Ren Ng

Aviad Levis, Pratul P. Srinivasan, Andrew A. Chael et al.

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 BH-NeRF 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.

Alex Yu, Ruilong Li, Matthew Tancik et al.

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 800x800 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

Matthew Tancik, Ben Mildenhall, Terrance Wang et al.

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.

Kyrollos Yanny, Nick Antipa, William Liberti et al.

Miniature fluorescence microscopes are a standard tool in systems biology. However, widefield miniature microscopes capture only 2D information, and modifications that enable 3D capabilities increase the size and weight and have poor resolution outside a narrow depth range. Here, we achieve the 3D capability by replacing the tube lens of a conventional 2D Miniscope with an optimized multifocal phase mask at the objective's aperture stop. Placing the phase mask at the aperture stop significantly reduces the size of the device, and varying the focal lengths enables a uniform resolution across a wide depth range. The phase mask encodes the 3D fluorescence intensity into a single 2D measurement, and the 3D volume is recovered by solving a sparsity-constrained inverse problem. We provide methods for designing and fabricating the phase mask and an efficient forward model that accounts for the field-varying aberrations in miniature objectives. We demonstrate a prototype that is 17 mm tall and weighs 2.5 grams, achieving 2.76 $μ$m lateral, and 15 $μ$m axial resolution across most of the 900x700x390 $μm^3$ volume at 40 volumes per second. The performance is validated experimentally on resolution targets, dynamic biological samples, and mouse brain tissue. Compared with existing miniature single-shot volume-capture implementations, our system is smaller and lighter and achieves a more than 2x better lateral and axial resolution throughout a 10x larger usable depth range. Our microscope design provides single-shot 3D imaging for applications where a compact platform matters, such as volumetric neural imaging in freely moving animals and 3D motion studies of dynamic samples in incubators and lab-on-a-chip devices.

Matthew Tancik, Pratul P. Srinivasan, Ben Mildenhall et al.

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 fails to learn high frequencies both in theory and in practice. 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.

Xuaner Cecilia Zhang, Jonathan T. Barron, Yun-Ta Tsai et al.

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

Ben Mildenhall, Pratul P. Srinivasan, Matthew Tancik et al.

We present a method that achieves state-of-the-art results for synthesizing novel views of complex scenes by optimizing an underlying continuous volumetric scene function using a sparse set of input views. Our algorithm represents a scene using a fully-connected (non-convolutional) deep network, whose input is a single continuous 5D coordinate (spatial location $(x,y,z)$ and viewing direction $(θ, φ)$) and whose output is the volume density and view-dependent emitted radiance at that spatial location. We synthesize views by querying 5D coordinates along camera rays and use classic volume rendering techniques to project the output colors and densities into an image. Because volume rendering is naturally differentiable, the only input required to optimize our representation is a set of images with known camera poses. We describe how to effectively optimize neural radiance fields to render photorealistic novel views of scenes with complicated geometry and appearance, and demonstrate results that outperform prior work on neural rendering and view synthesis. View synthesis results are best viewed as videos, so we urge readers to view our supplementary video for convincing comparisons.

Nick Antipa, Patrick Oare, Emrah Bostan et al.

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.

Xuaner Zhang, Kevin Matzen, Vivien Nguyen et al.

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.

Xuaner Cecilia Zhang, Qifeng Chen, Ren Ng et al.

This paper shows that when applying machine learning to digital zoom for photography, it is beneficial to use real, RAW sensor data for training. Existing learning-based super-resolution methods do not use real sensor data, instead operating on RGB images. In practice, these approaches result in loss of detail and accuracy in their digitally zoomed output when zooming in on distant image regions. 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. The key barrier to using real sensor data for training is that ground truth high-resolution imagery is missing. We show how to obtain the ground-truth data with optically zoomed images 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 (CoBi) that delivers critical robustness to mild misalignment in input-output image pairs. The trained network achieves state-of-the-art performance in 4X and 8X computational zoom.

Ben Mildenhall, Pratul P. Srinivasan, Rodrigo Ortiz-Cayon et al.

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 smartphone app that guides users to capture input images of a scene and viewers that enable realtime virtual exploration on desktop and mobile platforms.

Pratul P. Srinivasan, Richard Tucker, Jonathan T. Barron et al.

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 RGB$α$ 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. Please see our results video at: https://www.youtube.com/watch?v=aJqAaMNL2m4.

Matthew Tancik, Ben Mildenhall, Ren Ng

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.

Xuaner Zhang, Ren Ng, Qifeng Chen

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.

Ben Mildenhall, Jonathan T. Barron, Jiawen Chen et al.

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.

Pratul P. Srinivasan, Rahul Garg, Neal Wadhwa et al.

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.

Nick Antipa, Grace Kuo, Reinhard Heckel et al.

We demonstrate a compact and easy-to-build computational camera for single-shot 3D imaging. Our lensless system consists solely of a diffuser placed in front of a standard image sensor. Every point within the volumetric field-of-view projects a unique pseudorandom pattern of caustics on the sensor. By using a physical approximation and simple calibration scheme, we solve the large-scale inverse problem in a computationally efficient way. The caustic patterns enable compressed sensing, which exploits sparsity in the sample to solve for more 3D voxels than pixels on the 2D sensor. Our 3D voxel grid is chosen to match the experimentally measured two-point optical resolution across the field-of-view, resulting in 100 million voxels being reconstructed from a single 1.3 megapixel image. However, the effective resolution varies significantly with scene content. Because this effect is common to a wide range of computational cameras, we provide new theory for analyzing resolution in such systems.

Pratul P. Srinivasan, Tongzhou Wang, Ashwin Sreelal et al.

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. Please see our supplementary video at https://youtu.be/yLCvWoQLnms

Pratul P. Srinivasan, Ren Ng, Ravi Ramamoorthi

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 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.