Shape and Refractive Index from Polarisation
In this chapter, 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 occurring at dielectric s
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Shape and Refractive Index from Polarisation
We now discuss the recovery of the surface normals and the refractive index from spectro-polarimetric images captured from a single viewpoint. Shape and material properties such as refractive index are usually coexisting factors that influence the appearance of an object to an observer and the polarisation properties of the emitted radiation. In an early work (Torrance et al. 1966) the authors measured the specular reflectance distribution of rough surfaces for different polarisation orientations. The reflectance model attributes polarisation to specular reflection from a collection of small, randomly disposed, mirror-like facets that constitute the surface area. The model includes a specular reflection component based on the Fresnel reflection theory and a micro-facet distribution function. Other reflectance models such as the Torrance–Sparrow model (Torrance and Sparrow 1967) and the Wolff model (Wolff 1994) are motivated by the Fresnel reflection theory. As a result, these reflectance models consider the reflected light as a combination of polarisation components parallel and perpendicular to the plane of reflection, and are applicable to polarised light sources. In these models, the material properties and the geometry of the reflection process are expressed in a single equation with multiple degrees of freedom. As a result, the simultaneous recovery of the photometric and shape parameters becomes an under-constrained problem. In this chapter, we exploit the combination of the Fresnel reflection theory, material dispersion equations and the surface integrability constraint to estimate the shape and refractive index simultaneously. We draw constraints from the latter two to render the recovery problem well-posed. These two constraints reduce the number of parameters in the spectral dimension to the number of dispersion coefficients. As a result, the formulation permits the use of an iterative procedure to find an approximately optimal solution. Further, the iterative optimisation approach is computationally efficient due to the use of closed-form solutions for the recovery of the zenith angle of surface normals and the refractive index. The techniques discussed here are applicable to convex and continuously twicedifferentiable surfaces with material refractive index following a dispersion equation. Here, we focus on dielectric surfaces that undergo diffuse polarisation due to subsurface scattering and transmission from the object surface into the air. The difA. Robles-Kelly, C.P. Huynh, Imaging Spectroscopy for Scene Analysis, Advances in Computer Vision and Pattern Recognition, DOI 10.1007/978-1-4471-4652-0_11, © Springer-Verlag London 2013
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Shape and Refractive Index from Polarisation
fuse polarisation of the reflection process is modelled by the Fresnel reflection theory and Snell’s law. We depart from the phase angle and the maximal and minimal radiance recovered from the input polarimetric imagery as described in Sect. 10.1.2 to present, in Sect.
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