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.
When unpolarized light is reflected from a smooth dielectric surface, it becomes partially polarized. This is due to the orientation of dipoles induced in the reflecting medium and applies to both specular and diffuse reflection. This paper is concerned with exploiting polarization by surface reflection, using images of smooth dielectric objects, to recover surface normals and, hence, height. This paper presents the underlying physics of polarization by reflection, starting with the Fresnel equations. These equations are used to interpret images taken with a linear polarizer and digital camera, revealing the shape of the objects. Experimental results are presented that illustrate that the technique is accurate near object limbs, as the theory predicts, with less precise, but still useful, results elsewhere. A detailed analysis of the accuracy of the technique for a variety of materials is presented. A method for estimating refractive indices using a laser and linear polarizer is also given. 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). In this paper, we propose an approach to the problem of simultaneous shape and refractive index recovery from multispectral polarisation imagery captured from a single viewpoint. The focus of this paper is on dielectric surfaces which diffusely polarise light transmitted from the dielectric body into the air. The diffuse polarisation of the reflection process is modelled using a Transmitted Radiance Sinusoid curve and the Fresnel transmission theory. We provide a method of estimating the azimuth angle of surface normals from the spectral variation of the phase of polarisation. Moreover, to render the problem of simultaneous estimation of surface orientation and index of refraction well-posed, we enforce a generative model on the material dispersion equations for the index of refraction. This generative model, together with the Fresnel transmission ratio, permit the recovery of the index of refraction and the zenith angle simultaneously. We show results on shape recovery and rendering for real world and synthetic imagery. This paper presents a method to estimate geometrical, photometrical, and environmental information of a single-viewed object in one integrated framework under fixed viewing position and fixed illumination direction. These three types of information are important to render a photorealistic image of a real object. Photometrical information represents the texture and the surface roughness of an object, while geometrical and environmental information represent the 3D shape of an object and the illumination distribution, respectively. The proposed method estimates the 3D shape by computing the surface normal from polarization data, calculates the texture of the object from the diffuse only reflection component, determines the illumination directions from the position of the brightest intensity in the specular reflection component, and finally computes the surface roughness of the object by using the estimated illumination distribution. 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.