Green's function solution to subsurface light transport for BRDF computation

Matrix Green's function solution of closed-form singularity for functionally graded and transversely isotropic materials under circular ring force vector

Surface reflectance of real-world materials is now widely represented by the bidirectional reflectance distribution function (BRDF) and also by spatially varying representations such as SVBRDF and the bidirectional texture function (BTF). The raw surface reflectance measurements are typically compressed or fitted by analytical models, that always introduce a certain loss of accuracy. For its evaluation we need a distance function between a reference surface reflectance and its approximate version. Although some of the past techniques tried to reflect the perceptual sensitivity of human vision, they have neither optimized illumination and viewing conditions nor surface shape. In this paper, we suggest a new image-based methodology for comparing different anisotropic BRDFs. We use optimization techniques to generate a novel surface which has extensive coverage of incoming and outgoing light directions, while preserving its features and frequencies that are important for material appearance judgments. A single rendered image of such a surface along with simultaneously optimized lighting and viewing directions leads to the computation of a meaningful BRDF difference, by means of standard image difference predictors. A psychophysical experiments revealed that our surface provides richer information on material properties than the standard surfaces often used in computer graphics, e.g., sphere or blob.

Green's function solution and displacement potentials for Transformed Transversely Isotropic materials

A computationally efficient model for fracture propagation and fluid flow in naturally fractured reservoirs

Cosine lobes for interactive direct lighting in dynamic scenes

A laser range imaging system based on the triangulation method was designed and implemented for online high-resolution thickness calculation of poultry fillets. A laser pattern was projected onto the surface of the chicken fillet for calculation of the thickness of the meat. Because chicken fillets are relatively loosely-structured material, a laser light easily penetrates the meat, and scattering occurs both at and under the surface. When laser light is scattered under the surface it is reflected back and further blurs the laser line sharpness. To accurately calculate the thickness of the object, the light transportation has to be considered. In the system, the Bidirectional Reflectance Distribution Function (BSSRDF) was used to model the light transportation and the light pattern reflected into the cameras. BSSRDF gives the reflectance of a target as a function of illumination geometry and viewing geometry. Based on this function, an empirical method has been developed and it has been proven that this method can be used to accurately calculate the thickness of the object from a scattered laser profile. The laser range system is designed as a sub-system that complements the X-ray bone inspection system for non-invasive detection of hazardous materials in boneless poultry meat with irregular thickness.

Green's function solution of temperature field for flow in porous passages

In this study, we introduce a measurement method for the bidirectional reflectance distribution function (BRDF) for curved surfaces. Nearly all BRDF measurements assume that the target surface is planar. This is because if the object is non-planar, the reflection angle changes from position to position, making accurate measurement impossible. However, most real objects are curved. We have overcome this problem by applying the paraboloid reflection principle. If the curved target surface is a paraboloid, the light focused on its focal point is reflected as parallel light, as in a parabolic antenna. The BRDF can be measured as the deviation angle from this parallel light direction. Here, we demonstrate that this can significantly improve the BRDF measurement accuracy for curved surfaces.

Several ultrasound-based techniques for the estimation of soft tissue elasticity are currently being investigated. Most of them study the medium response to dynamic excitations. Such responses are usually modeled in a purely elastic medium using a Green's function solution of the motion equation. However, elasticity by itself is not necessarily a discriminant parameter for malignancy diagnosis. Modeling viscous properties of tissues could also be of great interest for tumor characterization. We report in this paper an explicit derivation of the Green's function in a viscous and elastic medium taking into account shear, bulk, and coupling waves. From this theoretical calculation, 3D simulations of mechanical waves in viscoelastic soft tissues are presented. The relevance of the viscoelastic Green's function is validated by comparing simulations with experimental data. The experiments were conducted using the supersonic shear imaging (SSI) technique which dynamically and remotely excites tissues using acoustic radiation force. We show that transient shear waves generated with SSI are modeled very precisely by the Green's function formalism. The combined influences of out-of-plane diffraction, beam shape, and shear viscosity on the shape of transient waves are carefully studied as they represent a major issue in ultrasound-based viscoelasticity imaging techniques.

Green's function solutions of the biaxial and uniaxial anisotropic layered-medium planar-structure is formulated in terms of Maxwell's equations. Diagonalized biaxial and uniaxial permittivity tensors in the coordinate system of interest are treated. The Green's function is found in the double Fourier transformed domain for three longitudinal-to-an-axis coupled electric-magnetic field sets applied to a simple layered structure. The approach is applicable to structures having discontinuities in two orthogonal planar directions such as patch radiators or resonators. Spectral Green's function is usable in method-of-moment calculations assisted by Galerkin's method.

We study light propagation in biological tissue using the radiative transport equation. The Green's function is the fundamental solution to the radiative transport equation from which all other solutions can be computed. We compute the Green's function as an expansion in plane-wave modes. We calculate these plane-wave modes numerically using the discrete-ordinate method. When scattering is sharply peaked, calculating the plane-wave modes for the transport equation is difficult. For that case we replace it with the Fokker-Planck equation since the latter gives a good approximation to the transport equation and requires less work to solve. We calculate the plane-wave modes for the Fokker-Planck equation numerically using a finite-difference approximation. The method of computing the Green's function for it is the same as for the transport equation. We demonstrate the use of the Green's function for the transport and Fokker-Planck equations by computing the point-spread function in a half-space composed of a uniform scattering and absorbing medium.

In this paper, we propose a method for measuring the reflectance of anisotropic materials using a simple apparatus consisting of two handheld cameras, a small LED light source, a turning table and a chessboard with markers. The system is configured to obtain the different incoming and outgoing light directions, and the brightness of pixels on the surface of the material. The anisotropic Ward BRDF (Bidirectional Reflectance Distribution Function) model is used to approximate the reflectance, and the model parameters are estimated from the incoming and outgoing angles and the brightness of pixels by using a non-linear optimization method. The initial values of the anisotropic direction are given based on the peak specular lobe on the surface, and the best-fitted one is chosen for the anisotropic direction. The optimized parameters show the well-fitted results between the observed brightness and the BRDF model for each RGB channel. It was confirmed that our system was able to measure the reflectance of different isotropic and anisotropic materials.

The bidirectional reflectance distribution function (BRDF) that describes an angle-resolved distribution of surface reflectance is available for characterizing surface properties of a material. A one-shot BRDF imaging system can capture an in-plane color mapping of light direction extracted from a surface BRDF distribution. A surface roughness identification method is then proposed here using the imaging system. A difference between surface properties of a matt paper and a glossy paper is experimentally shown to be detected using the method. A surface reconstruction method of an axisymmetric micro-object using the imaging system is also proposed here. The imaging system experimentally shows that it can reconstruct an axisymmetric aluminium cone surface with a height of 37 μm.

Analytic solutions for 2-D incompressible Stokes' flow with lateral variations in viscosity have been developed with a Green's function method and matrix propagator techniques. The analytic solutions are developed based on the observation that lateral variations in viscosity only result in mode coupling between viscosity and buoyancy in the horizontal dimension and not in the vertical dimension. The Green's function solution for flows with a viscosity that varies laterally with an exponential function indicates that, if the lateral variation in viscosity is within one order of magnitude, at very long wavelengths (for example degree 2) the mode coupling between viscosity and buoyancy does not greatly influence the geoid deduced from models ignoring the lateral variations in viscosity. The relatively short-wavelength geoid (degree 4 and higher modes), however, is seriously contaminated by mode coupling. The solutions for sharp lateral variations in viscosity calculated with propagator matrix techniques show that the topography varies rapidly across the viscosity boundaries.

A rigorous analysis of surface acoustic wave tags for wireless identification (ID) systems is developed based on Green's function technique and method of moments. The SAW ID-tags can be fabricated using arbitrary finite reflector structures placed in multiple tracks and channels. From the Green's function solutions, the P matrix parameters for the reflector bits and coupling transducer are deduced. These P matrices are cascaded and interconnected using network analysis to account for the resulting quasi-2D structure. To provide more physical insights into the scattering mechanism, the cascaded network is described in terms of the more illuminating global reflection and transmission coefficients. Simulation of prototype SAW tag configuration is carried out. Response in time domain is presented to show the spurious signals due to multiple reflections.