“…To remedy the ill-posedness nature of the problem, Miyazaki et al  has assumed that the histogram of zenith angles for a given object was similar to that for a sphere. He has used this property to recover a mapping from the degree of polarisation to the zenith angle.…”
“…Moreover, the mapping is not necessarily consistent across different material refractive indices. The related work in  and  employed the degree of polarisation in the visible and far-infrared regions to resolve ambiguities in determining the surface orientation of transparent objects. The main drawback of the method in  is the need for an omni-directional diffuse illumination source, which limits its applicability in real-world settings.…”
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.
“…This is not exclusive to our method but rather common across other reflectance parameter estimation approaches [13,31]. Specularity removal is often used to decompose the image radiance into specular and diffuse reflection.…”
In this paper, we present a method to recover the parameters governing the reflection of light from a surface making use of a single hyperspectral image. To do this, we view the image radiance as a combination of specular and diffuse reflection components and present a cost functional which can be used for purposes of iterative least squares optimisation. This optimisation process is quite general in nature and can be applied to a number of reflectance models widely used in the computer vision and graphics communities. We elaborate on the use of these models in our optimisation process and provide a variant of the Beckmann-Kirchhoff model which incorporates the Fresnel reflection term. We show results on synthetic images and illustrate how the recovered photometric parameters can be employed for skin recognition in real world imagery, where our estimated albedo yields a classification rate of 95.09 ± 4.26% as compared to an alternative, whose classification rate is of 90.94 ± 6.12%. We also show quantitative results on the estimation of the index of refraction, where our method delivers an average per-pixel angular error of 0.15 degrees. This is a considerable improvement with respect to an alternative, which yields an error of 9.9 degrees.
Abstract. This paper presents a combinatorial (decision tree induction) technique for transparent surface modeling from polarization images. This technique simultaneously uses the object's symmetry, brewster angle, and degree of polarization to select accurate reference points. The reference points contain information about surface's normals position and direction at near occluding boundary. We reconstruct rotationally symmetric objects by rotating these reference points.
“…Miyazaki et al 12 estimated the surface normal of a transparent object by analyzing the polarization state of the thermal radiation from the object. Miyazaki et al 13 attempted to estimate the surface normal of a diffuse object from a single view. Miyazaki et al 14 used a geometrical invariant to match the corresponding points from two views to estimate the surface normal of a transparent object.…”
Abstract. Polarization is a phenomenon that cannot be observed by the human eye, but it provides rich information regarding scenes. The proposed method estimates the surface normal of black specular objects through polarization analysis of reflected light. A unique surface normal cannot be determined from a polarization image observed from a single viewpoint; thus, we observe the object from multiple viewpoints. To analyze the polarization state of the reflected light at the corresponding points when observed from multiple viewpoints, the abstract shape is predetermined using a space carving technique. Unlike a conventional photometric stereo or multiview stereo, which cannot estimate the shape of a black specular object, the proposed method estimates the surface normal and three-dimensional coordinates of black specular objects via polarization analysis and space carving.
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