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Recent history has seen a tremendous growth of work exploring implicit representations of geometry and radiance, popularized through Neural Radiance Fields (NeRF). Such works are fundamentally based on a (implicit) volumetric representation of occupancy, allowing them to model diverse scene structure including translucent objects and atmospheric obscurants. But because the vast majority of real-world scenes are composed of well-defined surfaces, we introduce a surface analog of such implicit models called Neural Reflectance Surfaces (NeRS). NeRS learns a neural shape representation of a closed surface that is diffeomorphic to a sphere, guaranteeing water-tight reconstructions. Even more importantly, surface parameterizations allow NeRS to learn (neural) bidirectional surface reflectance functions (BRDFs) that factorize view-dependent appearance into environmental illumination, diffuse color (albedo), and specular "shininess." Finally, rather than illustrating our results on synthetic scenes or controlled in-the-lab capture, we assemble a novel dataset of multi-view images from online marketplaces for selling goods. Such "in-the-wild" multi-view image sets pose a number of challenges, including a small number of views with unknown/rough camera estimates. We demonstrate that surface-based neural reconstructions enable learning from such data, outperforming volumetric neural rendering-based reconstructions. We hope that NeRS serves as a first step toward building scalable, high-quality libraries of real-world shape, materials, and illumination. The project page with code and video visualizations can be found at //jasonyzhang.com/ners.

We consider the phase retrieval problem, in which the observer wishes to recover a $n$-dimensional real or complex signal $\mathbf{X}^\star$ from the (possibly noisy) observation of $|\mathbf{\Phi} \mathbf{X}^\star|$, in which $\mathbf{\Phi}$ is a matrix of size $m \times n$. We consider a \emph{high-dimensional} setting where $n,m \to \infty$ with $m/n = \mathcal{O}(1)$, and a large class of (possibly correlated) random matrices $\mathbf{\Phi}$ and observation channels. Spectral methods are a powerful tool to obtain approximate observations of the signal $\mathbf{X}^\star$ which can be then used as initialization for a subsequent algorithm, at a low computational cost. In this paper, we extend and unify previous results and approaches on spectral methods for the phase retrieval problem. More precisely, we combine the linearization of message-passing algorithms and the analysis of the \emph{Bethe Hessian}, a classical tool of statistical physics. Using this toolbox, we show how to derive optimal spectral methods for arbitrary channel noise and right-unitarily invariant matrix $\mathbf{\Phi}$, in an automated manner (i.e. with no optimization over any hyperparameter or preprocessing function).

The purpose of this work is to study spectral methods to approximate the eigenvalues of nonlocal integral operators. Indeed, even if the spatial domain is an interval, it is very challenging to obtain closed analytical expressions for the eigenpairs of peridynamic operators. Our approach is based on the weak formulation of eigenvalue problem and we consider as orthogonal basis to compute the eigenvalues a set of Fourier trigonometric or Chebyshev polynomials. We show the order of convergence for eigenvalues and eigenfunctions in $L^2$-norm, and finally, we perform some numerical simulations to compare the two proposed methods.

Retrieving accurate 3D reconstructions of objects from the way they reflect light is a very challenging task in computer vision. Despite more than four decades since the definition of the Photometric Stereo problem, most of the literature has had limited success when global illumination effects such as cast shadows, self-reflections and ambient light come into play, especially for specular surfaces. Recent approaches have leveraged the power of deep learning in conjunction with computer graphics in order to cope with the need of a vast number of training data in order to invert the image irradiance equation and retrieve the geometry of the object. However, rendering global illumination effects is a slow process which can limit the amount of training data that can be generated. In this work we propose a novel pixel-wise training procedure for normal prediction by replacing the training data (observation maps) of globally rendered images with independent per-pixel generated data. We show that global physical effects can be approximated on the observation map domain and this simplifies and speeds up the data creation procedure. Our network, PX-NET, achieves the state-of-the-art performance compared to other pixelwise methods on synthetic datasets, as well as the Diligent real dataset on both dense and sparse light settings.

We present an automated machine learning approach for uncalibrated photometric stereo (PS). Our work aims at discovering lightweight and computationally efficient PS neural networks with excellent surface normal accuracy. Unlike previous uncalibrated deep PS networks, which are handcrafted and carefully tuned, we leverage differentiable neural architecture search (NAS) strategy to find uncalibrated PS architecture automatically. We begin by defining a discrete search space for a light calibration network and a normal estimation network, respectively. We then perform a continuous relaxation of this search space and present a gradient-based optimization strategy to find an efficient light calibration and normal estimation network. Directly applying the NAS methodology to uncalibrated PS is not straightforward as certain task-specific constraints must be satisfied, which we impose explicitly. Moreover, we search for and train the two networks separately to account for the Generalized Bas-Relief (GBR) ambiguity. Extensive experiments on the DiLiGenT dataset show that the automatically searched neural architectures performance compares favorably with the state-of-the-art uncalibrated PS methods while having a lower memory footprint.

We present a modern solution to the multi-view photometric stereo problem (MVPS). Our work suitably exploits the image formation model in a MVPS experimental setup to recover the dense 3D reconstruction of an object from images. We procure the surface orientation using a photometric stereo (PS) image formation model and blend it with a multi-view neural radiance field representation to recover the object's surface geometry. Contrary to the previous multi-staged framework to MVPS, where the position, iso-depth contours, or orientation measurements are estimated independently and then fused later, our method is simple to implement and realize. Our method performs neural rendering of multi-view images while utilizing surface normals estimated by a deep photometric stereo network. We render the MVPS images by considering the object's surface normals for each 3D sample point along the viewing direction rather than explicitly using the density gradient in the volume space via 3D occupancy information. We optimize the proposed neural radiance field representation for the MVPS setup efficiently using a fully connected deep network to recover the 3D geometry of an object. Extensive evaluation on the DiLiGenT-MV benchmark dataset shows that our method performs better than the approaches that perform only PS or only multi-view stereo (MVS) and provides comparable results against the state-of-the-art multi-stage fusion methods.

Point cloud learning has lately attracted increasing attention due to its wide applications in many areas, such as computer vision, autonomous driving, and robotics. As a dominating technique in AI, deep learning has been successfully used to solve various 2D vision problems. However, deep learning on point clouds is still in its infancy due to the unique challenges faced by the processing of point clouds with deep neural networks. Recently, deep learning on point clouds has become even thriving, with numerous methods being proposed to address different problems in this area. To stimulate future research, this paper presents a comprehensive review of recent progress in deep learning methods for point clouds. It covers three major tasks, including 3D shape classification, 3D object detection and tracking, and 3D point cloud segmentation. It also presents comparative results on several publicly available datasets, together with insightful observations and inspiring future research directions.

We present DeepICP - a novel end-to-end learning-based 3D point cloud registration framework that achieves comparable registration accuracy to prior state-of-the-art geometric methods. Different from other keypoint based methods where a RANSAC procedure is usually needed, we implement the use of various deep neural network structures to establish an end-to-end trainable network. Our keypoint detector is trained through this end-to-end structure and enables the system to avoid the inference of dynamic objects, leverages the help of sufficiently salient features on stationary objects, and as a result, achieves high robustness. Rather than searching the corresponding points among existing points, the key contribution is that we innovatively generate them based on learned matching probabilities among a group of candidates, which can boost the registration accuracy. Our loss function incorporates both the local similarity and the global geometric constraints to ensure all above network designs can converge towards the right direction. We comprehensively validate the effectiveness of our approach using both the KITTI dataset and the Apollo-SouthBay dataset. Results demonstrate that our method achieves comparable or better performance than the state-of-the-art geometry-based methods. Detailed ablation and visualization analysis are included to further illustrate the behavior and insights of our network. The low registration error and high robustness of our method makes it attractive for substantial applications relying on the point cloud registration task.

Lidar based 3D object detection is inevitable for autonomous driving, because it directly links to environmental understanding and therefore builds the base for prediction and motion planning. The capacity of inferencing highly sparse 3D data in real-time is an ill-posed problem for lots of other application areas besides automated vehicles, e.g. augmented reality, personal robotics or industrial automation. We introduce Complex-YOLO, a state of the art real-time 3D object detection network on point clouds only. In this work, we describe a network that expands YOLOv2, a fast 2D standard object detector for RGB images, by a specific complex regression strategy to estimate multi-class 3D boxes in Cartesian space. Thus, we propose a specific Euler-Region-Proposal Network (E-RPN) to estimate the pose of the object by adding an imaginary and a real fraction to the regression network. This ends up in a closed complex space and avoids singularities, which occur by single angle estimations. The E-RPN supports to generalize well during training. Our experiments on the KITTI benchmark suite show that we outperform current leading methods for 3D object detection specifically in terms of efficiency. We achieve state of the art results for cars, pedestrians and cyclists by being more than five times faster than the fastest competitor. Further, our model is capable of estimating all eight KITTI-classes, including Vans, Trucks or sitting pedestrians simultaneously with high accuracy.

Spectral clustering is a leading and popular technique in unsupervised data analysis. Two of its major limitations are scalability and generalization of the spectral embedding (i.e., out-of-sample-extension). In this paper we introduce a deep learning approach to spectral clustering that overcomes the above shortcomings. Our network, which we call SpectralNet, learns a map that embeds input data points into the eigenspace of their associated graph Laplacian matrix and subsequently clusters them. We train SpectralNet using a procedure that involves constrained stochastic optimization. Stochastic optimization allows it to scale to large datasets, while the constraints, which are implemented using a special-purpose output layer, allow us to keep the network output orthogonal. Moreover, the map learned by SpectralNet naturally generalizes the spectral embedding to unseen data points. To further improve the quality of the clustering, we replace the standard pairwise Gaussian affinities with affinities leaned from unlabeled data using a Siamese network. Additional improvement can be achieved by applying the network to code representations produced, e.g., by standard autoencoders. Our end-to-end learning procedure is fully unsupervised. In addition, we apply VC dimension theory to derive a lower bound on the size of SpectralNet. State-of-the-art clustering results are reported on the Reuters dataset. Our implementation is publicly available at //github.com/kstant0725/SpectralNet .