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.
Polarisation with additional cues Rahmann and Canterakis @cite_11 combined a specular polarisation model with stereo cues. Similarly, Atkinson and Hancock @cite_14 used polarisation normals to segment an object into patches, simplifying stereo matching. Stereo polarisation cues have also been used for transparent surface modelling @cite_15 . Huynh al @cite_10 extended their earlier work to use multispectral measurements to estimate both shape and refractive index. Drbohlav and Sara @cite_22 showed how the Bas-relief ambiguity @cite_9 in uncalibrated photometric stereo could be resolved using polarisation. However, this approach requires a polarised light source. Recently, Kadambi al @cite_26 proposed an interesting approach in which a single polarisation image is combined with a depth map obtained by an RGBD camera. The depth map is used to disambiguate the normals and provide a base surface for integration.
@cite_14 @cite_26 @cite_22 @cite_9 @cite_15 @cite_10 @cite_11
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We present a novel process for acquiring detailed facial geometry with high resolution diffuse and specular photometric information from multiple viewpoints using polarized spherical gradient illumination. Key to our method is a new pair of linearly polarized lighting patterns which enables multiview diffuse-specular separation under a given spherical illumination condition from just two photographs. The patterns -- one following lines of latitude and one following lines of longitude -- allow the use of fixed linear polarizers in front of the cameras, enabling more efficient acquisition of diffuse and specular albedo and normal maps from multiple viewpoints. In a second step, we employ these albedo and normal maps as input to a novel multi-resolution adaptive domain message passing stereo reconstruction algorithm to create high resolution facial geometry. To do this, we formulate the stereo reconstruction from multiple cameras in a commonly parameterized domain for multiview reconstruction. We show competitive results consisting of high-resolution facial geometry with relightable reflectance maps using five DSLR cameras. Our technique scales well for multiview acquisition without requiring specialized camera systems for sensing multiple polarization states. 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. 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 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.