A differential approach to shape from polarization

© 2017. The copyright of this document resides with its authors. State-of-the-art formulations of the Shape from Polarisation problem consist of several steps based on merging physical principles that prevent this problem being described by a single mathematical framework. In addition, specular and diffuse reflections need to be separately considered, making the three-dimensional shape reconstruction not easily applicable to heterogeneous scenes consisting of different materials. In this work we derive a unified specular/diffuse reflection parametrisation of the Shape from Polarisation problem based on a linear partial differential equation capable of recovering the level-set of the surface. The inherent ambiguity of the Shape from Polarization problem becomes evident through the impossibility of reconstructing the whole surface with this differential approach. To overcome this limitation, we consider shading information elegantly embedding this new formulation into a two-lights calibrated photometric stereo approach. Thus we derive an albedo independent and well-posed differential model based on a system of hyperbolic PDEs capable of reconstructing the shape with no ambiguity. We validate the geometrical properties of the new differential model for the Shape from Polarisation problem using synthetic and real data by computing the isocontours of the shape under observation. Lastly, we show the suitability of this new model to elegantly fit into a variational solver that is able to provide 3D shape reconstructions from synthetic and real data

Linear Differential Constraints for Photo-polarimetric Height Estimation

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.Comment: To appear at International Conference on Computer Vision (ICCV), Venice, Italy, October 22-29, 201

Modified effective-range theory for low energy e-N2 scattering

We analyze the low-energy e-N2 collisions within the framework of the Modified-Effective Range Theory (MERT) for the long-range potentials, developed by O'Malley, Spruch and Rosenberg [Journal of Math. Phys. 2, 491 (1961)]. In comparison to the traditional MERT we do not expand the total cross-section in the series of the incident momentum \hbar k, but instead we apply the exact analytical solutions of the Schroedinger equation for the long-range polarization potential, as proposed in the original formulation of O'Malley et al. This extends the applicability of MERT up to few eV regime, as we confirm using some simplified model potential of the electron-molecule interaction. The parameters of the effective-range expansion (i.e. the scattering length and the effective range) are determined from experimental, integral elastic cross sections in the 0.1 - 1.0 eV energy range by fitting procedure. Surprisingly, our treatment predicts a shape resonance that appears slightly higher than experimentally well known resonance in the total cross section. Agreement with the experimentally observed shape-resonance can be improved by assuming the position of the resonance in a given partial wave. Influence of the quadrupole potential on resonances is also discussed: we show that it can be disregarded for N2. In conclusion, the modified-effective range formalism treating the long-range part of the potential in an exact way, reproduces well both the very low-energy behavior of the integral cross section as well as the presence of resonances in the few eV range.Comment: 9 pages, LaTex, 4 eps figures, EPJ style; extended and upgraded version of arXiv:0708.2991, now considering only e-N2 scatterin

Elastic scattering of low-energy electrons by benzene

We present elastic cross sections obtained from ab initio calculations for low-energy electron scattering by benzene, C6H6. The calculations employed the Schwinger multichannel method as implemented for parallel computers within both the static-exchange and static-exchange-polarization approximations. We compare our results with other theoretical calculations and with available experimental data. In general, agreement is good

Mueller matrix polarimetry of plasmon resonant silver nano-rods: biomedical prospects

Fundamental understanding of the light-matter interaction in the context of nano-particles is immensely bene- fited by the study of geometry dependent tunable Localized Surface Plasmon Resonance (LSPR) and has been demonstrated to have potential applications in various areas of science. The polarization characteristics of LSPR in addition to spectroscopic tuning can be suitably exploited in such systems as contrast enhancement mech- anisms and control parameters. Such polarization characteristics like diattenuation and retardance have been studied here using a novel combination of Muller-matrix polarimetry with the T-matrix matrix approach for silver nano-rods to show unprecedented control and sensitivity to local refractive index variations. The study carried out over various aspect ratios for a constant equal volume sphere radius shows the presence of longitu- dinal (dipolar and quadrupolar) and transverse (dipolar) resonances; arising due to differential contribution of polarizabilities in two directions. The overlap regions of these resonances and the resonances themselves exhibit enhanced retardance and diattenuation respectively. The spectral and amplitude tunability of these polarimetric parameters through the aspect ratios to span from the minimum to maximum ([0, 1] in the case of diattenuation and [0, {\pi}] in the case of retardance) presents a novel result that could be used to tailor systems for study of biological media. On the other hand, the high sensitivity of diattenuation dip (caused by equal contribution of polarizabilities) could be possibly used for medium characterization and bio-sensing or bio-imaging studies.Comment: 8 pages, 6 figures, Proceedings of the Saratov Fall Meeting, 201