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Depth separation results propose a possible theoretical explanation for the benefits of deep neural networks over shallower architectures, establishing that the former possess superior approximation capabilities. However, there are no known results in which the deeper architecture leverages this advantage into a provable optimization guarantee. We prove that when the data are generated by a distribution with radial symmetry which satisfies some mild assumptions, gradient descent can efficiently learn ball indicator functions using a depth 2 neural network with two layers of sigmoidal activations, and where the hidden layer is held fixed throughout training. By building on and refining existing techniques for approximation lower bounds of neural networks with a single layer of non-linearities, we show that there are $d$-dimensional radial distributions on the data such that ball indicators cannot be learned efficiently by any algorithm to accuracy better than $\Omega(d^{-4})$, nor by a standard gradient descent implementation to accuracy better than a constant. These results establish what is to the best of our knowledge, the first optimization-based separations where the approximation benefits of the stronger architecture provably manifest in practice. Our proof technique introduces new tools and ideas that may be of independent interest in the theoretical study of both the approximation and optimization of neural networks.

In many industrial applications, obtaining labeled observations is not straightforward as it often requires the intervention of human experts or the use of expensive testing equipment. In these circumstances, active learning can be highly beneficial in suggesting the most informative data points to be used when fitting a model. Reducing the number of observations needed for model development alleviates both the computational burden required for training and the operational expenses related to labeling. Online active learning, in particular, is useful in high-volume production processes where the decision about the acquisition of the label for a data point needs to be taken within an extremely short time frame. However, despite the recent efforts to develop online active learning strategies, the behavior of these methods in the presence of outliers has not been thoroughly examined. In this work, we investigate the performance of online active linear regression in contaminated data streams. Our study shows that the currently available query strategies are prone to sample outliers, whose inclusion in the training set eventually degrades the predictive performance of the models. To address this issue, we propose a solution that bounds the search area of a conditional D-optimal algorithm and uses a robust estimator. Our approach strikes a balance between exploring unseen regions of the input space and protecting against outliers. Through numerical simulations, we show that the proposed method is effective in improving the performance of online active learning in the presence of outliers, thus expanding the potential applications of this powerful tool.

We present a novel neural surface reconstruction method, called NeuS, for reconstructing objects and scenes with high fidelity from 2D image inputs. Existing neural surface reconstruction approaches, such as DVR and IDR, require foreground mask as supervision, easily get trapped in local minima, and therefore struggle with the reconstruction of objects with severe self-occlusion or thin structures. Meanwhile, recent neural methods for novel view synthesis, such as NeRF and its variants, use volume rendering to produce a neural scene representation with robustness of optimization, even for highly complex objects. However, extracting high-quality surfaces from this learned implicit representation is difficult because there are not sufficient surface constraints in the representation. In NeuS, we propose to represent a surface as the zero-level set of a signed distance function (SDF) and develop a new volume rendering method to train a neural SDF representation. We observe that the conventional volume rendering method causes inherent geometric errors (i.e. bias) for surface reconstruction, and therefore propose a new formulation that is free of bias in the first order of approximation, thus leading to more accurate surface reconstruction even without the mask supervision. Experiments on the DTU dataset and the BlendedMVS dataset show that NeuS outperforms the state-of-the-arts in high-quality surface reconstruction, especially for objects and scenes with complex structures and self-occlusion.

We survey and benchmark traditional and novel learning-based algorithms that address the problem of surface reconstruction from point clouds. Surface reconstruction from point clouds is particularly challenging when applied to real-world acquisitions, due to noise, outliers, non-uniform sampling and missing data. Traditionally, different handcrafted priors of the input points or the output surface have been proposed to make the problem more tractable. However, hyperparameter tuning for adjusting priors to different acquisition defects can be a tedious task. To this end, the deep learning community has recently addressed the surface reconstruction problem. In contrast to traditional approaches, deep surface reconstruction methods can learn priors directly from a training set of point clouds and corresponding true surfaces. In our survey, we detail how different handcrafted and learned priors affect the robustness of methods to defect-laden input and their capability to generate geometric and topologically accurate reconstructions. In our benchmark, we evaluate the reconstructions of several traditional and learning-based methods on the same grounds. We show that learning-based methods can generalize to unseen shape categories, but their training and test sets must share the same point cloud characteristics. We also provide the code and data to compete in our benchmark and to further stimulate the development of learning-based surface reconstruction //github.com/raphaelsulzer/dsr-benchmark.

Monocular scene reconstruction from posed images is challenging due to the complexity of a large environment. Recent volumetric methods learn to directly predict the TSDF volume and have demonstrated promising results in this task. However, most methods focus on how to extract and fuse the 2D features to a 3D feature volume, but none of them improve the way how the 3D volume is aggregated. In this work, we propose an SDF transformer network, which replaces the role of 3D CNN for better 3D feature aggregation. To reduce the explosive computation complexity of the 3D multi-head attention, we propose a sparse window attention module, where the attention is only calculated between the non-empty voxels within a local window. Then a top-down-bottom-up 3D attention network is built for 3D feature aggregation, where a dilate-attention structure is proposed to prevent geometry degeneration, and two global modules are employed to equip with global receptive fields. The experiments on multiple datasets show that this 3D transformer network generates a more accurate and complete reconstruction, which outperforms previous methods by a large margin. Remarkably, the mesh accuracy is improved by 41.8%, and the mesh completeness is improved by 25.3% on the ScanNet dataset. Project page: //weihaosky.github.io/sdfformer.

Spatial audio, which focuses on immersive 3D sound rendering, is widely applied in the acoustic industry. One of the key problems of current spatial audio rendering methods is the lack of personalization based on different anatomies of individuals, which is essential to produce accurate sound source positions. In this work, we address this problem from an interdisciplinary perspective. The rendering of spatial audio is strongly correlated with the 3D shape of human bodies, particularly ears. To this end, we propose to achieve personalized spatial audio by reconstructing 3D human ears with single-view images. First, to benchmark the ear reconstruction task, we introduce AudioEar3D, a high-quality 3D ear dataset consisting of 112 point cloud ear scans with RGB images. To self-supervisedly train a reconstruction model, we further collect a 2D ear dataset composed of 2,000 images, each one with manual annotation of occlusion and 55 landmarks, named AudioEar2D. To our knowledge, both datasets have the largest scale and best quality of their kinds for public use. Further, we propose AudioEarM, a reconstruction method guided by a depth estimation network that is trained on synthetic data, with two loss functions tailored for ear data. Lastly, to fill the gap between the vision and acoustics community, we develop a pipeline to integrate the reconstructed ear mesh with an off-the-shelf 3D human body and simulate a personalized Head-Related Transfer Function (HRTF), which is the core of spatial audio rendering. Code and data are publicly available at //github.com/seanywang0408/AudioEar.

LiDAR (Light Detection and Ranging) is an advanced active remote sensing technique working on the principle of time of travel (ToT) for capturing highly accurate 3D information of the surroundings. LiDAR has gained wide attention in research and development with the LiDAR industry expected to reach 2.8 billion $ by 2025. Although the LiDAR dataset is of rich density and high spatial resolution, it is challenging to process LiDAR data due to its inherent 3D geometry and massive volume. But such a high-resolution dataset possesses immense potential in many applications and has great potential in 3D object detection and recognition. In this research we propose Graph Neural Network (GNN) based framework to learn and identify the objects in the 3D LiDAR point clouds. GNNs are class of deep learning which learns the patterns and objects based on the principle of graph learning which have shown success in various 3D computer vision tasks.

Image reconstruction based on indirect, noisy, or incomplete data remains an important yet challenging task. While methods such as compressive sensing have demonstrated high-resolution image recovery in various settings, there remain issues of robustness due to parameter tuning. Moreover, since the recovery is limited to a point estimate, it is impossible to quantify the uncertainty, which is often desirable. Due to these inherent limitations, a sparse Bayesian learning approach is sometimes adopted to recover a posterior distribution of the unknown. Sparse Bayesian learning assumes that some linear transformation of the unknown is sparse. However, most of the methods developed are tailored to specific problems, with particular forward models and priors. Here, we present a generalized approach to sparse Bayesian learning. It has the advantage that it can be used for various types of data acquisitions and prior information. Some preliminary results on image reconstruction/recovery indicate its potential use for denoising, deblurring, and magnetic resonance imaging.

Estimating human pose and shape from monocular images is a long-standing problem in computer vision. Since the release of statistical body models, 3D human mesh recovery has been drawing broader attention. With the same goal of obtaining well-aligned and physically plausible mesh results, two paradigms have been developed to overcome challenges in the 2D-to-3D lifting process: i) an optimization-based paradigm, where different data terms and regularization terms are exploited as optimization objectives; and ii) a regression-based paradigm, where deep learning techniques are embraced to solve the problem in an end-to-end fashion. Meanwhile, continuous efforts are devoted to improving the quality of 3D mesh labels for a wide range of datasets. Though remarkable progress has been achieved in the past decade, the task is still challenging due to flexible body motions, diverse appearances, complex environments, and insufficient in-the-wild annotations. To the best of our knowledge, this is the first survey to focus on the task of monocular 3D human mesh recovery. We start with the introduction of body models and then elaborate recovery frameworks and training objectives by providing in-depth analyses of their strengths and weaknesses. We also summarize datasets, evaluation metrics, and benchmark results. Open issues and future directions are discussed in the end, hoping to motivate researchers and facilitate their research in this area. A regularly updated project page can be found at //github.com/tinatiansjz/hmr-survey.

Unsupervised domain adaptation has recently emerged as an effective paradigm for generalizing deep neural networks to new target domains. However, there is still enormous potential to be tapped to reach the fully supervised performance. In this paper, we present a novel active learning strategy to assist knowledge transfer in the target domain, dubbed active domain adaptation. We start from an observation that energy-based models exhibit free energy biases when training (source) and test (target) data come from different distributions. Inspired by this inherent mechanism, we empirically reveal that a simple yet efficient energy-based sampling strategy sheds light on selecting the most valuable target samples than existing approaches requiring particular architectures or computation of the distances. Our algorithm, Energy-based Active Domain Adaptation (EADA), queries groups of targe data that incorporate both domain characteristic and instance uncertainty into every selection round. Meanwhile, by aligning the free energy of target data compact around the source domain via a regularization term, domain gap can be implicitly diminished. Through extensive experiments, we show that EADA surpasses state-of-the-art methods on well-known challenging benchmarks with substantial improvements, making it a useful option in the open world. Code is available at //github.com/BIT-DA/EADA.