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.
Shape-from-polarisation The degree to which light is linearly polarised and the orientation associated with maximum reflection are related to the two degrees of freedom of surface orientation. In theory, this polarisation information alone restricts the surface normal at each pixel to two possible directions. Both Atkinson and Hancock @cite_7 and Miyazaki al @cite_2 solve the problem of disambiguating these polarisation normals via propagation from the boundary under an assumption of global convexity. Huynh al @cite_23 also disambiguate polarisation normals with a global convexity assumption but estimate refractive index in addition. These works all used a diffuse polarisation model while Morel al @cite_20 use a specular polarisation model for met als. Recently, Taamazyan al @cite_3 introduced a mixed specular diffuse polarisation model. All of these methods estimate surface normals that must be integrated into a height map. Moreover, since they rely entirely on the weak shape cue provided by polarisation and do not enforce integrability, the results are extremely sensitive to noise.
@cite_7 @cite_3 @cite_23 @cite_2 @cite_20
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We propose a new application of « Shape from Polarization » method to reconstruct surface shapes of specular met allic objects. Studying the polarization state of the reflected light is very useful to get information on the surface normals. After reflection, an unpolarized light wave becomes partially linearly polarized. Such a wave, can be described by its three parameters: intensity, degree of polarization, and angle of polarization. By using the refractive index of the surface, a relationship between the degree of polarization and the reflection angle can be established. Unfortunately, the relation commonly used for dielectrics, cannot be applied since the refractive index of met allic surfaces is complex. To get a similar relation, we apply a usual approximation valid in the visible region. The Fresnel reflectance model can also provide a relationship between the angle of polarization and the incidence plane orientation. Thus, the reflection angle and the incidence plane orientation give the surface normals. The shape is finally computed by integrating the normals with a relaxation algorithm. Applications on met allic objects made by stamping and polishing are also described, and show the efficiency of our system to discriminate shape defects. Future works will consist in integrating the system into an automatic process of defects detection. In this paper, we address the problem of the simultaneous recovery of the shape and refractive index of an object from a spectro-polarimetric image captured from a single view. Here, we focus on the diffuse polarisation process occuring at dielectric surfaces due to subsurface scattering and transmission from the object surface into the air. The diffuse polarisation of the reflection process is modelled by the Fresnel transmission theory. We present a method for estimating the azimuth angle of surface normals from the spectral variation of the phase of polarisation. Moreover, we estimate the zenith angle of surface normals and index of refraction simultaneously in a well-posed optimisation framework. We achieve well-posedness by introducing two additional constraints to the problem, including the surface integrability and the material dispersion equation. This yields an iterative solution which is computationally efficient due to the use of closed-form solutions for both the zenith angle and the refractive index in each iteration. To demonstrate the effectiveness of our approach, we show results of shape recovery and surface rendering for both real-world and synthetic imagery. 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. 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.