Real-time subsurface scattering techniques are widely used in translucent material rendering. Among advanced methods that rely on the bidirectional scattering-surface reflectance distribution function (BSSRDF), screen space algorithms exhibit limited translucency, while existing large-distance methods are inefficient and yield poor illumination details. To address these limitations for better large-distance scattering, we develop a novel algorithm by extending the photon beam diffusion (PBD) model within the light view and screen space. Unlike surface irradiance in prior methods, we incorporate the refracted beam in the medium into real-time scattering estimation, presenting a new consideration for photon beam utilization. Concretely, we store all photon beam samples in light view textures and utilize an adaptive sampling pattern for beam sample selection in large filtering kernel sizes. This can reduce the sample count based on surface attributes. In screen space, virtual sources are derived from samples to estimate PBD contributions, with an approximation that preserves boundary conditions. To avoid possible overestimation, we implement correction factors that scale contributions, effectively aligning our results with path-tracing references. Through these reformulations, our efficient PBD generates results closest to references among existing methods. The experiments accurately represent better front-face illumination details and backlit translucency effects, while significantly accelerating performance compared to previous large-distance methods.

Abstract Monte Carlo rendering of translucent objects with heterogeneous scattering properties is often expensive both in terms of memory and computation. If the scattering properties are described by a 3D texture, memory consumption is high. If we do path tracing and use a high dynamic range lighting environment, the computational cost of the rendering can easily become significant. We propose a compact and efficient neural method for representing and rendering the appearance of heterogeneous translucent objects. Instead of assuming only surface variation of optical properties, our method represents the appearance of a full object taking its geometry and volumetric heterogeneities into account. This is similar to a neural radiance field, but our representation works for an arbitrary distant lighting environment. In a sense, we present a version of neural precomputed radiance transfer that captures relighting of heterogeneous translucent objects. We use a multi‐layer perceptron (MLP) with skip connections to represent the appearance of an object as a function of spatial position, direction of observation, and direction of incidence. The latter is considered a directional light incident across the entire non‐self‐shadowed part of the object. We demonstrate the ability of our method to compactly store highly complex materials while having high accuracy when comparing to reference images of the represented object in unseen lighting environments. As compared with path tracing of a heterogeneous light scattering volume behind a refractive interface, our method more easily enables importance sampling of the directions of incidence and can be integrated into existing rendering frameworks while achieving interactive frame rates.

Soil moisture retrievals from the Advanced Scatterometer (ASCAT) have so far relied on the assumption that soil backscatter increases monotonically with soil moisture content. However, under dry soil conditions, discontinuities in the soil profile caused by the presence of stones, rocks, or distinct soil layers may disturb this relation, causing backscatter to decrease with increasing soil wetness. As of yet, subsurface scattering is a poorly understood phenomenon and some of its manifestations on ASCAT soil moisture retrievals have in the past been wrongly attributed to topographic effects or changes in soil surface roughness and vegetation. Therefore, this study aims at mapping subsurface scattering effects on a global scale, explore their dependency on land surface characteristics, and describe the impacts on ASCAT soil moisture retrievals. The results obtained with one statistical and two physically based indicators show that the subsurface scattering is not only widespread in desert regions but also in more humid climates with a dry season. Along with the dryness of the soil, the presence of coarse fragments in the soil profile and sparse vegetation cover are important factors that favor its occurrence. The impact on ASCAT soil moisture retrievals is severe, making subsurface scattering the most significant source of unaccounted errors in the current version of the ASCAT soil moisture data as provided by the EUMETSAT Satellite Application Facility on Support to Operational Hydrology and Water Management. Users of the product are recommended to mask soil moisture data affected by subsurface scattering effects using the indicators and masks developed in this study.

In low-moisture regimes, strongly-reflecting bedrock underlying soil could provide a dominant return. This offers a novel opportunity to retrieve both the volumetric moisture fraction (mv ) and depth (d) of a soil layer using a differential phase. A radar wave traversing the overlying soil slows in response to moisture state; moisture dynamics are thus recorded as variations in travel time—captured back at a radar platform as changes in phase. The Phase Scaled Dielectric (PSD) model introduced here converts phase changes to those in soil dielectric as an intermediate step to estimating mv . Simulations utilizing a real soil moisture timeseries from a site in Sudan were used to demonstrate the linked behaviors of the soil and radar variables, and detail the PSD principle. A laboratory validation used soil with a wet top layer variable in depth 1–2 cm and drying from mv ∼ 0.2 m3m−3, overlying a gravel layer at a depth of 11 cm. The scheme retrieved = 1.49 ± 0.33 cm and a change Δmv = 0.191–0.021 ± 0.009 m3m−3. The PSD scheme outlined here promises a new avenue for the diagnostic measurement of soil parameters which is not currently available to radar remote sensing.

Backscatter measured by scatterometers and Synthetic Aperture Radars is sensitive to the dielectric properties of the soil and normally increases with increasing soil moisture content. However, when the soil is dry, the radar waves penetrate deeper into the soil, potentially sensing subsurface scatterers such as near-surface rocks and stones. In this paper we propose an exponential model to describe the impact of such subsurface scatterers on C-Band backscatter measurements acquired by the Advanced Scatterometer (ASCAT) on board of the METOP satellites. The model predicts an increase of the subsurface scattering contributions with decreasing soil wetness that may counteract the signal from the soil surface. This may cause anomalous backscatter signals that deteriorate soil moisture retrievals from ASCAT. We test whether this new model is able to explain ASCAT observations better than a bare soil backscatter model without a subsurface scattering term, using k-fold cross validation and the Bayesian Information Criterion for model selection. We find that arid landscapes with Leptosols and Arenosols represent ideal environmental conditions for the occurrence of subsurface scattering. Nonetheless, subsurface scattering may also become important in more humid environments during dry spells. We conclude that subsurface scattering is a widespread phenomenon that (i) needs to be accounted for in active microwave soil moisture retrievals and (ii) has a potential for soil mapping, particularly in arid and semi-arid environments.

ABSTRACTInvestigating the near‐surface structure of the Earth through geophysical methods is a crucial aspect in many areas of study in geotechnical engineering, environmental science and exploration. Among several geophysical methods, seismic‐based ones are widely used for characterizing near‐surface features that are distinguished by contrasts in elastic parameters. In this paper, we model 3D elastodynamic wave propagation and scattering using a method based on domain‐type integral representation with Born approximation. We calculate the scattered wavefield by considering the first‐order perturbations in density and Lamé parameter contrasts of scatterers. Contrasts in Lamé parameters can be useful for determining the material properties of subsurface structures in cases of weak contrasts in velocities accompanying considerable Lamé parameter variations. We examine the effects of each parameter contrast on a series of models involving a subsurface scatterer. We also compare the seismograms obtained from our method with those from a 3D finite‐difference wavefield modelling program, where we observe good agreement between the modelling results. Sensitivity of the wavefield to the perturbation in each model parameter is also examined by calculating and analysing the Fréchet derivatives. In general, the method discussed here can provide a solid foundation for prospective imaging studies involving density and Lamé parameters simultaneously.

Faults, fractures, karst caves, and other small-scale geological targets are critical for carbonate oil and gas exploration. However, seismic responses of these small-scale geological targets are low-energy diffractions and it is difficult for traditional method to image them with high resolution. To identify these targets, the diffraction separation is a key technology. Based on the difference of diffractions and reflections in both kinematic and dynamic properties, the singular value decomposition (SVD) method can separate diffractions and reflections effectively. However, how to select the appropriate singular value sequence for diffractions and reflections is a key issue in the application. Based on the analysis of the singular value spectrum characteristics, we propose a second-order difference spectrum strategy to improve the SVD method. The improved SVD method can separate the diffractions and reflections with minimal error. It is stable when seismic data contain Gaussian noise. Reverse time migration (RTM) method is used in the diffraction imaging because it can keep the true shape of subsurface scatterers when diffractions information is complete. Synthetic examples demonstrate the effectiveness of this method.

We report the results of inelastic differential scattering experiments and full-dimensional molecular dynamics trajectory simulations for 2.76 eV H atoms colliding at a surface of solid xenon. The interaction potential is based on an effective medium theory (EMT) fit to density functional theory (DFT) energies. The translational energy-loss distributions derived from experiment and theory are in excellent agreement. By analyzing trajectories, we find that only a minority of the scattering results from simple single-bounce dynamics. The majority comes from multibounce collisions including subsurface scattering where the H atoms penetrate below the first layer of Xe atoms and subsequently re-emerge to the gas phase. This behavior leads to observable energy-losses as large as 0.5 eV, much larger than a prediction of the binary collision model (0.082 eV), which is often used to estimate the highest possible energy-loss in direct inelastic surface scattering. The sticking probability computed with the EMT-PES (0.15) is dramatically reduced (5 × 10–6) if we employ a full-dimensional potential energy surface (PES) based on Lennard-Jones (LJ) pairwise interactions. Although the LJ-PES accurately describes the interactions near the H–Xe and Xe–Xe energy minima, it drastically overestimates the effective size of the Xe atom seen by the colliding H atom at incidence energies above about 0.1 eV.

This study investigates the potential impact of subsurface light transport on gloss perception for the purposes of broadening our understanding of visual appearance in computer graphics applications. Gloss is an important attribute for characterizing material appearance. We hypothesize that subsurface scattering of light impacts the glossiness perception. However, gloss has been traditionally studied as a surface-related quality and the findings in the state-of-the-art are usually based on fully opaque materials, although the visual cues of glossiness can be impacted by light transmission as well. To address this gap and to test our hypothesis, we conducted psychophysical experiments and found that subjects are able to tell the difference in terms of gloss between stimuli that differ in subsurface light transport but have identical surface qualities and object shape. This gives us a clear indication that subsurface light transport contributes to a glossy appearance. Furthermore, we conducted additional experiments and found that the contribution of subsurface scattering to gloss varies across different shapes and levels of surface roughness. We argue that future research on gloss should include transparent and translucent media and to extend the perceptual models currently limited to surface scattering to more general ones inclusive of subsurface light transport.

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 One of the most critical issues associated with the analysis of lunar seismic data is the intense scattering, which prevents precise seismic phase identifications, thereby resulting in poor constraints on the internal structure of the Moon. Although some studies estimated subsurface scattering properties from analyses of the Apollo seismic data, the properties have large uncertainties and are still open issues to be resolved to improve the inner structure model of the Moon. While the previous studies tried to constrain the scattering features within the lunar crust mainly from data analysis, this study estimated them from a numerical approach. We constrained the scattering properties near Apollo 12 landing site by conducting seismic wave propagation simulations under various parameter settings and comparing the synthetics with the data. As a result, we succeeded in reproducing seismic signals excited by the Apollo artificial impacts. This led to a constraint on the scattering properties, such as typical scale and thickness of heterogeneity, around the Apollo 12 landing site. The derived structure suggests that the intense scattering structure exists down to 20 km at the northern portion of the region of the Apollo 12 landing site, and to 10 km at the southern region from the landing site. In addition, our model requires a smaller P‐ and S‐wave velocity ratio (1.2–1.4) compared with those conventionally considered (>1.73). This implies a dry and porous environment consistent with laboratory measurements of terrestrial samples and reasonable with the generalized lunar environment.

In this paper, we propose a method of reproducing freshly cooked rice using computer graphics animation. The physical properties of freshly cooked rice (rice grains) include shape, density, refractive index, transmittance, and reflectance. Based on these data, the objective is to render the texture and shape of a large amount of cooked rice in a photo-realistic way. Create rice grain polygon models with low resolution based on electron micrographs, rice grains with different shapes and considering the porous structure, we can create a large number of 3D rice grain models. Next, a large number of freshly cooked rice grains were transferred to XPBD (eXtended Position-Based Dynamics), we simulate aggregates by adding a constraint condition. This can be used to simulate the softness of freshly cooked rice. It also allows you to create any shape of rice structure. Finally, the Sub-Surface Scattering (SSS) also takes into account the water content, so that it can be used for the Curvature-dependent reflectance function (CDRF). Depending on the moisture content, different rice grains can be represented with different appearances. With such proposed method, a large number of rice grains are placed in a bowl of freshly cooked rice, rice balls, sushi rice, etc. is represented realistically.

Abstract Existing algorithms for rendering subsurface scattering in real time cannot deal well with scattering over longer distances. Kernels for image space algorithms become very large in these circumstances and separation does not work anymore, while geometry‐based algorithms cannot preserve details very well. We present a novel approach that deals with all these downsides. While for lower scattering distances, the advantages of geometry‐based methods are small, this is not the case anymore for high scattering distances (as we will show). Our proposed method takes advantage of the highly detailed results of image space algorithms and combines it with a geometry‐based method to add the essential scattering from sources not included in image space. Our algorithm does not require pre‐computation based on the scene's geometry, it can be applied to static and animated objects directly. Our method is able to provide results that come close to ray‐traced images which we will show in direct comparisons with images generated by PBRT. We will compare our results to state of the art techniques that are applicable in these scenarios and will show that we provide superior image quality while maintaining interactive rendering times.

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.

1-1 Spectral Analysis of Subsurface Scattering for Modeling Real Scenes

Monte Carlo photon tracking is used to render translucent materials such as marble, milk, skin, etc. The technique encompasses excessive amount of subsurface scattering that is computationally expensive. Faster approaches are based on approximate models derived from observed results. While such models are efficient, they tend to miss some translucency effects in the rendered results. We present an improved approximation model for real-time rendering of materials based upon computational graphs. Excellent results are obtained improving upon the previous studies.

通常の照明下においては，光は皮膚内部に透過し，皮膚表面下で散乱される。皮膚における表面下散乱は，素肌らしさや透明感をもたらす重要な光学的性質であるが，一般にファンデーションを塗布すれば，表面下散乱は減少し，肌らしい質感が失われていく。われわれは，皮膚における表面下散乱が波長によって異なることに注目し，皮膚における表面下散乱の減少を抑制する二種類のファンデーションを開発した。本稿では，その背景およびそのための色材設計について解説する。

Nondestructive evaluation methods rely on prior knowledge of the expected interaction of ultrasonic waves with defects to inform detection and characterization decisions. Wavefield imaging, which refers to the measurement of signals originating from a spatially fixed source on a 2-D rectilinear grid, can be applied to visualize the effect of a subsurface scatterer on surface-measured wave motion. Here, obliquely incident shear waves are directed at the far surface of a plate containing a through-hole using the well-known angle-beam ultrasonic inspection method. A laser vibrometer and laboratory scanner are used to record the resulting out-of-plane motion on the plate surface in the vicinity of the through-hole both before and after a far-surface corner notch is introduced and subsequently enlarged. Waves scattered from the notch are isolated from the incident and hole-scattered waves via baseline subtraction of wavefields. The scattered wavefields are then filtered in the frequency-wavenumber domain to separate Rayleigh, shear, and longitudinal contributions to the scattered wavefield. The filtered wavefields are interpolated in space to obtain 2-D radial wavefield slices originating at the base of the notch. Each radial slice is analyzed to quantify scattering as a function of observation direction, resulting in Rayleigh, shear, and longitudinal scattering profiles for each notch size. The results are compared for four different notch sizes and two transducer orientations.

Models of both the shape and material properties of physical objects are needed in many computer graphics applications. In many design applications, even if shape is not needed, it is desirable to start with the material properties of existing non-planar objects. We consider the design of a system to capture both shape and appearance of objects. We focus particularly on objects that exhibit significant subsurface scattering and inter-reflection effects. We present preliminary results from a system that uses coded light from a set of small, inexpensive projectors coupled with commodity digital cameras.

Rendering translucent materials using Monte Carlo ray tracing is computationally expensive due to a large number of subsurface scattering events. Faster approaches are based on analytical models derived from diffusion theory. While such analytical models are efficient, they miss out on some translucency effects in the rendered result. We present an improved analytical model for subsurface scattering that captures translucency effects present in the reference solutions but remaining absent with existing models. The key difference is that our model is based on ray source diffusion, rather than point source diffusion. A ray source corresponds better to the light that refracts through the surface of a translucent material. Using this ray source, we are able to take the direction of the incident light ray and the direction toward the point of emergence into account. We use a dipole construction similar to that of the standard dipole model, but we now have positive and negative ray sources with a mirrored pair of directions. Our model is as computationally efficient as existing models while it includes single scattering without relying on a separate Monte Carlo simulation, and the rendered images are significantly closer to the references. Unlike some previous work, our model is fully analytic and requires no precomputation.