Abstract Robust next‐event estimation (NEE) remains a challenge in scenes characterized by sparse or small‐scale geometry where indirect illumination is the primary transport mechanism. In these scenes, traditional path construction, which relies on local directional sampling, often fails to find intersections with the sparse geometry, and standard NEE also struggles as it typically connects vertices directly to emitters, failing when those connections are occluded or require intermediate bounces. We propose a novel approach that constructs paths via direct geometry sampling. Instead of relying on stochastic ray casting, we repurpose the scene's bounding volume hierarchy (BVH) as a hierarchical sampling structure. By performing a stochastic top‐down traversal, we transform the selection of the next path vertex into a hierarchical problem. To prioritize high‐throughput connections, the traversal is guided by a proxy contribution function evaluated at each internal node. This function leverages aggregated statistics of the geometry contained in the BVH nodes to efficiently estimate contribution during traversal. We demonstrate orders of magnitude improvements in complex scenarios such as indirect illumination from sparse geometry or rendering discrete scattering media.

Abstract Transient non-line-of-sight imaging techniques reconstruct hidden scenes by analyzing the time of flight of light scattered off a visible secondary surface, or relay wall. Despite many promising approaches, all face the inherent problem of the missing cone, which restricts surface visibility based on their position and orientations relative to the relay wall. Drawing inspiration from stereo technologies from computer vision, we devise a setup consisting of two distinct relay walls. We leverage phasor fields that computationally model both relay walls as generalized virtual camera apertures. This approach allows us to combine the contributions from each relay wall, including the signal obtained by illuminating one wall and capturing the other, information that would be lost otherwise. Our results demonstrate that our proposal diminishes the effect of the missing cone by making the problem better posed. Additionally, by analyzing the visibility conditions of the missing cone, we extract orientation cues from each relay wall contribution. We use this information to enhance visualizations.

Non-line-of-sight imaging employs ultra-fast illumination and sensing devices to reconstruct scenes outside their line of sight by analyzing the temporal profile of indirect scattered illumination on a secondary relay surface. Commonly, the NLOS methods transform the temporal domain into the frequency domain and operate on it, and then identify surface locations by locating the maxima in amplitude along the reconstruction volume. Phase information, which is virtual as it results from a Fourier transform, is very often discarded or ignored. We incorporate phase information into our novel Zero-Phase Phasor Fields imaging technique, which we derive for a confocal capture configuration. We show how, at positions that belong to the hidden geometry, we can ensure the phase is zero, so we can locate the hidden geometry with great precision by locating the zero crossings in the phase. This allows us to reconstruct at widely spaced locations and still achieve up to 125 micrometer depth precision, as our experimental validation shows with both synthetic and captured data, the latter publicly available. Moreover, the phase is robust to noise, as we demonstrate with decreasing signal-to-noise ratio using publicly available dataset captures of the same scene.

Abstract Cosmetic products have found their place in various aspects of human life, yet their digital appearance reproduction has received little attention. We present an appearance model for cosmetics, in particular for foundation layers, that reproduces a range of existing appearances of foundation cosmetics: from a glossy to a matte to an almost velvety look. Our model is a multilayered BSDF that reproduces the stacking of multiple layers of cosmetics. Inspired by the microscopic particulates used in cosmetics, we model each individual layer as a stochastic participating medium with two types of scatterers that mimic the most prominent visual features of cosmetics: spherical diffusers, resulting in a uniform distribution of radiance; and platelets, responsible for the glossy look of certain cosmetics. We implement our model on top of the position‐free Monte Carlo framework, that allows us to include multiple scattering. We validate our model against measured reflectance data, and demonstrate the versatility and expressiveness of our model by thoroughly exploring the range of appearances that it can produce.

Abstract The light field in an underwater environment is characterized by complex multiple scattering interactions and wavelength‐dependent attenuation, requiring significant computational resources for the simulation of underwater scenes. We present a novel approach that makes it possible to simulate multi‐spectral underwater scenes, in a physically‐based manner, in real time. Our key observation is the following: In the vertical direction, the steady decay in irradiance as a function of depth is characterized by the diffuse downwelling attenuation coefficient, which oceanographers routinely measure for different types of waters. We rely on a database of such real‐world measurements to obtain an analytical approximation to the Radiative Transfer Equation, allowing for real‐time spectral rendering with results comparable to Monte Carlo ground‐truth references, in a fraction of the time. We show results simulating underwater appearance for the different optical water types, including volumetric shadows and dynamic, spatially varying lighting near the water surface.

Abstract The appearance of a real‐world feather results from the complex interaction of light with its multi‐scale biological structure, including the central shaft, branching barbs, and interlocking barbules on those barbs. In this work, we propose a practical surface‐based appearance model for feathers. We represent the far‐field appearance of feathers using a BSDF that implicitly represents the light scattering from the main biological structures of a feather, such as the shaft, barb and barbules. Our model accounts for the particular characteristics of feather barbs such as the non‐cylindrical cross‐sections and the scattering media via a numerically‐based BCSDF. To model the relative visibility between barbs and barbules, we derive a masking term for the differential projected areas of the different components of the feather's microgeometry, which allows us to analytically compute the masking between barbs and barbules. As opposed to previous works, our model uses a lightweight representation of the geometry based on a 2D texture, and does not require explicitly representing the barbs as curves. We show the flexibility and potential of our appearance model approach to represent the most important visual features of several pennaceous feathers.

Acquisition and modeling of polarized light reflection and scattering help reveal the shape, structure, and physical characteristics of an object, which is increasingly important in computer graphics. However, current polarimetric acquisition systems are limited to static and opaque objects. Human faces, on the other hand, present a particularly difficult challenge, given their complex structure and reflectance properties, the strong presence of spatially-varying subsurface scattering, and their dynamic nature. We present a new polarimetric acquisition method for dynamic human faces, which focuses on capturing spatially varying appearance and precise geometry, across a wide spectrum of skin tones and facial expressions. It includes both single and heterogeneous subsurface scattering, index of refraction, and specular roughness and intensity, among other parameters, while revealing biophysically-based components such as inner- and outer-layer hemoglobin, eumelanin and pheomelanin. Our method leverages such components' unique multispectral absorption profiles to quantify their concentrations, which in turn inform our model about the complex interactions occurring within the skin layers. To our knowledge, our work is the first to simultaneously acquire polarimetric and spectral reflectance information alongside biophysically-based skin parameters and geometry of dynamic human faces. Moreover, our polarimetric skin model integrates seamlessly into various rendering pipelines.

The recently introduced Phasor Fields framework for non-line-of-sight imaging allows to image hidden scenes by treating a relay surface as a virtual camera. It formulates the problem as a diffractive wave propagation, solved by the Rayleigh–Sommerfeld diffraction (RSD) integral. Efficient Phasor Fields implementations employ RSD-based kernels to propagate waves from parallel planes by means of 2D convolutions. However, the kernel storage requisites are prohibitive, hampering the integration of these techniques in memory-constrained devices and applications like car safety.Instead of relying on expensive RSD kernels, we propose the use of alternative virtual lenses to focus on the incoming phasor field and image hidden scenes. In particular, we propose using zone plates (ZP), which require significant less memory. As our results show, our ZP virtual lenses allow us to obtain reasonable reconstructions of the hidden scene, offering an attractive trade-off for memory-constrained devices.

Non-line-of-sight (NLOS) imaging methods are capable of reconstructing complex scenes that are not visible to an observer using indirect illumination. However, they assume only third-bounce illumination, so they are currently limited to single-corner configurations, and present limited visibility when imaging surfaces at certain orientations. To reason about and tackle these limitations, we make the key observation that planar diffuse surfaces behave specularly at wavelengths used in the computational wave-based NLOS imaging domain. We call such surfaces virtual mirrors. We leverage this observation to expand the capabilities of NLOS imaging using illumination beyond the third bounce, addressing two problems: imaging single-corner objects at limited visibility angles, and imaging objects hidden behind two corners. To image objects at limited visibility angles, we first analyze the reflections of the known illuminated point on surfaces of the scene as an estimator of the position and orientation of objects with limited visibility. We then image those limited visibility objects by computationally building secondary apertures at other surfaces that observe the target object from a direct visibility perspective. Beyond single-corner NLOS imaging, we exploit the specular behavior of virtual mirrors to image objects hidden behind a second corner by imaging the space behind such virtual mirrors, where the mirror image of objects hidden around two corners is formed. No specular surfaces were involved in the making of this paper.

The capture and analysis of light in flight, or light in transient state, has enabled applications such as range imaging, reflectance estimation and especially non-line-of-sight (NLOS) imaging. For this last case, hidden geometry can be reconstructed using time-resolved measurements of indirect diffuse light emitted by a laser. Transient rendering is a key tool for developing such new applications, significantly more challenging than its steady-state counterpart. In this work, we introduce a set of simple yet effective subpath sampling techniques targeting transient light transport simulation in occluded scenes. We analyze the usual capture setups of NLOS scenes, where both the camera and light sources are focused on particular points in the scene. Also, the hidden geometry can be difficult to sample using conventional techniques. We leverage that configuration to reduce the integration path space. We implement our techniques in a modified version of Mitsuba 2 adapted for transient light transport, allowing us to support parallelization, polarization, and differentiable rendering.

Ellipsometry techniques allow to measure polarization information of materials, requiring precise rotations of optical components with different configurations of lights and sensors. This results in cumbersome capture devices, carefully calibrated in lab conditions, and in very long acquisition times, usually in the order of a few days per object. Recent techniques allow to capture polarimetric spatially-varying reflectance information, but limited to a single view, or to cover all view directions, but limited to spherical objects made of a single homogeneous material. We present sparse ellipsometry , a portable polarimetric acquisition method that captures both polarimetric SVBRDF and 3D shape simultaneously. Our handheld device consists of off-the-shelf, fixed optical components. Instead of days, the total acquisition time varies between twenty and thirty minutes per object. We develop a complete polarimetric SVBRDF model that includes diffuse and specular components, as well as single scattering, and devise a novel polarimetric inverse rendering algorithm with data augmentation of specular reflection samples via generative modeling. Our results show a strong agreement with a recent ground-truth dataset of captured polarimetric BRDFs of real-world objects.

In the curriculum of a Computer Engineering program, concepts like parallelism, concurrency, consistency, or atomicity are usually addressed in separate courses due to their thoroughness and extension. Isolating such concepts in courses helps students not only to focus on specific aspects, but also to experience the reality of working with modern computer systems, where those concepts are often detached in different abstraction levels. However, due to such an isolation, it exists a risk of inducing to the students an absence of interactions between these concepts, and, by extension, between the different abstraction levels of a system. This paper proposes a learning experience showcasing the interactions between abstraction levels addressed in laboratory sessions of different courses. The driving example is a parallel ray tracer. In the different courses, students implement and assemble components of this application from the algorithmic level of the tracer to the assembly instructions required to guarantee atomicity. Each lab focuses on a single abstraction level, but shows students the interactions with the rest of the levels. Technical results and student learning outcomes through the analysis of surveys validate the proposed experience and confirm the students learning improvement with a more integrated view of the system.

We present an unbiased numerical integration algorithm that handles both low-frequency regions and high-frequency details of multidimensional integrals. It combines quadrature and Monte Carlo integration by using a quadrature-based approximation as a control variate of the signal. We adaptively build the control variate constructed as a piecewise polynomial, which can be analytically integrated, and accurately reconstructs the low-frequency regions of the integrand. We then recover the high-frequency details missed by the control variate by using Monte Carlo integration of the residual. Our work leverages importance sampling techniques by working in primary space, allowing the combination of multiple mappings; this enables multiple importance sampling in quadrature-based integration. Our algorithm is generic and can be applied to any complex multidimensional integral. We demonstrate its effectiveness with four applications with low dimensionality: transmittance estimation in heterogeneous participating media, low-order scattering in homogeneous media, direct illumination computation, and rendering of distribution effects. Finally, we show how our technique is extensible to integrands of higher dimensionality by computing the control variate on Monte Carlo estimates of the high-dimensional signal, and accounting for such additional dimensionality on the residual as well. In all cases, we show accurate results and faster convergence compared to previous approaches.

Abstract Several image editing methods have been proposed in the past decades, achieving brilliant results. The most sophisticated of them, however, require additional information per‐pixel. For instance, dehazing requires a specific transmittance value per pixel, or depth of field blurring requires depth or disparity values per pixel. This additional per‐pixel value is obtained either through elaborated heuristics or through additional control over the capture hardware, which is very often tailored for the specific editing application. In contrast, however, we propose a generic editing paradigm that can become the base of several different applications. This paradigm generates both the needed per‐pixel values and the resulting edit at interactive rates, with minimal user input that can be iteratively refined. Our key insight for getting per‐pixel values at such speed is to cluster them into superpixels, but, instead of a constant value per superpixel (which yields accuracy problems), we have a mathematical expression for pixel values at each superpixel: in our case, an order two multinomial per superpixel. This leads to a linear least‐squares system, effectively enabling specific per‐pixel values at fast speeds. We illustrate this approach in three applications: depth of field blurring (from depth values), dehazing (from transmittance values) and tone mapping (from brightness and contrast local values), and our approach proves both favorably interactive and accurate in all three. Our technique is also evaluated with a common dataset and compared favorably.

Time-of-flight (ToF) imaging has become a widespread technique for depth estimation, allowing affordable off-the-shelf cameras to provide depth maps in real time. However, multipath interference (MPI) resulting from indirect illumination significantly degrades the captured depth. Most previous works have tried to solve this problem by means of complex hardware modifications or costly computations. In this work, we avoid these approaches and propose a new technique to correct errors in depth caused by MPI, which requires no camera modifications and takes just 10 milliseconds per frame. Our observations about the nature of MPI suggest that most of its information is available in image space; this allows us to formulate the depth imaging process as a spatially-varying convolution and use a convolutional neural network to correct MPI errors. Since the input and output data present similar structure, we base our network on an autoencoder, which we train in two stages. First, we use the encoder (convolution filters) to learn a suitable basis to represent MPI-corrupted depth images; then, we train the decoder (deconvolution filters) to correct depth from synthetic scenes, generated by using a physically-based, time-resolved renderer. This approach allows us to tackle a key problem in ToF, the lack of ground-truth data, by using a large-scale captured training set with MPI-corrupted depth to train the encoder, and a smaller synthetic training set with ground truth depth to train the decoder stage of the network. We demonstrate and validate our method on both synthetic and real complex scenarios, using an off-the-shelf ToF camera, and with only the captured, incorrect depth as input.

Abstract Rendering participating media is still a challenging and time consuming task. In such media light interacts at every differential point of its path. Several rendering algorithms are based on ray marching: dividing the path of light into segments and calculating interactions at each of them. In this work, we revisit and analyze ray marching both as a quadrature integrator and as an initial value problem solver, and apply higher order adaptive solvers that ensure several interesting properties, such as faster convergence, adaptiveness to the mathematical definition of light transport and robustness to singularities. We compare several numerical methods, including standard ray marching and Monte Carlo integration, and illustrate the benefits of different solvers for a variety of scenes. Any participating media rendering algorithm that is based on ray marching may benefit from the application of our approach by reducing the number of needed samples (and therefore, rendering time) and increasing accuracy.

Recent advances in ultra-fast imaging have triggered many promising applications in graphics and vision, such as capturing transparent objects, estimating hidden geometry and materials, or visualizing light in motion. There is, however, very little work regarding the effective simulation and analysis of transient light transport, where the speed of light can no longer be considered infinite. We first introduce the transient path integral framework, formally describing light transport in transient state. We then analyze the difficulties arising when considering the light's time-of-flight in the simulation (rendering) of images and videos. We propose a novel density estimation technique that allows reusing sampled paths to reconstruct time-resolved radiance, and devise new sampling strategies that take into account the distribution of radiance along time in participating media. We then efficiently simulate time-resolved phenomena (such as caustic propagation, fluorescence or temporal chromatic dispersion), which can help design future ultra-fast imaging devices using an analysis-by-synthesis approach, as well as to achieve a better understanding of the nature of light transport.

Abstract Decomposing an input image into its intrinsic shading and reflectance components is a long‐standing ill‐posed problem. We present a novel algorithm that requires no user strokes and works on a single image. Based on simple assumptions about its reflectance and luminance, we first find clusters of similar reflectance in the image, and build a linear system describing the connections and relations between them. Our assumptions are less restrictive than widely‐adopted Retinex‐based approaches, and can be further relaxed in conflicting situations. The resulting system is robust even in the presence of areas where our assumptions do not hold. We show a wide variety of results, including natural images, objects from the MIT dataset and texture images, along with several applications, proving the versatility of our method.

In this article, we derive a physically-based model for simulating rainbows. Previous techniques for simulating rainbows have used either geometric optics (ray tracing) or Lorenz-Mie theory. Lorenz-Mie theory is by far the most accurate technique as it takes into account optical effects such as dispersion, polarization, interference, and diffraction. These effects are critical for simulating rainbows accurately. However, as Lorenz-Mie theory is restricted to scattering by spherical particles, it cannot be applied to real raindrops which are nonspherical, especially for larger raindrops. We present the first comprehensive technique for simulating the interaction of a wavefront of light with a physically-based water drop shape. Our technique is based on ray tracing extended to account for dispersion, polarization, interference, and diffraction. Our model matches Lorenz-Mie theory for spherical particles, but it also enables the accurate simulation of nonspherical particles. It can simulate many different rainbow phenomena including double rainbows and supernumerary bows. We show how the nonspherical raindrops influence the shape of the rainbows, and we provide a simulation of the rare twinned rainbow, which is believed to be caused by nonspherical water drops.

Abstract This paper introduces a new method for simulating homogeneous subsurface light transport in translucent objects. Our approach is based on irradiance convolutions over a multi‐layered representation of the volume for light transport, which is general enough to obtain plausible depictions of translucent objects based on the diffusion approximation. We aim at providing an efficient physically based algorithm that can apply arbitrary diffusion profiles to general geometries. We obtain accurate results for a wide range of materials, on par with the hierarchical method by Jensen and Buhler.

Abstract We present a novel method to estimate an approximation of the reflectance characteristics of optically thick, homogeneous translucent materials using only a single photograph as input. First, we approximate the diffusion profile as a linear combination of piecewise constant functions, an approach that enables a linear system minimization and maximizes robustness in the presence of suboptimal input data inferred from the image. We then fit to a smoother monotonically decreasing model, ensuring continuity on its first derivative. We show the feasibility of our approach and validate it in controlled environments, comparing well against physical measurements from previous works. Next, we explore the performance of our method in uncontrolled scenarios, where neither lighting nor geometry are known. We show that these can be roughly approximated from the corresponding image by making two simple assumptions: that the object is lit by a distant light source and that it is globally convex, allowing us to capture the visual appearance of the photographed material. Compared with previous works, our technique offers an attractive balance between visual accuracy and ease of use, allowing its use in a wide range of scenarios including off‐the‐shelf, single images, thus extending the current repertoire of real‐world data acquisition techniques.

Abstract Simulating the in‐water ocean light field is a daunting task. Ocean waters are one of the richest participating media, where light interacts not only with water molecules, but with suspended particles and organic matter as well. The concentration of each constituent greatly affects these interactions, resulting in very different hues. Inelastic scattering events such as fluorescence or Raman scattering imply energy transfers that are usually neglected in the simulations. Our contributions in this paper are a bio‐optical model of ocean waters suitable for computer graphics simulations, along with an improved method to obtain an accurate solution of the in‐water light field based on radiative transfer theory. The method provides a link between the inherent optical properties that define the medium and its apparent optical properties, which describe how it looks. The bio‐optical model of the ocean uses published data from oceanography studies. For inelastic scattering we compute all frequency changes at higher and lower energy values, based on the spectral quantum efficiency function of the medium. The results shown prove the usability of the system as a predictive rendering algorithm. Areas of application for this research span from underwater imagery to remote sensing; the resolution method is general enough to be usable in any type of participating medium simulation.