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.
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. 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. Photometric stereo with uncalibrated lights determines surface orientations ambiguously up to any regular transformation. If the surface reflectance model is separable with respect to the illumination and viewing directions, its inherent symmetries enable to design two previously unrecognized constraints on normals that reduce this ambiguity. The two constraints represent projections of normals onto planes perpendicular to the viewing and illumination directions, respectively. We identify the classes of transformations that leave each constraint invariant. We construct the constraints using polarization measurement under the assumption of separable reflectance model for smooth dielectrics. We verify that applying the first constraint together with the integrability constraint results in bas-relief ambiguity, while application of the second constraint on integrable normals reduces the ambiguity to convex concave ambiguity. Importantly, the latter result is also obtained when the first and second constraints alone are combined.  We propose a method for measuring surface shapes of transparent objects by using a polarizing filter. Generally, the light reflected from an object is partially polarized. The degree of polarization depends upon the incident angle, which, in turn, depends upon the surface normal. Therefore, we can obtain surface normals of objects by observing the degree of polarization at each surface point. Unfortunately, the correspondence between the degree of polarization and the surface normal is not one to one. Hence, to obtain the correct surface normal, we have to solve the ambiguity problem. In this paper, we introduce a method to solve the ambiguity by comparing the polarization data in two objects, i.e., normal position and tilted with small angle position. We also discuss the geometrical features of the object surface and propose a method for matching two sets of polarization data at identical points on the object surface. 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. Traditional intensity imaging does not offer a general approach for the perception of textureless and specular reflecting surfaces. Intensity based methods for shape reconstruction of specular surfaces rely on virtual (i.e. mirrored) features moving over the surface under viewer motion. We present a novel method based on polarization imaging for shape recovery of specular surfaces. This method overcomes the limitations of the intensity based approach because no virtual features are required. It recovers whole surface patches and not only single curves on the surface. The presented solution is general as it is independent of the illumination. The polarization image encodes the projection of the surface normals onto the image and therefore provides constraints on the surface geometry. Taking polarization images from multiple views produces enough constraints to infer the complete surface shape. The reconstruction problem is solved by an optimization scheme where the surface geometry is modelled by a set of hierarchical basis functions. The optimization algorithm proves to be well converging, accurate and noise resistant. The work is substantiated by experiments on synthetic and real data.