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Sub‐surface scattering is always an important feature in translucent material rendering. When light travels through optically thick media, its transport within the medium can be approximated using diffusion theory, and is appropriately described by the bidirectional scattering‐surface reflectance distribution function (BSSRDF). BSSRDF methods rely on assumptions about object geometry and light distribution in the medium, which limits their applicability to general participating media problems. However, despite the high computational cost of path tracing, BSSRDF methods are often favoured due to their suitability for real‐time applications. We review these methods and discuss the most recent breakthroughs in this field. We begin by summarizing various BSSRDF models and then implement most of them in a 2D searchlight problem to demonstrate their differences. We focus on acceleration methods using BSSRDF, which we categorize into two primary groups: pre‐computation and texture methods. Then we go through some related topics, including applications and advanced areas where BSSRDF is used, as well as problems that are sometimes important yet are ignored in sub‐surface scattering estimation. In the end of this survey, we point out remaining constraints and challenges, which may motivate future work to facilitate sub‐surface scattering. [ABSTRACT FROM AUTHOR]

We have developed a system that separates and measures the optical properties of skin that determine its visual quality, that is, the surface reflection, diffuse reflection, and subsurface scattering components of the skin. This system includes two polarization filters that separate light from the skin into a surface reflection component image and a diffuse reflection component image. Furthermore, by using a projector as a light source and irradiating the skin using a high‐frequency binary illumination pattern, the subsurface scattering component image alone can be separated and generated. Application of an algorithm that calculates the luminance value Y for each component image not only makes it possible to analyze each light signal from the skin quantitatively, but also enables understanding of how each light signal is related to the skin's overall appearance. Using the proposed system, we performed a survey of 154 Japanese women aged from their 20s to their 70s and analyzed age‐related changes in the optical properties of their skin. The results revealed the following. First, the luminance value Y of the surface reflection from the cheek and its standard deviation within the analysis area increase with age. Second, the Y value of diffuse reflection from the skin decreases with age. Third, the amount of light in the subsurface scattering components also decreases with age. The proposed system is expected to be suitable for a wide range of applications, including color science, and various studies of the appearance of human skin. [ABSTRACT FROM AUTHOR]

• Proposed a 3D measurement method for translucent media base on deep Bayesian inference results in both fringe enhancement and phase reliability evaluation without the ground truth. • Incorporated numerical and physical constraints into network training for mitigating phase-shifted errors and improving the phase quality of translucent media measurement. • Established a Bayesian inference mechanism for optimizing the fringe output and providing the uncertainty self-evaluation based on Monte Carlo (MC) sampling statistics. Traditional structured light technique faces challenges in measuring translucent media due to low fringe modulation and strong random noise caused by subsurface scattering, thereby significantly reducing phase quality. In addition, the difficulty in obtaining ground truth makes it hard to assess reliability even though obtaining measured results. Here, we proposed a 3D measurement method for translucent media base on deep Bayesian inference to achieve both fringe enhancement and phase uncertainty evaluation. Specifically, a deep network incorporated with quatuor-branch residual block is developed to significantly enhance the fringe modulation and signal-to-noise ratio (SNR) for accurate phase recovery. Subsequently, a Bayesian inference mechanism is established for probabilistic statistics, which allows for the optimization of fringe output and provides uncertainty self-evaluation based on Monte Carlo (MC) sampling. Furthermore, by incorporating both numerical and physical constraints into the supervised learning, the network can effectively mitigate phase-shifted errors in the final results. The proposed method shows high efficiency and flexibility since it requires no additional patterns or hardware setup. Experiments validate the feasibility of the proposed method. [ABSTRACT FROM AUTHOR]

Our visual experience of the world relies on the interaction of light with the different substances, surfaces, and objects in our environment. These optical interactions generate images that contain a conflated mixture of different scene variables, which our visual system must somehow disentangle to extract information about the shape and material properties of the world. Such problems have historically been considered to be ill-posed, but recent work suggests that there are complex patterns of covariation in light that co-specify the 3D shape and material properties of surfaces. This work provides new insights into how the visual system acquired the ability to solve problems that have historically been considered intractable. There has been recent progress on understanding how our visual systems appear to extract the shape and material properties of surfaces, which was formally intractable. Recent work has provided evidence that the visual system solves these problems by exploiting complex patterns of covariation that arise between different environmental sources. This work suggests that attempts to study individual sources of image structure in isolation make the problem computationally harder, which overestimates the ambiguity of natural images. This work focuses on understanding how the visual system generates our experience of the world based on information available, which includes both 'veridical' percepts and perceptual errors. [ABSTRACT FROM AUTHOR]

Rendering a translucent material involves integrating the product of the transmittance-weighted irradiance and the BSSRDF over the surface of it. In previous methods, this spatial integral was computed by creating a dense distribution of discrete points over the surface or by importance-sampling based on the BSSRDF. Both of these approaches necessitate specifying the number of samples, which affects both the quality and the computation time for rendering. An insufficient number of samples leads to noise and artifacts in the rendered image and an excessive number results in a prohibitively long rendering time. In this article, we propose an error estimation method for translucent materials in a many-light rendering framework. Our adaptive sampling can automatically determine the number of samples so that the estimated relative error of each pixel intensity is less than a user-specified threshold. We also propose an efficient method to generate the sampling points that make large contributions to the pixel intensity taking into account the BSSRDF. This enables us to use a simple uniform sampling, instead of costly importance sampling based on the BSSRDF. The experimental results show that our method can accurately estimate the error. In addition, in comparison with the previous methods, our sampling method achieves better estimation accuracy in equal-time. [ABSTRACT FROM AUTHOR]

Functionally defined objects for realistic scenes are offered. We describe physically based visualization of three-dimensional objects based on perturbation functions; i.e., the rendering of materials occurs with regard to the laws of physics. Physically based reflection models are needed to obtain photorealistic images. The surface roughness, microrelief, and gloss suggest how smooth or rough the surface of the material is. The diffraction effects are shown taking into account the roughness of the surface. Subsurface light transport is considered and modeled using bidirectional surface scattering. [ABSTRACT FROM AUTHOR]

Accurately perceiving object surface material is critical for scene understanding and robotic manipulation. However, it is ill-posed because the imaging process entangles material, lighting, and geometry in a complex way. Appearance-based methods cannot disentangle lighting and geometry variance and have difficulties in textureless regions. We propose a novel multimodal fusion method for surface material perception using the depth camera shooting structured laser dots. The captured active infrared image was decomposed into diffusive and dot modalities and their connection with different material optical properties (i.e. reflection and scattering) were revealed separately. The geometry modality, which helps to disentangle material properties from geometry variations, is derived from the rendering equation and calculated based on the depth image obtained from the structured light camera. Further, together with the texture feature learned from the gray modality, a multimodal learning method is proposed for material perception. Experiments on synthesized and captured datasets validate the orthogonality of learned features. The final fusion method achieves 92.5% material accuracy, superior to state-of-the-art appearance-based methods (78.4%). [ABSTRACT FROM AUTHOR]

Radiative transfer equations (RTEs) with different scattering parameters can lead to identical solution radiance fields. Similarity theory studies this effect by introducing a hierarchy of equivalence relations called "similarity relations". Unfortunately, given a set of scattering parameters, it remains unclear how to find altered ones satisfying these relations, significantly limiting the theory's practical value. This paper presents a complete exposition of similarity theory, which provides fundamental insights into the structure of the RTE's parameter space. To utilize the theory in its general high-order form, we introduce a new approach to solve for the altered parameters including the absorption and scattering coefficients as well as a fully tabulated phase function. We demonstrate the practical utility of our work using two applications: forward and inverse rendering of translucent media. Forward rendering is our main application, and we develop an algorithm exploiting similarity relations to offer "free" speedups for Monte Carlo rendering of optically dense and forward-scattering materials. For inverse rendering, we propose a proof-of-concept approach which warps the parameter space and greatly improves the efficiency of gradient descent algorithms. We believe similarity theory is important for simulating and acquiring volume-based appearance, and our approach has the potential to benefit a wide range of future applications in this area. Copyright © ACM.

• A new subsurface scattering method based on screen space and texture space is proposed. • A mucus texture is mapped to the soft tissues and an improved two-layer surface reflection model is proposed to render the mucus. [Display omitted] High fidelity display has a big impact on the user's sense of immersion in virtual surgery. To achieve a high degree of visual realism, we propose a new subsurface scattering method, which is based on screen-space and texture-space and an improved two-layer surface reflection model, for living soft tissue rendering. The method can be described as a two-step strategy. First, the subsurface scattering in the screen space is computed. The biggest difference from traditional methods is that the back light information stored in the irradiance map of the texture space and the diffusion profile in the dipole model are used to calculate the subsurface scattering distribution formed by the light from the back of the object, which can render more rich details. Second, considering that the living soft tissues are usually covered with a thin layer of mucus, a mucus texture is mapped to the soft tissues as the second layer texture and an improved two-layer surface reflection model is proposed to render the mucus. Moreover, to show the viscosity and smoothness of the mucus, the calculation of highlight component is used in our model, which further enhances the reality of living soft tissue. Experimental results show that our method outperforms the two traditional methods of subsurface scattering based on texture space and screen space, and the rendering time of the proposed two-layer surface reflection model is 2/3 of that of the traditional model. We conducted a survey on the fidelity of soft tissues rendered using different algorithms, and the professional surgeons (60%-85%) thought that the rendered soft tissue with our method is more consistent with the characteristics of the in vivo soft tissues under a real surgical scene. [ABSTRACT FROM AUTHOR]

Computer simulation of virtual surgery is characterized by the visual presentation of the incision on the surface of the surgical organ, which usually has the minimum visual range . Therefore, high realistic presentation of the incision model is required. In this paper, the feasibility of rendering a simulation and visual incision model is studied by generating new geometric figures and texture maps in real time. The cut wound texture for surface visualization is generated at runtime to improve real-time performance and an extended subsurface scattering method is proposed to allow local discoloration to occur naturally in the area around the incision. This method completes the generating of incision model to high realistic presentation of the incision in less than 150 milli seconds, which can increase the realistic rendering of virtual incision in real-time application. [ABSTRACT FROM AUTHOR]

The problem of extracting the three-dimensional (3D) shape and material properties of surfaces from images is considered to be inherently ill posed. It is thought that a priori knowledge about either 3D shape is needed to infer material properties, or knowledge about material properties are needed to derive 3D shape. Here, we show that there is information in images that cospecify both the material composition and 3D shape of light permeable (translucent) materials. Specifically, we show that the intensity gradients generated by subsurface scattering, the shape of self-occluding contours, and the distribution of specular reflections covary in systematic ways that are diagnostic of both the surface's 3D shape and its material properties. These sources of image covariation emerge from being causally linked to a common environmental source: 3D surface curvature. We show that these sources of covariation take the form of "photogeometric constraints," which link variations in intensity (photometric constraints) to the sign and direction of 3D surface curvature (geometric constraints). We experimentally demonstrate that this covariation generates emergent cues that the visual system exploits to derive the 3D shape and material properties of translucent surfaces and demonstrate the potency of these cues by constructing counterfeit images that evoke vivid percepts of 3D shape and translucency. The concepts of covariation and cospecification articulated herein suggest a principled conceptual path forward for identifying emergent cues that can be used to solve problems in vision that have historically been assumed to be ill posed. [ABSTRACT FROM AUTHOR]

Usually the highlights can be calculated with the specular term of the bidirectional reflectance distribution functions developed for glossy or matte materials. However, as for the translucent materials, complex appearance could be caused by the scattering of light inside the medium. An efficient highlight generation model is presented to simulate the highlight effects on smooth or rough surfaces or around the boundaries of objects made from translucent materials. The presented model is derived from the directional dipole model approximation of the diffusive part of the bidirectional scattering surface reflectance distribution function. Unlike the previous specular reflection models, the presented model builds a relationship between the highlights and the scattered lights inside the medium by considering the refracted ray of the incident point and the ray toward the emergent point, which could represent the variation in fluence due to the internal scattering at the surface. By integrating a rendering process with the directional dipole model, the resulting highlight effects term could be represented in a similar way by the specular term of a bidirectional reflectance distribution function model. The number and the strength of the generated highlight pixels were compared among typical highlight generation models. It is demonstrated that the presented model could generate highlight effects at the appropriate positions and enhance the perceptual translucency of specific edge areas greatly. [ABSTRACT FROM AUTHOR]

In order to solve the problem of high realistic rendering of human liver, a method based on the combination of surface reflection and subsurface scattering is presented. Firstly, the surface reflection lighting model uses ambient lighting, diffuse lighting, highlight lighting, normal maps and shadow maps to simulate the visual effect of surface lighting. The propagation and transmission of light in liver tissue are simulated by combining subsurface scattering and transmission. Also, two one-dimensional convolutions are used to present subsurface scattering and to reduce execution time and memory consumption, giving rise to a realistic rendering based on subsurface scattering model. Experimental results show that the proposed method can achieve high realistic rendering of liver and achieve a real time rendering frame rate of 90 frames per second． [ABSTRACT FROM AUTHOR]

Screen-space subsurface scattering is currently the most common approach to represent translucent materials in real-time rendering. However, most of the current approaches approximate the diffuse reflectance profile of translucent materials as a symmetric function, whereas the profile has an asymmetric shape in nature. To address this problem, we propose LinSSS, a numerical representation of heterogeneous subsurface scattering for real-time screen-space rendering. Although our representation is built upon a previous method, it makes two contributions. First, LinSSS formulates the diffuse reflectance profile as a linear combination of radially symmetric Gaussian functions. Nevertheless, it can also represent the spatial variation and the radial asymmetry of the profile. Second, since LinSSS is formulated using only the Gaussian functions, the convolution of the diffuse reflectance profile can be efficiently calculated in screen space. To further improve the efficiency, we deform the rendering equation obtained using LinSSS by factoring common convolution terms and approximate the convolution processes using a MIP map. Consequently, our method works as fast as the state-of-the-art method, while our method successfully represents the heterogeneity of scattering. [ABSTRACT FROM AUTHOR]

This article presents the results of a laboratory investigation to explain anomalously high soil moisture estimates observed in retrievals from SAR and scatterometer backscatter, affecting extensive areas of the world associated with arid climates. High-resolution C-band tomographic profiling was applied in experiments to understand the mechanisms underlying these anomalous retrievals. The imagery captured unique high-resolution profiles of the variations in the vertical backscattering patterns through a sandy soil with moisture change. The relative strengths of the surface and subsurface returns were dependent upon both soil moisture and soil structure, incidence-angle, and polarization. Copolarized returns could be dominated by both surface and subsurface returns at times, whereas crosspolarized returns were strongly associated with subsurface features. The work confirms suspicions that anomalous moisture estimates can arise from the presence of subsurface features. Diversity in polarization and incidence angle may provide sufficient diagnostics to flag and correct these erroneous estimates, allowing their incorporation into global soil moisture products. [ABSTRACT FROM AUTHOR]

Subsurface scattering involves the complicated behavior of light beneath the surfaces of translucent objects that includes scattering and absorption inside the object's volume. Physically accurate numerical representation of subsurface scattering requires a large number of parameters because of the complex nature of this phenomenon. The large amount of data restricts the use of the data on memory-limited devices such as video game consoles and mobile phones. To address this problem, this paper proposes an efficient data compression method for heterogeneous subsurface scattering. The key insight of this study is that heterogeneous materials often comprise a limited number of base materials, and the size of the subsurface scattering data can be significantly reduced by parameterizing only a few base materials. In the proposed compression method, we represent the scattering property of a base material using a function referred to as the base scattering profile. A small subset of the base materials is assigned to each surface position, and the local scattering property near the position is described using a linear combination of the base scattering profiles in the log scale. The proposed method reduces the data by a factor of approximately 30 compared to a state-of-the-art method, without significant loss of visual quality in the rendered graphics. In addition, the compressed data can also be used as bidirectional scattering surface reflectance distribution functions (BSSRDF) without incurring much computational overhead. These practical aspects of the proposed method also facilitate the use of higher-resolution BSSRDFs in devices with large memory capacity. [ABSTRACT FROM AUTHOR]

This paper presents a material classification method using an off-the-shelf Time-of-Flight (ToF) camera. The proposed method is built upon a key observation that the depth measurement by a ToF camera is distorted for objects with certain materials, especially with translucent materials. We show that this distortion is due to the variation of time domain impulse responses across materials and also due to the measurement mechanism of the ToF cameras. Specifically, we reveal that the amount of distortion varies according to the modulation frequency of the ToF camera, the object material, and the distance between the camera and object. Our method uses the depth distortion of ToF measurements as a feature for classification and achieves material classification of a scene. Effectiveness of the proposed method is demonstrated by numerical evaluations and real-world experiments, showing its capability of material classification, even for visually indistinguishable objects. [ABSTRACT FROM AUTHOR]

Laser altimetry offers the potential to monitor ice-sheet elevation changes with millimeter accuracy. While previous missions have used infrared lasers to make these measurements, NASA's upcoming ICESat (Ice, Cloud, and land Elevation Satellite)-2 mission will use a green laser. Because ice absorbs green light very weakly, in the absence of light-absorbing impurities, green photons can scatter off many snow grains before returning to the surface, delaying the return pulse and leading to an apparent downward shift in the snow surface. In this paper, we explore the effects of snow-grain size and impurity content on these measurements, and investigate strategies that might help minimize the biases they introduce. We find that an uninformed choice of measurement parameters (a windowed mean including a large range of photons around the surface) can result in >0.45 m of apparent surface-height variation between large and small grain sizes. Other choices of measurement parameters, such as a windowed median, can reduce this uncertainty by a factor of two to three. In addition, measurements of surface reflectance at green and infrared wavelengths, and interpretation of return-pulse shapes may be used to estimate and correct for these biases. [ABSTRACT FROM AUTHOR]

Based on bidirectional reflectance distribution function (BRDF), we proposed a concept of bidirectional transmittance distribution function (BTDF). By using subsurface scattering theory, the single scattering and multiple scattering of light beams transmitted in the oil-emulsion seawater were discussed. Then a high-efficiency model for BRDF of oil-emulsion seawater was built. Finally, the comparison of simulation results between our model and Monte Carlo method were also discussed. [ABSTRACT FROM AUTHOR]

Rendering translucent materials with physically based Monte Carlo methods tends to be computationally expensive due to the long chains of volumetric scattering interactions. In the case of strongly forward scattering materials, the problem gets compounded since each scattering interaction becomes highly anisotropic and near-specular. Various well-known approaches try to avoid the resulting sampling problem through analytical approximations based on diffusion theory. Although these methods are computationally efficient, their assumption of diffusive, isotropic scattering can lead to considerable errors when rendering forward scattering materials, even in the optically dense limit. In this paper, we present an analytical subsurface scattering model, derived with the explicit assumption of strong forward scattering. Our model is not based on diffusion theory, but follows from a connection that we identified between the functional integral formulation of radiative transport and the partition function of a worm-like chain in polymer physics. Our resulting model does not need a separate Monte Carlo solution for unscattered or single-scattered contributions, nor does it require ad-hoc regularization procedures. It has a single singularity by design, corresponding to the initial unscattered propagation, which can be accounted for by the extensive analytical importance sampling scheme that we provide. Our model captures the full behaviour of forward scattering media, ranging from unscattered straight-line propagation to the fully diffusive limit. Moreover, we derive a novel forward scattering BRDF as limiting case of our subsurface scattering model, which can be used in a level of detail hierarchy. We show how our model can be integrated in existing Monte Carlo rendering algorithms, and make comparisons to previous approaches. [ABSTRACT FROM AUTHOR]