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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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. 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). This paper presents a novel method for 3D surface reconstruction that uses polarization and shading information from two views. The method relies on the polarization data acquired using a standard digital camera and a linear polarizer. Fresnel theory is used to process the raw images and to obtain initial estimates of surface normals, assuming that the reflection type is diffuse. Based on this idea, the paper presents two novel contributions to the problem of surface reconstruction. The first is a technique to enhance the surface normal estimates by incorporating shading information into the method. This is done using robust statistics to estimate how the measured pixel brightnesses depend on the surface orientation. This gives an estimate of the object material reflectance function, which is used to refine the estimates of the surface normals. The second contribution is to use the refined estimates to establish correspondence between two views of an object. To do this, surface patches are extracted from each view, which are then aligned by minimising an energy functional based on the surface normal estimates and local topographic properties. The optimum alignment parameters for different patch pairs are then used to establish stereo correspondence. This process results in an unambiguous field of surface normals, which can be integrated to recover the surface depth. Our technique is most suited to smooth nonmet allic surfaces. It complements existing stereo algorithms since it does not require salient surface features to obtain correspondences. An extensive set of experiments, yielding reconstructed objects and reflectance functions, are presented and compared to ground truth.