We propose a deep autoencoder with graph topology inference and filtering to achieve compact representations of unorganized 3D point clouds in an unsupervised manner. The encoder of the proposed networks adopts similar architectures as in PointNet, which is a well-acknowledged method for supervised learning of 3D point clouds. The decoder of the proposed networks involves three novel modules: the folding module, the graph-topology-inference module, and the graph-filtering module. The folding module folds a canonical 2D lattice to the underlying surface of a 3D point cloud, achieving coarse reconstruction; the graph-topology-inference module learns a graph topology to represent pairwise relationships between 3D points; and the graph-filtering module designs graph filters based on the learnt graph topology to obtain the refined reconstruction. We further provide theoretical analyses of the proposed architecture. We provide an upper bound for the reconstruction loss and further show the superiority of graph smoothness over spatial smoothness as a prior to model 3D point clouds. In the experiments, we validate the proposed networks in three tasks, including reconstruction, visualization, and classification. The experimental results show that (1) the proposed networks outperform the state-of-the-art methods in various tasks, including reconstruction and transfer classification; (2) a graph topology can be inferred as auxiliary information without specific supervision on graph topology inference; and (3) graph filtering refines the reconstruction, leading to better performances.
Compared to supervised learning where training data is associated with ground-truth labels, unsupervised learning does not have any label and uses self-organization to model raw data. Some common unsupervised-learning methods include @math -means clustering, Gaussian mixture models principal component analysis @cite_45 , matrix factorization @cite_38 , autoencoders, and generative adversarial networks @cite_25 . Recently, a series of unsupervised-learning models are proposed to learn from 3D point clouds @cite_57 @cite_21 @cite_67 @cite_42 @cite_16 . For example, 3D GAN converts 3D points to 3D voxels @cite_29 , which introduces a lot of empty voxels and loses precision; LatentGAN handles 3D point clouds directly @cite_60 ; however, the decoder uses fully-connected layers, which does not explore specific geometric structures of 3D point clouds and requires a huge number of training parameters; and VIP-GAN uses recurrent-neural-network-based architecture to solve multiple view inter-prediction tasks for each shape @cite_62 ; @cite_63 learns a continuous signed distance function representation of a class of shapes that enables high quality shape representation, interpolation and completion from partial and noisy 3D input data. In this work, we use deep autoencoder to directly handle unorganized 3D points and propose graph-based operations to explore geometric structures of 3D point clouds.
@cite_38 @cite_67 @cite_62 @cite_60 @cite_29 @cite_21 @cite_42 @cite_57 @cite_45 @cite_63 @cite_16 @cite_25
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The development and use of low-rank approximate nonnegative matrix factorization (NMF) algorithms for feature extraction and identification in the fields of text mining and spectral data analysis are presented. The evolution and convergence properties of hybrid methods based on both sparsity and smoothness constraints for the resulting nonnegative matrix factors are discussed. The interpretability of NMF outputs in specific contexts are provided along with opportunities for future work in the modification of NMF algorithms for large-scale and time-varying data sets. What is a good vector representation of an object? We believe that it should be generative in 3D, in the sense that it can produce new 3D objects; as well as be predictable from 2D, in the sense that it can be perceived from 2D images. We propose a novel architecture, called the TL-embedding network, to learn an embedding space with these properties. The network consists of two components: (a) an autoencoder that ensures the representation is generative; and (b) a convolutional network that ensures the representation is predictable. This enables tackling a number of tasks including voxel prediction from 2D images and 3D model retrieval. Extensive experimental analysis demonstrates the usefulness and versatility of this embedding. In this paper we present a novel unsupervised representation learning approach for 3D shapes, which is an important research challenge as it avoids the manual effort required for collecting supervised data. Our method trains an RNN-based neural network architecture to solve multiple view inter-prediction tasks for each shape. Given several nearby views of a shape, we define view inter-prediction as the task of predicting the center view between the input views, and reconstructing the input views in a low-level feature space. The key idea of our approach is to implement the shape representation as a shape-specific global memory that is shared between all local view inter-predictions for each shape. Intuitively, this memory enables the system to aggregate information that is useful to better solve the view inter-prediction tasks for each shape, and to leverage the memory as a view-independent shape representation. Our approach obtains the best results using a combination of L_2 and adversarial losses for the view inter-prediction task. We show that VIP-GAN outperforms state-of-the-art methods in unsupervised 3D feature learning on three large scale 3D shape benchmarks. We study the problem of 3D object generation. We propose a novel framework, namely 3D Generative Adversarial Network (3D-GAN), which generates 3D objects from a probabilistic space by leveraging recent advances in volumetric convolutional networks and generative adversarial nets. The benefits of our model are three-fold: first, the use of an adversarial criterion, instead of traditional heuristic criteria, enables the generator to capture object structure implicitly and to synthesize high-quality 3D objects; second, the generator establishes a mapping from a low-dimensional probabilistic space to the space of 3D objects, so that we can sample objects without a reference image or CAD models, and explore the 3D object manifold; third, the adversarial discriminator provides a powerful 3D shape descriptor which, learned without supervision, has wide applications in 3D object recognition. Experiments demonstrate that our method generates high-quality 3D objects, and our unsupervisedly learned features achieve impressive performance on 3D object recognition, comparable with those of supervised learning methods. A large number of 3D models are created and available on the Web, since more and more 3D modelling and digitizing tools are developed for ever increasing applications. The techniques for content-based 3D model retrieval then become necessary. In this paper, a visual similarity-based 3D model retrieval system is proposed. This approach measures the similarity among 3D models by visual similarity, and the main idea is that if two 3D models are similar, they also look similar from all viewing angles. Therefore, one hundred orthogonal projections of an object, excluding symmetry, are encoded both by Zernike moments and Fourier descriptors as features for later retrieval. The visual similarity-based approach is robust against similarity transformation, noise, model degeneracy etc., and provides 42 , 94 and 25 better performance (precision-recall evaluation diagram) than three other competing approaches: (1)the spherical harmonics approach developed by , (2)the MPEG-7 Shape 3D descriptors, and (3)the MPEG-7 Multiple View Descriptor. The proposed system is on the Web for practical trial use (http: 3d.csie.ntu.edu.tw), and the database contains more than 10,000 publicly available 3D models collected from WWW pages. Furthermore, a user friendly interface is provided to retrieve 3D models by drawing 2D shapes. The retrieval is fast enough on a server with Pentium IV 2.4GHz CPU, and it takes about 2 seconds and 0.1 seconds for querying directly by a 3D model and by hand drawn 2D shapes, respectively. With the advent of affordable depth sensors, 3D capture becomes more and more ubiquitous and already has made its way into commercial products. Yet, capturing the geometry or complete shapes of everyday objects using scanning devices (e.g. Kinect) still comes with several challenges that result in noise or even incomplete shapes. One of the challenges in 3D shape matching arises from the fact that in many applications, models should be considered to be the same if they differ by a rotation. Consequently, when comparing two models, a similarity metric implicitly provides the measure of similarity at the optimal alignment. Explicitly solving for the optimal alignment is usually impractical. So, two general methods have been proposed for addressing this issue: (1) Every model is represented using rotation invariant descriptors. (2) Every model is described by a rotation dependent descriptor that is aligned into a canonical coordinate system defined by the model. In this paper, we describe the limitations of canonical alignment and discuss an alternate method, based on spherical harmonics, for obtaining rotation invariant representations. We describe the properties of this tool and show how it can be applied to a number of existing, orientation dependent descriptors to improve their matching performance. The advantages of this tool are two-fold: First, it improves the matching performance of many descriptors. Second, it reduces the dimensionality of the descriptor, providing a more compact representation, which in turn makes comparing two models more efficient. Cristopher M. BishopInformation Science and StatisticsSpringer 2006, 738 pagesAs the author writes in the preface of the book, pattern recognition has its origin inengineering, whereas machine learning grew out of computer science. However, theseactivities can be viewed as two facets of the same ﬁeld, and they have undergonesubstantial development over the past years.Bayesian methods are widely used, while graphical models have emerged as a generalframework for describing and applying probabilistic models. Similarly new modelsbased on kernels have had signiﬁcant impact on both algorithms and applications.This textbook reﬂects these recent developments while providing a comprehensiveintroduction to the ﬁelds of pattern recognition and machine learning. It is aimedat advanced undergraduate or ﬁrst year PhD students, as well as researchers andpractitioners. It can be consider as an introductory course to the subject.The ﬁrst four chapters are devoted to the concepts of Probability and Statistics that areneededforreadingtherestofthebook,sowecanimaginethatthespeedishighinorderto get from zero to inﬁnity. I believe that it is better to study the book after a previouscourse on Probability and Statistics. On the other hand, a basic knowledge of linearalgebra and multivariate calculus is assumed.The other chapters give to a classic probabilist or statistician a point of view on someapplications that are very interesting but far from his usual world. In all the text themathematical aspects are at the second level in relation withthe ideas and intuitionsthatthe author wants to communicate.The book is supported by a great deal of additional material, including lecture slides aswell as the complete set of ﬁgures used in it, and the reader is encouraged to visit thebook web site for the latest information. So it can be very useful for a course or a talkabout the subject. Computer graphics, 3D computer vision and robotics communities have produced multiple approaches to representing 3D geometry for rendering and reconstruction. These provide trade-offs across fidelity, efficiency and compression capabilities. In this work, we introduce DeepSDF, a learned continuous Signed Distance Function (SDF) representation of a class of shapes that enables high quality shape representation, interpolation and completion from partial and noisy 3D input data. DeepSDF, like its classical counterpart, represents a shape's surface by a continuous volumetric field: the magnitude of a point in the field represents the distance to the surface boundary and the sign indicates whether the region is inside (-) or outside (+) of the shape, hence our representation implicitly encodes a shape's boundary as the zero-level-set of the learned function while explicitly representing the classification of space as being part of the shapes interior or not. While classical SDF's both in analytical or discretized voxel form typically represent the surface of a single shape, DeepSDF can represent an entire class of shapes. Furthermore, we show state-of-the-art performance for learned 3D shape representation and completion while reducing the model size by an order of magnitude compared with previous work.