Smoke in real-world scenes can severely degrade image quality and hamper visibility. Recent image restoration methods either rely on data-driven priors that are susceptible to hallucinations, or are limited to static low-density smoke. We introduce SmokeSeer, a method for simultaneous 3D scene reconstruction and smoke removal from multi-view video sequences. Our method uses thermal and RGB images, leveraging the reduced scattering in thermal images to see through smoke. We build upon 3D Gaussian splatting to fuse information from the two image modalities, and decompose the scene into smoke and non-smoke components. Unlike prior work, SmokeSeer handles a broad range of smoke densities and adapts to temporally varying smoke. We validate our method on synthetic data and a new real-world smoke dataset with RGB and thermal images. We provide an opensource implementation and data on the project website.1https://imaging.cs.cmu.edu/smokeseer

We describe a method for computing signed distance to point clouds that allows fast pointwise evaluation at arbitrary spatial resolution. As input, our method takes a point cloud with normals; as output, it provides an analytical parameterization that allows queries of signed distance to the approximate underlying surface at arbitrary points — simultaneously providing reconstruction and distance. Our key idea is to reconstruct shapes by locally fitting point clouds with tori, which have closed-form signed distance functions. Tori are fitted in a feed-forward manner, using a pre-trained network to output per-point curvature and shift parameters. Importantly, our method does not require costly global optimization or spatial discretization, and is easily parallelizable. Underlying our method is a new theory that unifies signed distance with the classic reconstruction methods of winding numbers and Poisson surface reconstruction. We use our method to compute signed distance to point clouds arising from photogrammetry, meshes, 3D Gaussians, and neural implicits. Our method allows point clouds to be used directly in applications, without explicit surface reconstruction: as examples, we take offsets of point clouds, apply morphological and Boolean operations, and directly visualize offset surfaces using sphere tracing.

We introduce a method that automatically and jointly updates both continuous and discrete parameters of a compound lens design, to improve its performance in terms of sharpness, speed, or both. Previous methods for compound lens design use gradient-based optimization to update continuous parameters (e.g., curvature of individual lens elements) of a given lens topology, requiring extensive expert intervention to realize topology changes. By contrast, our method can additionally optimize discrete parameters such as number and type (e.g., singlet or doublet) of lens elements. Our method achieves this capability by combining gradient-based optimization with a tailored Markov chain Monte Carlo sampling algorithm, using transdimensional mutation and paraxial projection operations for efficient global exploration. We show experimentally on a variety of lens design tasks that our method effectively explores an expanded design space of compound lenses, producing better designs than previous methods and pushing the envelope of speed-sharpness tradeoffs achievable by automated lens design.

We consider the problem of solving partial differential equations (PDEs) in domains with complex microparticle geometry that is impractical, or intractable, to model explicitly. Drawing inspiration from volume rendering, we propose tackling this problem by treating the domain as a participating medium that models microparticle geometry stochastically , through aggregate statistical properties (e.g., particle density). We first introduce the problem setting of PDE simulation in participating media. We then specialize to exponential media and describe the properties that make them an attractive model of microparticle geometry for PDE simulation problems. We use these properties to develop two new algorithms, volumetric walk on spheres and volumetric walk on stars , that generalize previous Monte Carlo algorithms to enable efficient and discretization-free simulation of linear elliptic PDEs (e.g., Laplace) in participating media. We demonstrate experimentally that our algorithms can solve Laplace boundary value problems with complex microparticle geometry more accurately and more efficiently than previous approaches, such as ensemble averaging and homogenization.

We develop a theory for the representation of opaque solids as volumes. Starting from a stochastic representation of opaque solids as random indicator functions, we prove the conditions under which such solids can be modeled using exponential volumetric transport. We also derive expressions for the volumetric attenuation coefficient as a functional of the probability distributions of the underlying indicator functions. We generalize our theory to account for isotropic and anisotropic scattering at different parts of the solid, and for representations of opaque solids as stochastic implicit surfaces. We derive our volumetric representation from first principles, which ensures that it satisfies physical constraints such as reciprocity and reversibility. We use our theory to explain, compare, and correct previous volumetric representations, as well as propose meaningful extensions that lead to improved performance in 3D reconstruction tasks.

Abstract Let $$\textbf{p}$$ p be a configuration of n points in $$\mathbb R^d$$ R d for some n and some $$d \ge 2$$ d ≥ 2 . Each pair of points defines an edge, which has a Euclidean length in the configuration. A path is an ordered sequence of the points, and a loop is a path that begins and ends at the same point. A path or loop, as a sequence of edges, also has a Euclidean length, which is simply the sum of its Euclidean edge lengths. We are interested in reconstructing $$\textbf{p}$$ p given a set of edge, path and loop lengths. In particular, we consider the unlabeled setting where the lengths are given simply as a set of real numbers, and are not labeled with the combinatorial data describing which paths or loops gave rise to these lengths. In this paper, we study the question of when $$\textbf{p}$$ p will be uniquely determined (up to an unknowable Euclidean transform) from some given set of path or loop lengths through an exhaustive trilateration process. Such a process has already been used for the simpler problem of reconstruction using unlabeled edge lengths. This paper also provides a complete proof that this process must work in that edge-setting when given a sufficiently rich set of edge measurements and assuming that $$\textbf{p}$$ p is generic.

We introduce a method for high-quality 3D reconstruction from multi-view images. Our method uses a new point-based representation, the regularized dipole sum, which generalizes the winding number to allow for interpolation of per-point attributes in point clouds with noisy or outlier points. Using regularized dipole sums, we represent implicit geometry and radiance fields as per-point attributes of a dense point cloud, which we initialize from structure from motion. We additionally derive Barnes-Hut fast summation schemes for accelerated forward and adjoint dipole sum queries. These queries facilitate the use of ray tracing to efficiently and differentiably render images with our point-based representations, and thus update their point attributes to optimize scene geometry and appearance. We evaluate our method in inverse rendering applications against state-of-the-art alternatives, based on ray tracing of neural representations or rasterization of Gaussian point-based representations. Our method significantly improves 3D reconstruction quality and robustness at equal runtimes, while also supporting more general rendering methods such as shadow rays for direct illumination.

Numerous scientific and engineering applications require solutions to boundary value problems (BVPs) involving elliptic partial differential equations, such as the Laplace or Poisson equations, on geometrically intricate domains. We develop a Monte Carlo method for solving such BVPs with arbitrary first-order linear boundary conditions---Dirichlet, Neumann, and Robin. Our method directly generalizes the walk on stars (WoSt) algorithm, which previously tackled only the first two types of boundary conditions, with a few simple modifications. Unlike conventional numerical methods, WoSt does not need finite element meshing or global solves. Similar to Monte Carlo rendering, it instead computes pointwise solution estimates by simulating random walks along star-shaped regions inside the BVP domain, using efficient ray-intersection and distance queries. To ensure WoSt produces bounded-variance estimates in the presence of Robin boundary conditions, we show that it is sufficient to modify how WoSt selects the size of these star-shaped regions. Our generalized WoSt algorithm reduces estimation error by orders of magnitude relative to alternative grid-free methods such as the walk on boundary algorithm. We also develop bidirectional and boundary value caching strategies to further reduce estimation error. Our algorithm is trivial to parallelize, scales sublinearly with increasing geometric detail, and enables progressive and view-dependent evaluation.

We introduce a Monte Carlo method for computing derivatives of the solution to a partial differential equation (PDE) with respect to problem parameters (such as domain geometry or boundary conditions). Derivatives can be evaluated at arbitrary points, without performing a global solve or constructing a volumetric grid or mesh. The method is hence well suited to inverse problems with complex geometry, such as PDE-constrained shape optimization. Like other walk on spheres (WoS) algorithms, our method is trivial to parallelize, and is agnostic to boundary representation (meshes, splines, implicit surfaces, etc. ), supporting large topological changes. We focus in particular on screened Poisson equations, which model diverse problems from scientific and geometric computing. As in differentiable rendering, we jointly estimate derivatives with respect to all parameters---hence, cost does not grow significantly with parameter count. In practice, even noisy derivative estimates exhibit fast, stable convergence for stochastic gradient-based optimization, as we show through examples from thermal design, shape from diffusion, and computer graphics.

We introduce a method that recovers full-surround 3D reconstructions from a single kaleidoscopic image using a neural surface representation. Full-surround 3D reconstruction is critical for many applications, such as augmented and virtual reality. A kaleidoscope, which uses a single camera and multiple mirrors, is a convenient way of achieving full-surround coverage, as it redistributes light directions and thus captures multiple viewpoints in a single image. This enables single-shot and dynamic full-surround 3D reconstruction. However, using a kaleidoscopic image for multiview stereo is challenging, as we need to decompose the image into multi-view images by identifying which pixel corresponds to which virtual camera, a process we call labeling. To address this challenge, pur approach avoids the need to explicitly estimate labels, but instead “sculpts” a neural surface representation through the careful use of silhouette, background, foreground, and texture information present in the kaleidoscopic image. We demonstrate the advantages of our method in a range of simulated and real experiments, on both static and dynamic scenes.

We introduce an interferometric technique for passive time-of-flight imaging and depth sensing at micrometer axial resolutions. Our technique uses a full-field Michelson interferometer, modified to use sunlight as the only light source. The large spectral bandwidth of sunlight makes it possible to acquire micrometer-resolution time-resolved scene responses, through a simple axial scanning operation. Additionally, the angular bandwidth of sunlight makes it possible to capture time-of-flight measurements insensitive to indirect illumination effects, such as interreflections and subsurface scattering. We build an experimental prototype that we operate outdoors, under direct sunlight, and in adverse environment conditions such as machine vibrations and vehicle traffic. We use this prototype to demonstrate, for the first time, passive imaging capabilities such as micrometer-scale depth sensing robust to indirect illumination, direct-only imaging, and imaging through diffusers.

We present a new imaging technique, swept-angle synthetic wavelength interferometry, for full-field micron-scale 3D sensing. As in conventional synthetic wavelength interferometry, our technique uses light consisting of two narrowly-separated optical wavelengths, resulting in per-pixel inter-ferometric measurements whose phase encodes scene depth. Our technique additionally uses a new type of light source that, by emulating spatially-incoherent illumination, makes interferometric measurements insensitive to aberrations and (sub)surface scattering, effects that corrupt phase measurements. The resulting technique combines the robustness to such corruptions of scanning interferometric setups, with the speed of full-field interferometric setups. Overall, our technique can recover full-frame depth at a lateral and axial resolution of 5 µm, at frame rates of 5 Hz, even under strong ambient light. We build an experimental prototype, and use it to demonstrate these capabilities by scanning a variety of objects, including objects representative of applications in inspection and fabrication, and objects that contain challenging light scattering effects.

We introduce a light steering technology that operates at megahertz frequencies, has no moving parts, and costs less than a hundred dollars. Our technology can benefit many projector and imaging systems that critically rely on high-speed, reliable, low-cost, and wavelength-independent light steering, including laser scanning projectors, LiDAR sensors, and fluorescence microscopes. Our technology uses ultrasound waves to generate a spatiotemporally-varying refractive index field inside a compressible medium, such as water, turning the medium into a dynamic traveling lens. By controlling the electrical input of the ultrasound transducers that generate the waves, we can change the lens, and thus steer light, at the speed of sound (1.5 km/s in water). We build a physical prototype of this technology, use it to realize different scanning techniques at megahertz rates (three orders of magnitude faster than commercial alternatives such as galvo mirror scanners), and demonstrate proof-of-concept projector and LiDAR applications. To encourage further innovation towards this new technology, we derive theory for its fundamental limits and develop a physically-accurate simulator for virtual design. Our technology offers a promising solution for achieving high-speed and low-cost light steering in a variety of applications.

We present a technique for dense 3D reconstruction of objects using an imaging sonar, also known as forward-looking sonar (FLS). Compared to previous methods that model the scene geometry as point clouds or volumetric grids, we represent the geometry as a neural implicit function. Additionally, given such a representation, we use a differentiable volumetric renderer that models the propagation of acoustic waves to synthesize imaging sonar measurements. We perform experiments on real and synthetic datasets and show that our algorithm reconstructs high-fidelity surface geometry from multi-view FLS images at much higher quality than was possible with previous techniques and without suffering from their associated memory overhead.

We introduce Doppler time-of-flight (D-ToF) rendering, an extension of ToF rendering for dynamic scenes, with applications in simulating D-ToF cameras. D-ToF cameras use high-frequency modulation of illumination and exposure, and measure the Doppler frequency shift to compute the radial velocity of dynamic objects. The time-varying scene geometry and high-frequency modulation functions used in such cameras make it challenging to accurately and efficiently simulate their measurements with existing ToF rendering algorithms. We overcome these challenges in a twofold manner: To achieve accuracy, we derive path integral expressions for D-ToF measurements under global illumination and form unbiased Monte Carlo estimates of these integrals. To achieve efficiency, we develop a tailored time-path sampling technique that combines antithetic time sampling with correlated path sampling. We show experimentally that our sampling technique achieves up to two orders of magnitude lower variance compared to naive time-path sampling. We provide an open-source simulator that serves as a digital twin for D-ToF imaging systems, allowing imaging researchers, for the first time, to investigate the impact of modulation functions, material properties, and global illumination on D-ToF imaging performance.

Grid-free Monte Carlo methods such as walk on spheres can be used to solve elliptic partial differential equations without mesh generation or global solves. However, such methods independently estimate the solution at every point, and hence do not take advantage of the high spatial regularity of solutions to elliptic problems. We propose a fast caching strategy which first estimates solution values and derivatives at randomly sampled points along the boundary of the domain (or a local region of interest). These cached values then provide cheap, output-sensitive evaluation of the solution (or its gradient) at interior points, via a boundary integral formulation. Unlike classic boundary integral methods, our caching scheme introduces zero statistical bias and does not require a dense global solve. Moreover we can handle imperfect geometry (e.g., with self-intersections) and detailed boundary/source terms without repairing or resampling the boundary representation. Overall, our scheme is similar in spirit to virtual point light methods from photorealistic rendering: it suppresses the typical salt-and-pepper noise characteristic of independent Monte Carlo estimates, while still retaining the many advantages of Monte Carlo solvers: progressive evaluation, trivial parallelization, geometric robustness, etc. We validate our approach using test problems from visual and geometric computing.

Grid-free Monte Carlo methods based on the walk on spheres (WoS) algorithm solve fundamental partial differential equations (PDEs) like the Poisson equation without discretizing the problem domain or approximating functions in a finite basis. Such methods hence avoid aliasing in the solution, and evade the many challenges of mesh generation. Yet for problems with complex geometry, practical grid-free methods have been largely limited to basic Dirichlet boundary conditions. We introduce the walk on stars (WoSt) algorithm, which solves linear elliptic PDEs with arbitrary mixed Neumann and Dirichlet boundary conditions. The key insight is that one can efficiently simulate reflecting Brownian motion (which models Neumann conditions) by replacing the balls used by WoS with star-shaped domains. We identify such domains via the closest point on the visibility silhouette, by simply augmenting a standard bounding volume hierarchy with normal information. Overall, WoSt is an easy modification of WoS, and retains the many attractive features of grid-free Monte Carlo methods such as progressive and view-dependent evaluation, trivial parallelization, and sublinear scaling to increasing geometric detail.

Single-photon avalanche diodes (SPADs) are growing in popularity for depth sensing tasks. However, SPADs still struggle in the presence of high ambient light due to the effects of pile-up. Conventional techniques leverage fixed or asynchronous gating to minimize pile-up effects, but these gating schemes are all non-adaptive, as they are unable to incorporate factors such as scene priors and previous photon detections into their gating strategy. We propose an adaptive gating scheme built upon Thompson sampling. Adaptive gating periodically updates the gate position based on prior photon observations in order to minimize depth errors. Our experiments show that our gating strategy results in significantly reduced depth reconstruction error and acquisition time, even when operating outdoors under strong sunlight conditions.

Abstract Mathematically representing the shape of an object is a key ingredient for solving inverse rendering problems. Explicit representations like meshes are efficient to render in a differentiable fashion but have difficulties handling topology changes. Implicit representations like signed‐distance functions, on the other hand, offer better support of topology changes but are much more difficult to use for physics‐based differentiable rendering. We introduce a new physics‐based inverse rendering pipeline that uses both implicit and explicit representations. Our technique enjoys the benefit of both representations by supporting both topology changes and differentiable rendering of complex effects such as environmental illumination, soft shadows, and interreflection. We demonstrate the effectiveness of our technique using several synthetic and real examples.

Reconstructing and designing media with continuously-varying refractive index fields remains a challenging problem in computer graphics. A core difficulty in trying to tackle this inverse problem is that light travels inside such media along curves, rather than straight lines. Existing techniques for this problem make strong assumptions on the shape of the ray inside the medium, and thus limit themselves to media where the ray deflection is relatively small. More recently, differentiable rendering techniques have relaxed this limitation, by making it possible to differentiably simulate curved light paths. However, the automatic differentiation algorithms underlying these techniques use large amounts of memory, restricting existing differentiable rendering techniques to relatively small media and low spatial resolutions. We present a method for optimizing refractive index fields that both accounts for curved light paths and has a small, constant memory footprint. We use the adjoint state method to derive a set of equations for computing derivatives with respect to the refractive index field of optimization objectives that are subject to nonlinear ray tracing constraints. We additionally introduce discretization schemes to numerically evaluate these equations, without the need to store nonlinear ray trajectories in memory, significantly reducing the memory requirements of our algorithm. We use our technique to optimize high-resolution refractive index fields for a variety of applications, including creating different types of displays (multiview, lightfield, caustic), designing gradient-index optics, and reconstructing gas flows.

Coherent images of scattering materials, such as biological tissue, typically exhibit high-frequency intensity fluctuations known as speckle. These seemingly noise-like speckle patterns have strong statistical correlation properties that have been successfully utilized by computational imaging systems in different application areas. Unfortunately, these properties are not well-understood, in part due to the difficulty of simulating physically-accurate speckle patterns. In this work, we propose a new model for speckle statistics based on a single scattering approximation, that is, the assumption that all light contributing to speckle correlation has scattered only once. Even though single-scattering models have been used in computer vision and graphics to approximate intensity images due to scattering, such models usually hold only for very optically thin materials, where light indeed does not scatter more than once. In contrast, we show that the single-scattering model for speckle correlation remains accurate for much thicker materials. We evaluate the accuracy of the single-scattering correlation model through exhaustive comparisons against an exact speckle correlation simulator. We additionally demonstrate the model's accuracy through comparisons with real lab measurements. We show, that for many practical application settings, predictions from the single-scattering model are more accurate than those from other approximate models popular in optics, such as the diffusion and Fokker-Planck models. We show how to use the single-scattering model to derive closed-form expressions for speckle correlation, and how these expressions can facilitate the study of statistical speckle properties. In particular, we demonstrate that these expressions provide simple explanations for previously reported speckle properties, and lead to the discovery of new ones. Finally, we discuss potential applications for future computational imaging systems.

We present a method that takes as input a single dual-pixel image, and simultaneously estimates the image’s defocus map—the amount of defocus blur at each pixel—and recovers an all-in-focus image. Our method is inspired from recent works that leverage the dual-pixel sensors available in many consumer cameras to assist with autofocus, and use them for recovery of defocus maps or all-in-focus images. These prior works have solved the two recovery problems independently of each other, and often require large labeled datasets for supervised training. By contrast, we show that it is beneficial to treat these two closely-connected problems simultaneously. To this end, we set up an optimization problem that, by carefully modeling the optics of dual-pixel images, jointly solves both problems. We use data captured with a consumer smartphone camera to demonstrate that, after a one-time calibration step, our approach improves upon prior works for both defocus map estimation and blur removal, despite being entirely unsupervised.

Full surround 3D imaging for shape acquisition is essential for generating digital replicas of real-world objects. Surrounding an object we seek to scan with a kaleidoscope, that is, a configuration of multiple planar mirrors, produces an image of the object that encodes information from a combinatorially large number of virtual viewpoints. This information is practically useful for the full surround 3D reconstruction of the object, but cannot be used directly, as we do not know what virtual viewpoint each image pixel corresponds---the pixel label. We introduce a structured light system that combines a projector and a camera with a kaleidoscope. We then prove that we can accurately determine the labels of projector and camera pixels, for arbitrary kaleidoscope configurations, using the projector-camera epipolar geometry. We use this result to show that our system can serve as a multi-view structured light system with hundreds of virtual projectors and cameras. This makes our system capable of scanning complex shapes precisely and with full coverage. We demonstrate the advantages of the kaleidoscopic structured light system by scanning objects that exhibit a large range of shapes and reflectances.

Recent advances in computational imaging have significantly expanded our ability to image through scattering layers such as biological tissues by exploiting the auto-correlation properties of captured speckle intensity patterns. However, most experimental demonstrations of this capability focus on the far-field imaging setting, where obscured light sources are very far from the scattering layer. By contrast, medical imaging applications such as fluorescent imaging operate in the near-field imaging setting, where sources are inside the scattering layer. We provide a theoretical and experimental study of the similarities and differences between the two settings, highlighting the increased challenges posed by the near-field setting. We then draw insights from this analysis to develop a new algorithm for imaging through scattering that is tailored to the near-field setting by taking advantage of unique properties of speckle patterns formed under this setting, such as their local support. We present a theoretical analysis of the advantages of our algorithm and perform real experiments in both far-field and near-field configurations, showing an order-of magnitude expansion in both the range and the density of the obscured patterns that can be recovered.

Conventional Computed Tomography (CT) systems use a single X-ray source and an arc of detectors mounted on a rotating gantry to acquire a set of projection data. Novel CT systems are now being pioneered in which a complete ring of distributed X-ray sources and detectors are electronically turned on and off, without any mechanical motion, to acquire a set of projections for tomographic reconstruction. This paper discusses new sensing and reconstruction paradigms enabled by this new CT architecture.

Given images of translucent objects, of unknown shape and lighting, we aim to use learning to infer the optical parameters controlling subsurface scattering of light inside the objects. We introduce a new architecture, the inverse transport network (ITN), that aims to improve generalization of an encoder network to unseen scenes, by connecting it with a physically-accurate, differentiable Monte Carlo renderer capable of estimating image derivatives with respect to scattering material parameters. During training, this combination forces the encoder network to predict parameters that not only match groundtruth values, but also reproduce input images. During testing, the encoder network is used alone, without the renderer, to predict material parameters from a single input image. Drawing insights from the physics of radiative transfer, we additionally use material parameterizations that help reduce estimation errors due to ambiguities in the scattering parameter space. Finally, we augment the training loss with pixelwise weight maps that emphasize the parts of the image most informative about the underlying scattering parameters. We demonstrate that this combination allows neural networks to generalize to scenes with completely unseen geometries and illuminations better than traditional networks, with 38.06% reduced parameter error on average.

Reflectometry is the task for acquiring the bidirectional reflectance distribution function (BRDFs) of real-world materials. The typical reflectometry pipeline in computer vision, computer graphics, and computational imaging involves capturing images of a convex shape under multiple illumination and imaging conditions; due to the convexity of the shape, which implies that all paths from the light source to the camera perform a single reflection, the intensities in these images can subsequently be analytically mapped to BRDF values. We deviate from this pipeline by investigating the utility of higher-order light transport effects, such as the interreflections arising when illuminating and imaging a concave object, for reflectometry. We show that interreflections provide a rich set of contraints on the unknown BRDF, significantly exceeding those available in equivalent measurements of convex shapes. We develop a differentiable rendering pipeline to solve an inverse rendering problem that uses these constraints to produce high-fidelity BRDF estimates from even a single input image. Finally, we take first steps towards designing new concave shapes that maximize the amount of information about the unknown BRDF available in image measurements. We perform extensive simulations to validate the utility of this reflectometry from interreflections approach.

We present a novel framework for object-level 3D underwater reconstruction using imaging sonar sensors. We demonstrate that imaging sonar reconstruction is analogous to the problem of confocal non-line-of-sight (NLOS) reconstruction. Drawing upon this connection, we formulate the problem as one of solving for volumetric albedo, where the scene of interest is modeled as a directionless albedo field. After discretization, reconstruction reduces to a convex linear optimization problem, which we can augment with a variety of priors and regularization terms. We show how to solve the resulting regularized problems using the alternating direction method of multipliers (ADMM) algorithm. We demonstrate the effectiveness of the proposed approach in simulation and on real-world datasets collected in a controlled, test tank environment with several different sonar elevation apertures.

In this work, we present a novel method for reconstructing particular 3D surface points using an imaging sonar sensor. We derive the two-dimensional Fermat flow equation, which may be applied to the planes defined by each discrete azimuth angle in the sonar image. We show that the Fermat flow equation applies to boundary points and surface points which correspond to specular reflections within the 2D plane defined by their azimuth angle measurement. The Fermat flow equation can be used to resolve the 2D location of these surface points within the plane, and therefore also their full 3D location. This is achieved by translating the sensor to estimate the spatial gradient of the range measurement. This method does not rely on the precise image intensity values or the reflectivity of the imaged surface to solve for the surface point locations. We demonstrate the effectiveness of our proposed method by reconstructing 3D object points on both simulated and real-world datasets.

We introduce rendering algorithms for the simulation of speckle statistics observed in scattering media under coherent near-field imaging conditions. Our work is motivated by the recent proliferation of techniques that use speckle correlations for tissue imaging applications: The ability to simulate the image measurements used by these speckle imaging techniques in a physically-accurate and computationally-efficient way can facilitate the widespread adoption and improvement of these techniques. To this end, we draw inspiration from recently-introduced Monte Carlo algorithms for rendering speckle statistics under far-field conditions (collimated sensor and illumination). We derive variants of these algorithms that are better suited to the near-field conditions (focused sensor and illumination) required by tissue imaging applications. Our approach is based on using Gaussian apodization to approximate the sensor and illumination aperture, as well as von Mises-Fisher functions to approximate the phase function of the scattering material. We show that these approximations allow us to derive closed-form expressions for the focusing operations involved in simulating near-field speckle patterns. As we demonstrate in our experiments, these approximations accelerate speckle rendering simulations by a few orders of magnitude compared to previous techniques, at the cost of negligible bias. We validate the accuracy of our algorithms by reproducing ground truth speckle statistics simulated using wave-optics solvers, and real-material measurements available in the literature. Finally, we use our algorithms to simulate biomedical imaging techniques for focusing through tissue.

We introduce a new interferometric imaging methodology that we term interferometry with coded mutual intensity, which allows selectively imaging photon paths based on attributes such as their length and endpoints. At the core of our methodology is a new technical result that shows that manipulating the spatial coherence properties of the light source used in an interferometric system is equivalent, through a Fourier transform, to implementing light path probing patterns. These patterns can be applied to either the coherent transmission matrix, or the incoherent light transport matrix describing the propagation of light in a scene. We test our theory by building a prototype inspired by the Michelson interferometer, extended to allow for programmable phase and amplitude modulation of the illumination injected in the interferometer. We use our prototype to perform experiments such as visualizing complex fields, capturing direct and global transport components, acquiring light transport matrices, and performing anisotropic descattering, both in steady-state imaging and, by combining our technique with optical coherence tomography, in transient imaging.

We introduce a suite of Langevin Monte Carlo algorithms for efficient photorealistic rendering of scenes with complex light transport effects, such as caustics, interreflections, and occlusions. Our algorithms operate in primary sample space, and use the Metropolis-adjusted Langevin algorithm (MALA) to generate new samples. Drawing inspiration from state-of-the-art stochastic gradient descent procedures, we combine MALA with adaptive preconditioning and momentum schemes that re-use previously-computed first-order gradients, either in an online or in a cache-driven fashion. This combination allows MALA to adapt to the local geometry of the primary sample space, without the computational overhead associated with previous Hessian-based adaptation algorithms. We use the theory of controlled Markov chain Monte Carlo to ensure that these combinations remain ergodic, and are therefore suitable for unbiased Monte Carlo rendering. Through extensive experiments, we show that our algorithms, MALA with online and cache-driven adaptation, can successfully handle complex light transport in a large variety of scenes, leading to improved performance (on average more than 3× variance reduction at equal time, and 7× for motion blur) compared to state-of-the-art Markov chain Monte Carlo rendering algorithms.

Rendering radiative transfer through media with a heterogeneous refractive index is challenging because the continuous refractive index variations result in light traveling along curved paths. Existing algorithms are based on photon mapping techniques, and thus are biased and result in strong artifacts. On the other hand, existing unbiased methods such as path tracing and bidirectional path tracing cannot be used in their current form to simulate media with a heterogeneous refractive index. We change this state of affairs by deriving unbiased path tracing estimators for this problem. Starting from the refractive radiative transfer equation (RRTE), we derive a path-integral formulation, which we use to generalize path tracing with next-event estimation and bidirectional path tracing to the heterogeneous refractive index setting. We then develop an optimization approach based on fast analytic derivative computations to produce the point-to-point connections required by these path tracing algorithms. We propose several acceleration techniques to handle complex scenes (surfaces and volumes) that include participating media with heterogeneous refractive fields. We use our algorithms to simulate a variety of scenes combining heterogeneous refraction and scattering, as well as tissue imaging techniques based on ultrasonic virtual waveguides and lenses. Our algorithms and publicly-available implementation can be used to characterize imaging systems such as refractive index microscopy, schlieren imaging, and acousto-optic imaging, and can facilitate the development of inverse rendering techniques for related applications.

Physics-based differentiable rendering, the estimation of derivatives of radiometric measures with respect to arbitrary scene parameters, has a diverse array of applications from solving analysis-by-synthesis problems to training machine learning pipelines incorporating forward rendering processes. Unfortunately, general-purpose differentiable rendering remains challenging due to the lack of efficient estimators as well as the need to identify and handle complex discontinuities such as visibility boundaries. In this paper, we show how path integrals can be differentiated with respect to arbitrary differentiable changes of a scene. We provide a detailed theoretical analysis of this process and establish new differentiable rendering formulations based on the resulting differential path integrals. Our path-space differentiable rendering formulation allows the design of new Monte Carlo estimators that offer significantly better efficiency than state-of-the-art methods in handling complex geometric discontinuities and light transport phenomena such as caustics. We validate our method by comparing our derivative estimates to those generated using the finite-difference method. To demonstrate the effectiveness of our technique, we compare inverse-rendering performance with a few state-of-the-art differentiable rendering methods.

Non-line-of-sight (NLOS) imaging is the problem of reconstructing properties of scenes occluded from a sensor, using measurements of light that indirectly travels from the occluded scene to the sensor through intermediate diffuse reflections. We introduce an analysis-by-synthesis framework that can reconstruct complex shape and reflectance of an NLOS object. Our framework deviates from prior work on NLOS reconstruction, by directly optimizing for a surface representation of the NLOS object, in place of commonly employed volumetric representations. At the core of our framework is a new rendering formulation that efficiently computes derivatives of radiometric measurements with respect to NLOS geometry and reflectance, while accurately modeling the underlying light transport physics. By coupling this with stochastic optimization and geometry processing techniques, we are able to reconstruct NLOS surface at a level of detail significantly exceeding what is possible with previous volumetric reconstruction methods.

We present a novel theory of Fermat paths of light between a known visible scene and an unknown object not in the line of sight of a transient camera. These light paths either obey specular reflection or are reflected by the object's boundary, and hence encode the shape of the hidden object. We prove that Fermat paths correspond to discontinuities in the transient measurements. We then derive a novel constraint that relates the spatial derivatives of the path lengths at these discontinuities to the surface normal. Based on this theory, we present an algorithm, called Fermat Flow, to estimate the shape of the non-line-of-sight object. Our method allows, for the first time, accurate shape recovery of complex objects, ranging from diffuse to specular, that are hidden around the corner as well as hidden behind a diffuser. Finally, our approach is agnostic to the particular technology used for transient imaging. As such, we demonstrate mm-scale shape recovery from pico-second scale transients using a SPAD and ultrafast laser, as well as micron-scale reconstruction from femto-second scale transients using interferometry. We believe our work is a significant advance over the state-of-the-art in non-line-of-sight imaging.

Image sensors that can measure the time of travel of photons are gaining importance in a myriad of applications such as LIDAR, non-line of sight imaging, light-in-flight imaging, and imaging through scattering media. While the price of these sensors is dramatically shrinking, there remains a trade-off between spatial resolution and temporal resolution. While single-pixel detectors using the single photon avalanche diode (SPAD) technology can achieve 10-30 ps time resolution, the current generation array detectors can only produce an order of magnitude lower temporal resolution due to space-related fabrication constraints. Moreover, this limit is due to bandwidth, read-out and circuit-area constraints on the detector array and therefore unlikely to dramatically change in the next few years.In this paper, we demonstrate a computational imaging approach that utilizes multiple measurements with calibrated sub-temporal resolution delays on the illumination pulse and super-resolution post-processing algorithms that together can achieve an order of magnitude improvement in the time resolution of the acquired transients. We build an experimental prototype, using a 32 × 32 SPAD detector array with 400ps time resolution and demonstrate recovery of transients with ≈ 50ps time resolution, an 8× improvement in time resolution resulting in a 5× improvement in depth reconstruction error.

Non-line-of-sight (NLOS) imaging aims to reconstruct scenes outside the field of view of an imaging system. A common approach is to measure the so-called light transients, which facilitates reconstructions through ellipsoidal tomography that involves solving a linear least-squares. Unfortunately, the corresponding linear operator is very high-dimensional and lacks structures that facilitate fast solvers, and so, the ensuing optimization is a computationally daunting task. We introduce a computationally tractable framework for solving the ellipsoidal tomography problem. Our main observation is that the Gram of the ellipsoidal tomography operator is convolutional, either exactly under certain idealized imaging conditions, or approximately in practice. This, in turn, allows us to obtain the ellipsoidal tomography solution by using efficient deconvolution procedures to solve a linear least-squares problem involving the Gram operator. The computational tractability of our approach also facilitates the use of various regularizers during the deconvolution procedure. We demonstrate the advantages of our framework in a variety of simulated and real experiments.

We present a Monte Carlo rendering framework for the physically-accurate simulation of speckle patterns arising from volumetric scattering of coherent waves. These noise-like patterns are characterized by strong statistical properties, such as the so-called memory effect. These properties are at the core of imaging techniques for applications as diverse as tissue imaging, motion tracking, and non-line-of-sight imaging. Our rendering framework can replicate these properties computationally, in a way that is orders of magnitude more efficient than alternatives based on directly solving the wave equations. At the core of our framework is a path-space formulation for the covariance of speckle patterns arising from a scattering volume, which we derive from first principles. We use this formulation to develop two Monte Carlo rendering algorithms, for computing speckle covariance as well as directly speckle fields. While approaches based on wave equation solvers require knowing the microscopic position of wavelength-sized scatterers, our approach takes as input only bulk parameters describing the statistical distribution of these scatterers inside a volume. We validate the accuracy of our framework by comparing against speckle patterns simulated using wave equation solvers, use it to simulate memory effect observations that were previously only possible through lab measurements, and demonstrate its applicability for computational imaging tasks.

During the last decade, we have been witnessing the continued development of new time-of-flight imaging devices, and their increased use in numerous and varied applications. However, physics-based rendering techniques that can accurately simulate these devices are still lacking: while existing algorithms are adequate for certain tasks, such as simulating transient cameras, they are very inefficient for simulating time-gated cameras because of the large number of wasted path samples. We take steps towards addressing these deficiencies, by introducing a procedure for efficiently sampling paths with a predetermined length, and incorporating it within rendering frameworks tailored towards simulating time-gated imaging. We use our open-source implementation of the above to empirically demonstrate improved rendering performance in a variety of applications, including simulating proximity sensors, imaging through occlusions, depth-selective cameras, transient imaging in dynamic scenes, and non-line-of-sight imaging.

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.

Edges in images of translucent objects are very different from edges in images of opaque objects. The physical causes for these differences are hard to characterize analytically and are not well understood. This paper considers one class of translucency edges-those caused by a discontinuity in surface orientation-and describes the physical causes of their appearance. We simulate thousands of translucency edge profiles using many different scattering material parameters, and we explain the resulting variety of edge patterns by qualitatively analyzing light transport. We also discuss the existence of shape and material metamers, or combinations of distinct shape or material parameters that generate the same edge profile. This knowledge is relevant to visual inference tasks that involve translucent objects, such as shape or material estimation.

We present a computational imaging system, inspired by the optical coherence tomography (OCT) framework, that uses interferometry to produce decompositions of light transport in small scenes or volumes. The system decomposes transport according to various attributes of the paths that photons travel through the scene, including where on the source the paths originate, their pathlengths from source to camera through the scene, their wavelength, and their polarization. Since it uses interference, the system can achieve high pathlength resolutions, with the ability to distinguish paths whose lengths differ by as little as ten microns. We describe how to construct and optimize an optical assembly for this technique, and we build a prototype to measure and visualize three-dimensional shape, direct and indirect reflection components, and properties of scattering, refractive/dispersive, and birefringent materials.

Achieving computer vision on microscale devices is a challenge. On these platforms, the power and mass constraints are severe enough for even the most common computations (matrix manipulations, convolution, etc.) to be difficult. This paper proposes and analyzes a class of miniature vision sensors that can help overcome these constraints. These sensors reduce power requirements through template-based optical convolution, and they enable a wide field-of-view within a small form through a refractive optical design. We describe the tradeoffs between the field-of-view, volume, and mass of these sensors and we provide analytic tools to navigate the design space. We demonstrate milliscale prototypes for computer vision tasks such as locating edges, tracking targets, and detecting faces. Finally, we utilize photolithographic fabrication tools to further miniaturize the optical designs and demonstrate fiducial detection onboard a small autonomous air vehicle.

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 article 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 functions 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.

Translucent materials are ubiquitous, and simulating their appearance requires accurate physical parameters. However, physically-accurate 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 single-scattering 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.

Achieving computer vision on micro-scale devices is a challenge. On these platforms, the power and mass constraints are severe enough for even the most common computations (matrix manipulations, convolution, etc.) to be difficult. This paper proposes and analyzes a class of miniature vision sensors that can help overcome these constraints. These sensors reduce power requirements through template-based optical convolution, and they enable a wide field-of-view within a small form through a novel optical design. We describe the trade-offs between the field of view, volume, and mass of these sensors and we provide analytic tools to navigate the design space. We also demonstrate milli-scale prototypes for computer vision tasks such as locating edges, tracking targets, and detecting faces.

We propose an approach for linear unsupervised dimensionality reduction, based on the sparse linear model that has been used to probabilistically interpret sparse coding. We formulate an optimization problem for learning a linear projection from the original signal domain to a lower-dimensional one in a way that approximately preserves, in expectation, pairwise inner products in the sparse domain. We derive solutions to the problem, present nonlinear extensions, and discuss relations to compressed sensing. Our experiments using facial images, texture patches, and images of object categories suggest that the approach can improve our ability to recover meaningful structure in many classes of signals.

We propose an alternative interpretation of Bayesian surprise in the spatial domain, to account for saliency arising from contrast in image context. Our saliency formulation is integrated in three different application scenaria, with considerable improvements in performance: 1) visual attention prediction, validated using eye- and mouse-tracking data, 2) region of interest detection, to improve scale selection and localization, 3) image quality assessment to achieve better agreement with subjective human evaluations.