It is a mystery how the brain decodes color vision purely from the optic nerve signals it receives, with a core inferential challenge being how it disentangles internal perception with the correct color dimensionality from the unknown encoding properties of the eye. In this paper, we introduce a computational framework for modeling this emergence of human color vision by simulating both the eye and the cortex. Existing research often overlooks how the cortex develops color vision or represents color space internally, assuming that the color dimensionality is known a priori; however, we argue that the visual cortex has the capability and the challenge of inferring the color dimensionality purely from fluctuations in the optic nerve signals. To validate our theory, we introduce a simulation engine for biological eyes based on established vision science and generate optic nerve signals resulting from looking at natural images. Further, we propose a bio-plausible model of cortical learning based on self-supervised prediction of optic nerve signal fluctuations under natural eye motions. We show that this model naturally learns to generate color vision by disentangling retinal invariants from the sensory signals. When the retina contains $N$ types of color photoreceptors, our simulation shows that $N$-dimensional color vision naturally emerges, verified through formal colorimetry. Using this framework, we also present the first simulation work that successfully boosts the color dimensionality, as observed in gene therapy on squirrel monkeys, and demonstrates the possibility of enhancing human color vision from 3D to 4D.

Genetic studies indicate that more than 50% of women are genetically tetrachromatic, expressing four distinct types of color photoreceptors (cone cells) in the retina. At least one functional tetrachromat has been identified in laboratory tests. We hypothesize that there is a large latent group in the population capable of fundamentally richer color experience, but we are not yet aware of this group because of a lack of tetrachromatic colors in the visual environment. This paper develops theory and engineering practice for fabricating tetrachromatic colors and potentially identifying tetrachromatic color vision in the wild. First, we apply general d -dimensional color theory to derive and compute all the key color structures of human tetrachromacy for the first time, including its 4D space of possible object colors, 3D space of chromaticities, and yielding a predicted 2D sphere of tetrachromatic hues. We compare this predicted hue sphere to the familiar hue circle of trichromatic color, extending the theory to predict how the higher dimensional topology produces an expanded color experience for tetrachromats. Second, we derive the four reflectance functions for the ideal tetrachromatic inkset, analogous to the well-known CMY printing basis for trichromacy. Third, we develop a method for prototyping tetrachromatic printers using a library of fountain pen inks and a multi-pass inkjet printing platform. Fourth, we generalize existing color tests - sensitive hue ordering tests and rapid isochromatic plate screening tests - to higher-dimensional vision, and prototype variants of these tests for identifying and characterizing tetrachromacy in the wild.

Measurements from the Event Horizon Telescope enabled the visualization of light emission around a black hole for the first time. So far, these measurements have been used to recover a 2D image under the assumption that the emission field is static over the period of acquisition. In this work, we propose BH-NeRF, a novel tomography approach that leverages gravitational lensing to recover the continuous 3D emission field near a black hole. Compared to other 3D reconstruction or tomography settings, this task poses two significant challenges: first, rays near black holes follow curved paths dictated by general relativity, and second, we only observe measurements from a single viewpoint. Our method captures the unknown emission field using a continuous volumetric function parameterized by a coordinate-based neural network, and uses knowledge of Keplerian orbital dynamics to establish correspondence between 3D points over time. Together, these enable BHNeRF to recover accurate 3D emission fields, even in challenging situations with sparse measurements and uncertain orbital dynamics. This work takes the first steps in showing how future measurements from the Event Horizon Telescope could be used to recover evolving 3D emission around the supermassive black hole in our Galactic center.

Coordinate-based neural representations have shown significant promise as an alternative to discrete, array-based representations for complex low dimensional signals. However, optimizing a coordinate-based network from randomly initialized weights for each new signal is inefficient. We propose applying standard meta-learning algorithms to learn the initial weight parameters for these fully-connected networks based on the underlying class of signals being represented (e.g., images of faces or 3D models of chairs). Despite requiring only a minor change in implementation, using these learned initial weights enables faster convergence during optimization and can serve as a strong prior over the signal class being modeled, resulting in better generalization when only partial observations of a given signal are available. We explore these benefits across a variety of tasks, including representing 2D images, reconstructing CT scans, and recovering 3D shapes and scenes from 2D image observations.

We present a method for optimization-based recovery of eye motion from rolling shutter video of the retina. Our approach formulates eye tracking as an optimization problem that jointly estimates the retina’s motion and appearance using convex optimization and a constrained version of gradient descent. By incorporating the rolling shutter imaging model into the formulation of our joint optimization, we achieve state-of-the-art accuracy both offline and in real-time. We apply our method to retina video captured with an adaptive optics scanning laser ophthalmoscope (AOSLO), demonstrating eye tracking at 1 kHz with accuracies below one arcminute—over an order of magnitude higher than conventional eye tracking systems.

We introduce a method to render Neural Radiance Fields (NeRFs) in real time using PlenOctrees, an octree-based 3D representation which supports view-dependent effects. Our method can render 800×800 images at more than 150 FPS, which is over 3000 times faster than conventional NeRFs. We do so without sacrificing quality while preserving the ability of NeRFs to perform free-viewpoint rendering of scenes with arbitrary geometry and view-dependent effects. Real-time performance is achieved by pre-tabulating the NeRF into a PlenOctree. In order to preserve view-dependent effects such as specularities, we factorize the appearance via closed-form spherical basis functions. Specifically, we show that it is possible to train NeRFs to predict a spherical harmonic representation of radiance, removing the viewing direction as an input to the neural network. Furthermore, we show that PlenOctrees can be directly optimized to further minimize the reconstruction loss, which leads to equal or better quality compared to competing methods. Moreover, this octree optimization step can be used to reduce the training time, as we no longer need to wait for the NeRF training to converge fully. Our real-time neural rendering approach may potentially enable new applications such as 6-DOF industrial and product visualizations, as well as next generation AR/VR systems. PlenOctrees are amenable to in-browser rendering as well; please visit the project page for the interactive online demo, as well as video and code: https://alexyu.net/plenoctrees.

Printed and digitally displayed photos have the ability to hide imperceptible digital data that can be accessed through internet-connected imaging systems. Another way to think about this is physical photographs that have unique QR codes invisibly embedded within them. This paper presents an architecture, algorithms, and a prototype implementation addressing this vision. Our key technical contribution is StegaStamp, a learned steganographic algorithm to enable robust encoding and decoding of arbitrary hyperlink bitstrings into photos in a manner that approaches perceptual invisibility. StegaStamp comprises a deep neural network that learns an encoding/decoding algorithm robust to image perturbations approximating the space of distortions resulting from real printing and photography. We demonstrates real-time decoding of hyperlinks in photos from in-the-wild videos that contain variation in lighting, shadows, perspective, occlusion and viewing distance. Our prototype system robustly retrieves 56 bit hyperlinks after error correction -- sufficient to embed a unique code within every photo on the internet.

We show that passing input points through a simple Fourier feature mapping enables a multilayer perceptron (MLP) to learn high-frequency functions in low-dimensional problem domains. These results shed light on recent advances in computer vision and graphics that achieve state-of-the-art results by using MLPs to represent complex 3D objects and scenes. Using tools from the neural tangent kernel (NTK) literature, we show that a standard MLP has impractically slow convergence to high frequency signal components. To overcome this spectral bias, we use a Fourier feature mapping to transform the effective NTK into a stationary kernel with a tunable bandwidth. We suggest an approach for selecting problem-specific Fourier features that greatly improves the performance of MLPs for low-dimensional regression tasks relevant to the computer vision and graphics communities.

Holographic displays can create high quality 3D images while maintaining a small form factor suitable for head-mounted virtual and augmented reality systems. However, holographic displays have limited étendue based on the number of pixels in their spatial light modulators, creating a tradeoff between the eyebox size and the field-of-view. Scattering-based étendue expansion, in which coherent light is focused into an image after being scattered by a static mask, is a promising avenue to break this tradeoff. However, to date, this approach has been limited to very sparse content consisting of, for example, only tens of spots. In this work, we introduce new algorithms to scattering-based étendue expansion that support dense, photorealistic imagery at the native resolution of the spatial light modulator, offering up to a 20 dB improvement in peak signal to noise ratio over baseline methods. We propose spatial and frequency constraints to optimize performance for human perception, and performance is characterized both through simulation and a preliminary benchtop prototype. We further demonstrate the ability to generate content at multiple depths, and we provide a path for the miniaturization of our benchtop prototype into a sunglasses-like form factor.

Casually-taken portrait photographs often suffer from unflattering lighting and shadowing because of suboptimal conditions in the environment. Aesthetic qualities such as the position and softness of shadows and the lighting ratio between the bright and dark parts of the face are frequently determined by the constraints of the environment rather than by the photographer. Professionals address this issue by adding light shaping tools such as scrims, bounce cards, and flashes. In this paper, we present a computational approach that gives casual photographers some of this control, thereby allowing poorly-lit portraits to be relit post-capture in a realistic and easily-controllable way. Our approach relies on a pair of neural networks---one to remove foreign shadows cast by external objects, and another to soften facial shadows cast by the features of the subject and to add a synthetic fill light to improve the lighting ratio. To train our first network we construct a dataset of real-world portraits wherein synthetic foreign shadows are rendered onto the face, and we show that our network learns to remove those unwanted shadows. To train our second network we use a dataset of Light Stage scans of human subjects to construct input/output pairs of input images harshly lit by a small light source, and variably softened and fill-lit output images of each face. We propose a way to explicitly encode facial symmetry and show that our dataset and training procedure enable the model to generalize to images taken in the wild. Together, these networks enable the realistic and aesthetically pleasing enhancement of shadows and lights in real-world portrait images. 1

We explore the problem of view synthesis from a narrow baseline pair of images, and focus on generating high-quality view extrapolations with plausible disocclusions. Our method builds upon prior work in predicting a multiplane image (MPI), which represents scene content as a set of RGBA planes within a reference view frustum and renders novel views by projecting this content into the target viewpoints. We present a theoretical analysis showing how the range of views that can be rendered from an MPI increases linearly with the MPI disparity sampling frequency, as well as a novel MPI prediction procedure that theoretically enables view extrapolations of up to 4 times the lateral viewpoint movement allowed by prior work. Our method ameliorates two specific issues that limit the range of views renderable by prior methods: 1) We expand the range of novel views that can be rendered without depth discretization artifacts by using a 3D convolutional network architecture along with a randomized-resolution training procedure to allow our model to predict MPIs with increased disparity sampling frequency. 2) We reduce the repeated texture artifacts seen in disocclusions by enforcing a constraint that the appearance of hidden content at any depth must be drawn from visible content at or behind that depth.

This paper shows that when applying machine learning to digital zoom, it is beneficial to operate on real, RAW sensor data. Existing learning-based super-resolution methods do not use real sensor data, instead operating on processed RGB images. We show that these approaches forfeit detail and accuracy that can be gained by operating on raw data, particularly when zooming in on distant objects. The key barrier to using real sensor data for training is that ground-truth high-resolution imagery is missing. We show how to obtain such ground-truth data via optical zoom and contribute a dataset, SR-RAW, for real-world computational zoom. We use SR-RAW to train a deep network with a novel contextual bilateral loss that is robust to mild misalignment between input and outputs images. The trained network achieves state-of-the-art performance in 4X and 8X computational zoom. We also show that synthesizing sensor data by resampling high-resolution RGB images is an oversimplified approximation of real sensor data and noise, resulting in worse image quality.

Because image sensor chips have a finite bandwidth with which to read out pixels, recording video typically requires a trade-off between frame rate and pixel count. Compressed sensing techniques can circumvent this trade-off by assuming that the image is compressible. Here, we propose using multiplexing optics to spatially compress the scene, enabling information about the whole scene to be sampled from a row of sensor pixels, which can be read off quickly via a rolling shutter CMOS sensor. Conveniently, such multiplexing can be achieved with a simple lensless, diffuser-based imaging system. Using sparse recovery methods, we are able to recover 140 video frames at over 4,500 frames per second, all from a single captured image with a rolling shutter sensor. Our proof-of-concept system uses easily-fabricated diffusers paired with an off-the-shelf sensor. The resulting prototype enables compressive encoding of high frame rate video into a single rolling shutter exposure, and exceeds the sampling-limited performance of an equivalent global shutter system for sufficiently sparse objects.

We present a practical and robust deep learning solution for capturing and rendering novel views of complex real world scenes for virtual exploration. Previous approaches either require intractably dense view sampling or provide little to no guidance for how users should sample views of a scene to reliably render high-quality novel views. Instead, we propose an algorithm for view synthesis from an irregular grid of sampled views that first expands each sampled view into a local light field via a multiplane image (MPI) scene representation, then renders novel views by blending adjacent local light fields. We extend traditional plenoptic sampling theory to derive a bound that specifies precisely how densely users should sample views of a given scene when using our algorithm. In practice, we apply this bound to capture and render views of real world scenes that achieve the perceptual quality of Nyquist rate view sampling while using up to 4000X fewer views. We demonstrate our approach's practicality with an augmented reality smart-phone app that guides users to capture input images of a scene and viewers that enable realtime virtual exploration on desktop and mobile platforms.

In cinema, large camera lenses create beautiful shallow depth of field (DOF), but make focusing difficult and expensive. Accurate cinema focus usually relies on a script and a person to control focus in realtime. Casual videographers often crave cinematic focus, but fail to achieve it. We either sacrifice shallow DOF, as in smartphone videos; or we struggle to deliver accurate focus, as in videos from larger cameras. This paper is about a new approach in the pursuit of cinematic focus for casual videography. We present a system that synthetically renders refocusable video from a deep DOF video shot with a smartphone, and analyzes future video frames to deliver context-aware autofocus for the current frame. To create refocusable video, we extend recent machine learning methods designed for still photography, contributing a new dataset for machine training, a rendering model better suited to cinema focus, and a filtering solution for temporal coherence. To choose focus accurately for each frame, we demonstrate autofocus that looks at upcoming video frames and applies AI-assist modules such as motion, face, audio and saliency detection. We also show that autofocus benefits from machine learning and a large-scale video dataset with focus annotation, where we use our RVR-LAAF GUI to create this sizable dataset efficiently. We deliver, for example, a shallow DOF video where the autofocus transitions onto each person before she begins to speak. This is impossible for conventional camera autofocus because it would require seeing into the future.

We present a technique for jointly denoising bursts of images taken from a handheld camera. In particular, we propose a convolutional neural network architecture for predicting spatially varying kernels that can both align and denoise frames, a synthetic data generation approach based on a realistic noise formation model, and an optimization guided by an annealed loss function to avoid undesirable local minima. Our model matches or outperforms the state-of-the-art across a wide range of noise levels on both real and synthetic data.

We present a novel method to train machine learning algorithms to estimate scene depths from a single image, by using the information provided by a camera's aperture as supervision. Prior works use a depth sensor's outputs or images of the same scene from alternate viewpoints as supervision, while our method instead uses images from the same viewpoint taken with a varying camera aperture. To enable learning algorithms to use aperture effects as supervision, we introduce two differentiable aperture rendering functions that use the input image and predicted depths to simulate the depth-of-field effects caused by real camera apertures. We train a monocular depth estimation network end-to-end to predict the scene depths that best explain these finite aperture images as defocus-blurred renderings of the input all-in-focus image.

We present an approach to separating reflection from a single image. The approach uses a fully convolutional network trained end-to-end with losses that exploit low-level and high-level image information. Our loss function includes two perceptual losses: a feature loss from a visual perception network, and an adversarial loss that encodes characteristics of images in the transmission layers. We also propose a novel exclusion loss that enforces pixel-level layer separation. We create a dataset of real-world images with reflection and corresponding ground-truth transmission layers for quantitative evaluation and model training. We validate our method through comprehensive quantitative experiments and show that our approach outperforms state-of-the-art reflection removal methods in PSNR, SSIM, and perceptual user study. We also extend our method to two other image enhancement tasks to demonstrate the generality of our approach.

We study the problem of deblurring light fields of general 3D scenes captured under 3D camera motion and present both theoretical and practical contributions. By analyzing the motion-blurred light field in the primal and Fourier domains, we develop intuition into the effects of camera motion on the light field, show the advantages of capturing a 4D light field instead of a conventional 2D image for motion deblurring, and derive simple analytical methods of motion deblurring in certain cases. We then present an algorithm to blindly deblur light fields of general scenes without any estimation of scene geometry, and demonstrate that we can recover both the sharp light field and the 3D camera motion path of real and synthetically-blurred light fields.

We present a machine learning algorithm that takes as input a 2D RGB image and synthesizes a 4D RGBD light field (color and depth of the scene in each ray direction). For training, we introduce the largest public light field dataset, consisting of over 3300 plenoptic camera light fields of scenes containing flowers and plants. Our synthesis pipeline consists of a convolutional neural network (CNN) that estimates scene geometry, a stage that renders a Lambertian light field using that geometry, and a second CNN that predicts occluded rays and non-Lambertian effects. Our algorithm builds on recent view synthesis methods, but is unique in predicting RGBD for each light field ray and improving unsupervised single image depth estimation by enforcing consistency of ray depths that should intersect the same scene point.

Computer-graphics engineers and vision scientists want to generate images that reproduce realistic depth-dependent blur. Current rendering algorithms take into account scene geometry, aperture size, and focal distance, and they produce photorealistic imagery as with a high-quality camera. But to create immersive experiences, rendering algorithms should aim instead for perceptual realism. In so doing, they should take into account the significant optical aberrations of the human eye. We developed a method that, by incorporating some of those aberrations, yields displayed images that produce retinal images much closer to the ones that occur in natural viewing. In particular, we create displayed images taking the eye's chromatic aberration into account. This produces different chromatic effects in the retinal image for objects farther or nearer than current focus. We call the method ChromaBlur. We conducted two experiments that illustrate the benefits of ChromaBlur. One showed that accommodation (eye focusing) is driven quite effectively when ChromaBlur is used and that accommodation is not driven at all when conventional methods are used. The second showed that perceived depth and realism are greater with imagery created by ChromaBlur than in imagery created conventionally. ChromaBlur can be coupled with focus-adjustable lenses and gaze tracking to reproduce the natural relationship between accommodation and blur in HMDs and other immersive devices. It may thereby minimize the adverse effects of vergence-accommodation conflicts.

We capture 4D light field data in a single 2D sensor image by encoding spatio-angular information into a speckle field (causticpattern) through a phase diffuser. Using wave-optics theory and a coherent phase retrieval method, we calibrate the system by measuring the diffuser surface height from through-focus images. Wave-optics theory further informs the design of system geometry such that a purely additive ray-optics model is valid. Light field reconstruction is done using nonlinear matrix inversion methods, including ℓ1 minimization. We demonstrate a prototype system and present empirical results of 4D light field reconstruction and computational refocusing from a single diffuser-encoded 2D image.

2D spatial image windows are used for comparing pixel values in computer vision applications such as correspondence for optical flow and 3D reconstruction, bilateral filtering, and image segmentation. However, pixel window comparisons can suffer from varying defocus blur and perspective at different depths, and can also lead to a loss of precision. In this paper, we leverage the recent use of light-field cameras to propose alternative oriented light-field windows that enable more robust and accurate pixel comparisons. For Lambertian surfaces focused to the correct depth, the 2D distribution of angular rays from a pixel remains consistent. We build on this idea to develop an oriented 4D light-field window that accounts for shearing (depth), translation (matching), and windowing. Our main application is to scene flow, a generalization of optical flow to the 3D vector field describing the motion of each point in the scene. We show significant benefits of oriented light-field windows over standard 2D spatial windows. We also demonstrate additional applications of oriented light-field windows for bilateral filtering and image segmentation.

This paper presents a method for efficient compression and relighting with high-resolution, precomputed light transport matrices. We accomplish this using a 4D wavelet transform, transforming the columns of the transport matrix, in addition to the 2D row transform used in previous work. We show that a standard 4D wavelet transform can actually inflate portions of the matrix, because high-frequency lights lead to high-frequency images that cannot easily be compressed. Therefore, we present an adaptive 4D wavelet transform that terminates at a level that avoids inflation and maximizes sparsity in the matrix data. Finally, we present an algorithm for fast relighting from adaptively compressed transport matrices. Combined with a GPU-based precomputation pipeline, this results in an image and geometry relighting system that performs significantly better than 2D compression techniques, on average 2x-3x better in terms of storage cost and rendering speed for equal quality matrices.

By inserting a microlens array into the optical train of a conventional microscope, one can capture light fields of biological specimens in a single photograph. Although diffraction places a limit on the product of spatial and angular resolution in these light fields, we can nevertheless produce useful perspective views and focal stacks from them. Since microscopes are inherently orthographic devices, perspective views represent a new way to look at microscopic specimens. The ability to create focal stacks from a single photograph allows moving or light-sensitive specimens to be recorded. Applying 3D deconvolution to these focal stacks, we can produce a set of cross sections, which can be visualized using volume rendering. In this paper, we demonstrate a prototype light field microscope (LFM), analyze its optical performance, and show perspective views, focal stacks, and reconstructed volumes for a variety of biological specimens. We also show that synthetic focusing followed by 3D deconvolution is equivalent to applying limited-angle tomography directly to the 4D light field.

This paper contributes to the theory of photograph formation from light fields. The main result is a theorem that, in the Fourier domain, a photograph formed by a full lens aperture is a 2D slice in the 4D light field. Photographs focused at different depths correspond to slices at different trajectories in the 4D space. The paper demonstrates the utility of this theorem in two different ways. First, the theorem is used to analyze the performance of digital refocusing, where one computes photographs focused at different depths from a single light field. The analysis shows in closed form that the sharpness of refocused photographs increases linearly with directional resolution. Second, the theorem yields a Fourier-domain algorithm for digital refocusing, where we extract the appropriate 2D slice of the light field's Fourier transform, and perform an inverse 2D Fourier transform. This method is faster than previous approaches.

This paper focuses on efficient rendering based on pre-computed light transport, with realistic materials and shadows under all-frequency direct lighting such an environment maps. The basic difficulty is representation and computation in the 6D space of light direction, view direction, and surface position. While image-based and synthetic methods for real-time rendering have been proposed, they do not scale to high sampling rates with variation of both lighting and viewpoint. Current approaches are therefore limited to lower dimensionality (only lighting or viewpoint variation, not both) or lower sampling rates (low frequency lighting and materials). We propose a new mathematical and computational analysis of pre-computed light transport. We use factored forms, separately pre-computing and representing visibility and material properties. Rendering then requires computing triple product integrals at each vertex, involving the lighting, visibility and BRDF. Our main contribution is a general analysis of these triple product integrals, which are likely to have broad applicability in computer graphics and numerical analysis. We first determine the computational complexity in a number of bases like point samples, spherical harmonics and wavelets. We then give efficient linear and sublinear-time algorithms for Haar wavelets, incorporating non-linear wavelet approximation of lighting and BRDFs. Practically, we demonstrate rendering of images under new lighting and viewing conditions in a few seconds, significantly faster than previous techniques.

We present a method, based on pre-computed light transport, for real-time rendering of objects under all-frequency, time-varying illumination represented as a high-resolution environment map. Current techniques are limited to small area lights, with sharp shadows, or large low-frequency lights, with very soft shadows. Our main contribution is to approximate the environment map in a wavelet basis, keeping only the largest terms (this is known as a non-linear approximation ). We obtain further compression by encoding the light transport matrix sparsely but accurately in the same basis. Rendering is performed by multiplying a sparse light vector by a sparse transport matrix, which is very fast. For accurate rendering, using non-linear wavelets is an order of magnitude faster than using linear spherical harmonics, the current best technique.

We describe Chromium, a system for manipulating streams of graphics API commands on clusters of workstations. Chromium's stream filters can be arranged to create sort-first and sort-last parallel graphics architectures that, in many cases, support the same applications while using only commodity graphics accelerators. In addition, these stream filters can be extended programmatically, allowing the user to customize the stream transformations performed by nodes in a cluster. Because our stream processing mechanism is completely general, any cluster-parallel rendering algorithm can be either implemented on top of or embedded in Chromium. In this paper, we give examples of real-world applications that use Chromium to achieve good scalability on clusters of workstations, and describe other potential uses of this stream processing technology. By completely abstracting the underlying graphics architecture, network topology, and API command processing semantics, we allow a variety of applications to run in different environments.