Reconstruction of a continuous surface of two-dimensional manifold from its raw, discrete point cloud observation is a long-standing problem in computer vision and graphics research. The problem is technically ill-posed, and becomes more difficult considering that various sensing imperfections would appear in the point clouds obtained by practical depth scanning. In literature, a rich set of methods has been proposed, and reviews of existing methods are also provided. However, existing reviews are short of thorough investigations on a common benchmark. The present paper aims to review and benchmark existing methods in the new era of deep learning surface reconstruction. To this end, we contribute a large-scale benchmarking dataset consisting of both synthetic and real-scanned data; the benchmark includes object- and scene-level surfaces and takes into account various sensing imperfections that are commonly encountered in practical depth scanning. We conduct thorough empirical studies by comparing existing methods on the constructed benchmark, and pay special attention on robustness of existing methods against various scanning imperfections; we also study how different methods generalize in terms of reconstructing complex surface shapes. Our studies help identity the best conditions under which different methods work, and suggest some empirical findings. For example, while deep learning methods are increasingly popular in the research community, our systematic studies suggest that, surprisingly, a few classical methods perform even better in terms of both robustness and generalization; our studies also suggest that the practical challenges of misalignment of point sets from multi-view scanning , missing of surface points , and point outliers remain unsolved by all the existing surface reconstruction methods. We expect that the benchmark and our studies would be valuable both for practitioners and as a guidance for new innovations in future research.

Machine learning models have been shown to be vulnerable to adversarial examples. While most of the existing methods for adversarial attack and defense work on the 2D image domain, a few recent attempts have been made to extend them to 3D point cloud data. However, adversarial results obtained by these methods typically contain point outliers, which are both noticeable and easy to defend against using the simple techniques of outlier removal. Motivated by the different mechanisms by which humans perceive 2D images and 3D shapes, in this paper we propose the new design of geometry-aware objectives , whose solutions favor (the discrete versions of) the desired surface properties of smoothness and fairness. To generate adversarial point clouds, we use a targeted attack misclassification loss that supports continuous pursuit of increasingly malicious signals. Regularizing the targeted attack loss with our proposed geometry-aware objectives results in our proposed method, Geometry-Aware Adversarial Attack ($GeoA^3$GeoA3) . The results of $GeoA^3$ tend to be more harmful, arguably harder to defend against, and of the key adversarial characterization of being imperceptible to humans. While the main focus of this paper is to learn to generate adversarial point clouds, we also present a simple but effective algorithm termed $Geo_{+}A^3$ -IterNormPro, with Iterative Normal Projection (IterNorPro) that solves a new objective function $Geo_{+}A^3$ , towards surface-level adversarial attacks via generation of adversarial point clouds. We quantitatively evaluate our methods on both synthetic and physical objects in terms of attack success rate and geometric regularity. For a qualitative evaluation, we conduct subjective studies by collecting human preferences from Amazon Mechanical Turk. Comparative results in comprehensive experiments confirm the advantages of our proposed methods. Our source codes are publicly available at https://github.com/Yuxin-Wen/GeoA3 .

In this paper, we propose a framework of transforming images from a source image space to a target image space, based on learning coupled dictionaries from a training set of paired images. The framework can be used for applications such as image super-resolution and estimation of image intrinsic components (shading and albedo). It is based on a local parametric regression approach, using sparse feature representations over learned coupled dictionaries across the source and target image spaces. After coupled dictionary learning, sparse coefficient vectors of training image patch pairs are partitioned into easily retrievable local clusters. For any test image patch, we can fast index into its closest local cluster and perform a local parametric regression between the learned sparse feature spaces. The obtained sparse representation (together with the learned target space dictionary) provides multiple constraints for each pixel of the target image to be estimated. The final target image is reconstructed based on these constraints. The contributions of our proposed framework are three-fold. 1) We propose a concept of coupled dictionary learning based on coupled sparse coding which requires the sparse coefficient vectors of a pair of corresponding source and target image patches to have the same support, i.e., the same indices of nonzero elements. 2) We devise a space partitioning scheme to divide the high-dimensional but sparse feature space into local clusters. The partitioning facilitates extremely fast retrieval of closest local clusters for query patches. 3) Benefiting from sparse feature-based image transformation, our method is more robust to corrupted input data, and can be considered as a simultaneous image restoration and transformation process. Experiments on intrinsic image estimation and super-resolution demonstrate the effectiveness and efficiency of our proposed method.

In this paper, we study the formalism of unsupervised multi-class domain adaptation (multi-class UDA), which underlies a few recent algorithms whose learning objectives are only motivated empirically. Multi-Class Scoring Disagreement (MCSD) divergence is presented by aggregating the absolute margin violations in multi-class classification, and this proposed MCSD is able to fully characterize the relations between any pair of multi-class scoring hypotheses. By using MCSD as a measure of domain distance, we develop a new domain adaptation bound for multi-class UDA; its data-dependent, probably approximately correct bound is also developed that naturally suggests adversarial learning objectives to align conditional feature distributions across source and target domains. Consequently, an algorithmic framework of Multi-class Domain-adversarial learning Networks (McDalNets) is developed, and its different instantiations via surrogate learning objectives either coincide with or resemble a few recently popular methods, thus (partially) underscoring their practical effectiveness. Based on our identical theory for multi-class UDA, we also introduce a new algorithm of Domain-Symmetric Networks (SymmNets), which is featured by a novel adversarial strategy of domain confusion and discrimination. SymmNets affords simple extensions that work equally well under the problem settings of either closed set, partial, or open set UDA. We conduct careful empirical studies to compare different algorithms of McDalNets and our newly introduced SymmNets. Experiments verify our theoretical analysis and show the efficacy of our proposed SymmNets. In addition, we have made our implementation code publicly available.