In this paper we present a differential approach to photo-polarimetric shape estimation. We propose several alternative differential constraints based on polarisation and photometric shading information and show how to express them in a unified partial differential system. Our method uses the image ratios technique to combine shading and polarisation information in order to directly reconstruct surface height, without first computing surface normal vectors. Moreover, we are able to remove the non-linearities so that the problem reduces to solving a linear differential problem. We also introduce a new method for estimating a polarisation image from multichannel data and, finally, we show it is possible to estimate the illumination directions in a two source setup, extending the method into an uncalibrated scenario. From a numerical point of view, we use a least-squares formulation of the discrete version of the problem. To the best of our knowledge, this is the first work to consider a unified differential approach to solve photo-polarimetric shape estimation directly for height. Numerical results on synthetic and real-world data confirm the effectiveness of our proposed method.
The polarisation state of light reflected by a surface provides a cue to the material properties of the surface and, via a relationship with surface orientation, the shape. Polarisation has been used for a number of applications, including early work on material segmentation @cite_1 and diffuse specular reflectance separation @cite_6 . However, there has been a resurgent interest @cite_17 @cite_26 @cite_3 @cite_13 in using polarisation information for shape estimation.
@cite_26 @cite_1 @cite_3 @cite_6 @cite_13 @cite_17
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Coarse depth maps can be enhanced by using the shape information from polarization cues. We propose a framework to combine surface normals from polarization (hereafter polarization normals) with an aligned depth map. Polarization normals have not been used for depth enhancement before. This is because polarization normals suffer from physics-based artifacts, such as azimuthal ambiguity, refractive distortion and fronto-parallel signal degradation. We propose a framework to overcome these key challenges, allowing the benefits of polarization to be used to enhance depth maps. Our results demonstrate improvement with respect to state-of-the-art 3D reconstruction techniques. Shape from Polarization (SfP) estimates surface normals using photos captured at different polarizer rotations. Fundamentally, the SfP model assumes that light is reflected either diffusely or specularly. However, this model is not valid for many real-world surfaces exhibiting a mixture of diffuse and specular properties. To address this challenge, previous methods have used a sequential solution: first, use an existing algorithm to separate the scene into diffuse and specular components, then apply the appropriate SfP model. In this paper, we propose a new method that jointly uses viewpoint and polarization data to holistically separate diffuse and specular components, recover refractive index, and ultimately recover 3D shape. By involving the physics of polarization in the separation process, we demonstrate competitive results with a benchmark method, while recovering additional information (e.g. refractive index). We introduce a method to recover the shape of a smooth dielectric object from polarization images taken with a light source from different directions. We present two constraints on shading and polarization and use both in a single optimization scheme. This integration is motivated by the fact that photometric stereo and polarization-based methods have complementary abilities. The polarization-based method can give strong cues for the surface orientation and refractive index, which are independent of the light direction. However, it has ambiguities in selecting between two ambiguous choices of the surface orientation, in the relationship between refractive index and zenith angle (observing angle), and limited performance for surface points with small zenith angles, where the polarization effect is weak. In contrast, photometric stereo method with multiple light sources can disambiguate the surface orientation and give a strong relationship between the surface normals and light directions. However, it has limited performance for large zenith angles, refractive index estimation, and faces the ambiguity in case the light direction is unknown. Taking their advantages, our proposed method can recover the surface normals for both small and large zenith angles, the light directions, and the refractive indexes of the object. The proposed method is successfully evaluated by simulation and real-world experiments. 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.