Translucency is an important aspect of material appearance. To some extent, humans are able to estimate translucency in a consistent way across different shapes and lighting conditions, i.e., to exhibit translucency constancy. However, Fleming and Bülthoff (2005) have shown that that there can be large failures of constancy, with lighting direction playing an important role. In this paper, we explore the interaction of shape, illumination, and degree of translucency constancy more deeply by including in our analysis the variations in translucent appearance that are induced by the shape of the scattering phase function. This is an aspect of translucency that has been largely neglected. We used appearance matching to measure how perceived translucency depends on both lighting and phase function. The stimuli were rendered scenes that contained a figurine and the lighting direction was represented by spherical harmonic basis function. Observers adjusted the density of a figurine under one lighting condition to match the material property of a target figurine under another lighting condition. Across the trials, we varied both the lighting direction and the phase function of the target. The phase functions were sampled from a 2D space proposed by Gkioulekas et al. (2013) to span an important range of translucent appearance. We find the degree of translucency constancy depends strongly on the phase function's location in the same 2D space, suggesting that the space captures useful information about different types of translucency. We also find that the geometry of an object is important. We compare the case of a torus, which has a simple smooth shape, with that of the figurine, which has more complex geometric features. The complex shape shows a greater range of apparent translucencies and a higher degree of constancy failure. In summary, humans show significant failures of translucency constancy across changes in lighting direction, but the effect depends both on the shape complexity and the translucency phase function.
Translucent materials are ubiquitous, and simulating their appearance requires accurate physical parameters. However, physicallyaccurate parameters for scattering materials are difficult to acquire. We introduce an optimization framework for measuring bulk scattering properties of homogeneous materials (phase function, scattering coefficient, and absorption coefficient) that is more accurate, and more applicable to a broad range of materials. The optimization combines stochastic gradient descent with Monte Carlo rendering and a material dictionary to invert the radiative transfer equation. It offers several advantages: (1) it does not require isolating singlescattering events; (2) it allows measuring solids and liquids that are hard to dilute; (3) it returns parameters in physically-meaningful units; and (4) it does not restrict the shape of the phase function using Henyey-Greenstein or any other low-parameter model. We evaluate our approach by creating an acquisition setup that collects images of a material slab under narrow-beam RGB illumination. We validate results by measuring prescribed nano-dispersions and showing that recovered parameters match those predicted by Lorenz-Mie theory. We also provide a table of RGB scattering parameters for some common liquids and solids, which are validated by simulating color images in novel geometric configurations that match the corresponding photographs with less than 5% error.
Physics-based differentiable rendering is the task of estimating the derivatives of radiometric measures with respect to scene parameters. The ability to compute these derivatives is necessary for enabling gradient-based optimization in a diverse array of applications: from solving analysis-by-synthesis problems to training machine learning pipelines incorporating forward rendering processes. Unfortunately, physics-based differentiable rendering remains challenging, due to the complex and typically nonlinear relation between pixel intensities and scene parameters. We introduce a differential theory of radiative transfer, which shows how individual components of the radiative transfer equation (RTE) can be differentiated with respect to arbitrary differentiable changes of a scene. Our theory encompasses the same generality as the standard RTE, allowing differentiation while accurately handling a large range of light transport phenomena such as volumetric absorption and scattering, anisotropic phase functions, and heterogeneity. To numerically estimate the derivatives given by our theory, we introduce an unbiased Monte Carlo estimator supporting arbitrary surface and volumetric configurations. Our technique differentiates path contributions symbolically and uses additional boundary integrals to capture geometric discontinuities such as visibility changes. We validate our method by comparing our derivative estimations to those generated using the finite-difference method. Furthermore, we use a few synthetic examples inspired by real-world applications in inverse rendering, non-line-of-sight (NLOS) and biomedical imaging, and design, to demonstrate the practical usefulness of our technique.
Multiple scattering contributes critically to the characteristic translucent appearance of food, liquids, skin, and crystals; but little is known about how it is perceived by human observers. This paper explores the perception of translucency by studying the image effects of variations in one factor of multiple scattering: the phase function. We consider an expanded space of phase functions created by linear combinations of Henyey-Greenstein and von Mises-Fisher lobes, and we study this physical parameter space using computational data analysis and psychophysics.Our study identifies a two-dimensional embedding of the physical scattering parameters in a perceptually-meaningful appearance space. Through our analysis of this space, we find uniform parameterizations of its two axes by analytical expressions of moments of the phase function, and provide an intuitive characterization of the visual effects that can be achieved at different parts of it. We show that our expansion of the space of phase func- Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies show this notice on the first page or initial screen of a display along with the full citation. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, to republish, to post on servers, to redistribute to lists, or to use any component of this work in other works requires prior specific permission and/or a fee. Permissions may be requested from Publications Dept., ACM, Inc., 2 Penn Plaza, Suite 701, New York, NY 10121-0701 USA, fax +1 (212) 869-0481, or permissions@acm.org. © YYYY ACM 0730-0301/YYYY/13-ARTXXX $10.00 DOI 10.1145/XXXXXXX.YYYYYYY http://doi.acm.org/10.1145/XXXXXXX.YYYYYYY tions enlarges the range of achievable translucent appearance compared to traditional single-parameter phase function models. Our findings highlight the important role phase function can have in controlling translucent appearance, and provide tools for manipulating its effect in material design applications.
Speckle image Scattering Medium Coherent IlluminationMonte Carlo Rendering 0°0.0025°0.0075°g = 0 g = 0.9
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