contains supplementary material, which is available to authorized users. c Springer International Publishing AG 2016 B. Leibe et al. (Eds.): ECCV 2016, Part VIII, LNCS 9912, pp. 109–125, 2016. DOI: 10.1007/978-3-319-46484-8 7
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W.A.P. Smith et al.
Fig. 1. Overview of method: from a single polarisation image of a homogenous, glossy object in uncontrolled (possibly outdoor) illumination, we estimate lighting and compute depth directly.
However, there are a number of drawbacks to using SfP in a practical setting. The polarisation cue alone provides only ambiguous estimates of surface orientation. Hence, previous work focuses on developing heuristics to locally disambiguate the surface normals. Even having done so, surface orientation is only a 2.5D shape cue and so the estimated normal field must be integrated in order to recover surface depth [2] or used to refine a depth map captured using other cues [3]. This two step
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