In this paper we consider the problem of reconstructing an image that is downsampled in the space of its $SE(2)$ wavelet transform, which is motivated by classical models of simple cells receptive fields and feature preference maps in primary visual cortex. We prove that, whenever the problem is solvable, the reconstruction can be obtained by an elementary project and replace iterative scheme based on the reproducing kernel arising from the group structure, and show numerical results on real images.
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The Laplace-Beltrami problem on closed surfaces embedded in three dimensions arises in many areas of physics, including molecular dynamics (surface diffusion), electromagnetics (harmonic vector fields), and fluid dynamics (vesicle deformation). Using classical potential theory,the Laplace-Beltrami operator can be pre-/post-conditioned with integral operators whose kernel is translation invariant, resulting in well-conditioned Fredholm integral equations of the second-kind. These equations have the standard Laplace kernel from potential theory, and therefore the equations can be solved rapidly and accurately using a combination of fast multipole methods (FMMs) and high-order quadrature corrections. In this work we detail such a scheme, presenting two alternative integral formulations of the Laplace-Beltrami problem, each of whose solution can be obtained via FMM acceleration. We then present several applications of the solvers, focusing on the computation of what are known as harmonic vector fields, relevant for many applications in electromagnetics. A battery of numerical results are presented for each application, detailing the performance of the solver in various geometries.
Neural Radiance Fields (NeRF) is a technique for high quality novel view synthesis from a collection of posed input images. Like most view synthesis methods, NeRF uses tonemapped low dynamic range (LDR) as input; these images have been processed by a lossy camera pipeline that smooths detail, clips highlights, and distorts the simple noise distribution of raw sensor data. We modify NeRF to instead train directly on linear raw images, preserving the scene's full dynamic range. By rendering raw output images from the resulting NeRF, we can perform novel high dynamic range (HDR) view synthesis tasks. In addition to changing the camera viewpoint, we can manipulate focus, exposure, and tonemapping after the fact. Although a single raw image appears significantly more noisy than a postprocessed one, we show that NeRF is highly robust to the zero-mean distribution of raw noise. When optimized over many noisy raw inputs (25-200), NeRF produces a scene representation so accurate that its rendered novel views outperform dedicated single and multi-image deep raw denoisers run on the same wide baseline input images. As a result, our method, which we call RawNeRF, can reconstruct scenes from extremely noisy images captured in near-darkness.
We present Gradient-SDF, a novel representation for 3D geometry that combines the advantages of implict and explicit representations. By storing at every voxel both the signed distance field as well as its gradient vector field, we enhance the capability of implicit representations with approaches originally formulated for explicit surfaces. As concrete examples, we show that (1) the Gradient-SDF allows us to perform direct SDF tracking from depth images, using efficient storage schemes like hash maps, and that (2) the Gradient-SDF representation enables us to perform photometric bundle adjustment directly in a voxel representation (without transforming into a point cloud or mesh), naturally a fully implicit optimization of geometry and camera poses and easy geometry upsampling. Experimental results confirm that this leads to significantly sharper reconstructions. Since the overall SDF voxel structure is still respected, the proposed Gradient-SDF is equally suited for (GPU) parallelization as related approaches.
Recent advances in implicit neural representations show great promise when it comes to generating numerical solutions to partial differential equations. Compared to conventional alternatives, such representations employ parameterized neural networks to define, in a mesh-free manner, signals that are highly-detailed, continuous, and fully differentiable. In this work, we present a novel machine learning approach for topology optimization -- an important class of inverse problems with high-dimensional parameter spaces and highly nonlinear objective landscapes. To effectively leverage neural representations in the context of mesh-free topology optimization, we use multilayer perceptrons to parameterize both density and displacement fields. Our experiments indicate that our method is highly competitive for minimizing structural compliance objectives, and it enables self-supervised learning of continuous solution spaces for topology optimization problems.
Recently, data-driven single-view reconstruction methods have shown great progress in modeling 3D dressed humans. However, such methods suffer heavily from depth ambiguities and occlusions inherent to single view inputs. In this paper, we tackle this problem by considering a small set of input views and investigate the best strategy to suitably exploit information from these views. We propose a data-driven end-to-end approach that reconstructs an implicit 3D representation of dressed humans from sparse camera views. Specifically, we introduce three key components: first a spatially consistent reconstruction that allows for arbitrary placement of the person in the input views using a perspective camera model; second an attention-based fusion layer that learns to aggregate visual information from several viewpoints; and third a mechanism that encodes local 3D patterns under the multi-view context. In the experiments, we show the proposed approach outperforms the state of the art on standard data both quantitatively and qualitatively. To demonstrate the spatially consistent reconstruction, we apply our approach to dynamic scenes. Additionally, we apply our method on real data acquired with a multi-camera platform and demonstrate our approach can obtain results comparable to multi-view stereo with dramatically less views.
3D Morphable Model (3DMM) based methods have achieved great success in recovering 3D face shapes from single-view images. However, the facial textures recovered by such methods lack the fidelity as exhibited in the input images. Recent work demonstrates high-quality facial texture recovering with generative networks trained from a large-scale database of high-resolution UV maps of face textures, which is hard to prepare and not publicly available. In this paper, we introduce a method to reconstruct 3D facial shapes with high-fidelity textures from single-view images in-the-wild, without the need to capture a large-scale face texture database. The main idea is to refine the initial texture generated by a 3DMM based method with facial details from the input image. To this end, we propose to use graph convolutional networks to reconstruct the detailed colors for the mesh vertices instead of reconstructing the UV map. Experiments show that our method can generate high-quality results and outperforms state-of-the-art methods in both qualitative and quantitative comparisons.
Machine learning methods are powerful in distinguishing different phases of matter in an automated way and provide a new perspective on the study of physical phenomena. We train a Restricted Boltzmann Machine (RBM) on data constructed with spin configurations sampled from the Ising Hamiltonian at different values of temperature and external magnetic field using Monte Carlo methods. From the trained machine we obtain the flow of iterative reconstruction of spin state configurations to faithfully reproduce the observables of the physical system. We find that the flow of the trained RBM approaches the spin configurations of the maximal possible specific heat which resemble the near criticality region of the Ising model. In the special case of the vanishing magnetic field the trained RBM converges to the critical point of the Renormalization Group (RG) flow of the lattice model. Our results suggest an alternative explanation of how the machine identifies the physical phase transitions, by recognizing certain properties of the configuration like the maximization of the specific heat, instead of associating directly the recognition procedure with the RG flow and its fixed points. Then from the reconstructed data we deduce the critical exponent associated to the magnetization to find satisfactory agreement with the actual physical value. We assume no prior knowledge about the criticality of the system and its Hamiltonian.
Importance sampling is one of the most widely used variance reduction strategies in Monte Carlo rendering. In this paper, we propose a novel importance sampling technique that uses a neural network to learn how to sample from a desired density represented by a set of samples. Our approach considers an existing Monte Carlo rendering algorithm as a black box. During a scene-dependent training phase, we learn to generate samples with a desired density in the primary sample space of the rendering algorithm using maximum likelihood estimation. We leverage a recent neural network architecture that was designed to represent real-valued non-volume preserving ('Real NVP') transformations in high dimensional spaces. We use Real NVP to non-linearly warp primary sample space and obtain desired densities. In addition, Real NVP efficiently computes the determinant of the Jacobian of the warp, which is required to implement the change of integration variables implied by the warp. A main advantage of our approach is that it is agnostic of underlying light transport effects, and can be combined with many existing rendering techniques by treating them as a black box. We show that our approach leads to effective variance reduction in several practical scenarios.
In recent years, many publications showed that convolutional neural network based features can have a superior performance to engineered features. However, not much effort was taken so far to extract local features efficiently for a whole image. In this paper, we present an approach to compute patch-based local feature descriptors efficiently in presence of pooling and striding layers for whole images at once. Our approach is generic and can be applied to nearly all existing network architectures. This includes networks for all local feature extraction tasks like camera calibration, Patchmatching, optical flow estimation and stereo matching. In addition, our approach can be applied to other patch-based approaches like sliding window object detection and recognition. We complete our paper with a speed benchmark of popular CNN based feature extraction approaches applied on a whole image, with and without our speedup, and example code (for Torch) that shows how an arbitrary CNN architecture can be easily converted by our approach.
Partial person re-identification (re-id) is a challenging problem, where only some partial observations (images) of persons are available for matching. However, few studies have offered a flexible solution of how to identify an arbitrary patch of a person image. In this paper, we propose a fast and accurate matching method to address this problem. The proposed method leverages Fully Convolutional Network (FCN) to generate certain-sized spatial feature maps such that pixel-level features are consistent. To match a pair of person images of different sizes, hence, a novel method called Deep Spatial feature Reconstruction (DSR) is further developed to avoid explicit alignment. Specifically, DSR exploits the reconstructing error from popular dictionary learning models to calculate the similarity between different spatial feature maps. In that way, we expect that the proposed FCN can decrease the similarity of coupled images from different persons and increase that of coupled images from the same person. Experimental results on two partial person datasets demonstrate the efficiency and effectiveness of the proposed method in comparison with several state-of-the-art partial person re-id approaches. Additionally, it achieves competitive results on a benchmark person dataset Market1501 with the Rank-1 accuracy being 83.58%.
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