109 research outputs found

    Discovering Causal Relations and Equations from Data

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    Physics is a field of science that has traditionally used the scientific method to answer questions about why natural phenomena occur and to make testable models that explain the phenomena. Discovering equations, laws and principles that are invariant, robust and causal explanations of the world has been fundamental in physical sciences throughout the centuries. Discoveries emerge from observing the world and, when possible, performing interventional studies in the system under study. With the advent of big data and the use of data-driven methods, causal and equation discovery fields have grown and made progress in computer science, physics, statistics, philosophy, and many applied fields. All these domains are intertwined and can be used to discover causal relations, physical laws, and equations from observational data. This paper reviews the concepts, methods, and relevant works on causal and equation discovery in the broad field of Physics and outlines the most important challenges and promising future lines of research. We also provide a taxonomy for observational causal and equation discovery, point out connections, and showcase a complete set of case studies in Earth and climate sciences, fluid dynamics and mechanics, and the neurosciences. This review demonstrates that discovering fundamental laws and causal relations by observing natural phenomena is being revolutionised with the efficient exploitation of observational data, modern machine learning algorithms and the interaction with domain knowledge. Exciting times are ahead with many challenges and opportunities to improve our understanding of complex systems.Comment: 137 page

    MSECNet: Accurate and Robust Normal Estimation for 3D Point Clouds by Multi-Scale Edge Conditioning

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    Estimating surface normals from 3D point clouds is critical for various applications, including surface reconstruction and rendering. While existing methods for normal estimation perform well in regions where normals change slowly, they tend to fail where normals vary rapidly. To address this issue, we propose a novel approach called MSECNet, which improves estimation in normal varying regions by treating normal variation modeling as an edge detection problem. MSECNet consists of a backbone network and a multi-scale edge conditioning (MSEC) stream. The MSEC stream achieves robust edge detection through multi-scale feature fusion and adaptive edge detection. The detected edges are then combined with the output of the backbone network using the edge conditioning module to produce edge-aware representations. Extensive experiments show that MSECNet outperforms existing methods on both synthetic (PCPNet) and real-world (SceneNN) datasets while running significantly faster. We also conduct various analyses to investigate the contribution of each component in the MSEC stream. Finally, we demonstrate the effectiveness of our approach in surface reconstruction.Comment: Accepted for ACM MM 202

    Point cloud geometry compression using neural implicit representations

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    openIn recent years, the increasing prominence of 3D point clouds in various applications has led to an escalating need for efficient storage and transmission methods. The sheer size of these point cloud datasets presents challenges in rendering, transmission, and general usability. This thesis introduces a novel approach to point cloud geometry compression leveraging neural implicit representations, specifically through the use of a DiGS network model. By training this model on a single point cloud, we achieve a compact neural representation of its geometry. Notably, this representation allows for the reconstruction of the point cloud with an arbitrary resolution. After training a reconstructing network, dynamic quantization is applied on the trained weights, significantly reducing its overall bitrate without strongly compromising the quality of the reconstructed point cloud. A dequantization is then used to rebuild a high-fidelity representation of the original point cloud. Our experimental results demonstrate the efficacy of this approach in terms of compression ratios and reconstruction quality, assessed using PSNR relative to the bitrate. This research provides a promising direction for efficient point cloud geometry storage and transmission, addressing some of the growing demands of the 3D data era

    Multi-Sample Consensus Driven Unsupervised Normal Estimation for 3D Point Clouds

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    Deep normal estimators have made great strides on synthetic benchmarks. Unfortunately, their performance dramatically drops on the real scan data since they are supervised only on synthetic datasets. The point-wise annotation of ground truth normals is vulnerable to inefficiency and inaccuracies, which totally makes it impossible to build perfect real datasets for supervised deep learning. To overcome the challenge, we propose a multi-sample consensus paradigm for unsupervised normal estimation. The paradigm consists of multi-candidate sampling, candidate rejection, and mode determination. The latter two are driven by neighbor point consensus and candidate consensus respectively. Two primary implementations of the paradigm, MSUNE and MSUNE-Net, are proposed. MSUNE minimizes a candidate consensus loss in mode determination. As a robust optimization method, it outperforms the cutting-edge supervised deep learning methods on real data at the cost of longer runtime for sampling enough candidate normals for each query point. MSUNE-Net, the first unsupervised deep normal estimator as far as we know, significantly promotes the multi-sample consensus further. It transfers the three online stages of MSUNE to offline training. Thereby its inference time is 100 times faster. Besides that, more accurate inference is achieved, since the candidates of query points from similar patches can form a sufficiently large candidate set implicitly in MSUNE-Net. Comprehensive experiments demonstrate that the two proposed unsupervised methods are noticeably superior to some supervised deep normal estimators on the most common synthetic dataset. More importantly, they show better generalization ability and outperform all the SOTA conventional and deep methods on three real datasets: NYUV2, KITTI, and a dataset from PCV [1]

    Alternately denoising and reconstructing unoriented point sets

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    We propose a new strategy to bridge point cloud denoising and surface reconstruction by alternately updating the denoised point clouds and the reconstructed surfaces. In Poisson surface reconstruction, the implicit function is generated by a set of smooth basis functions centered at the octnodes. When the octree depth is properly selected, the reconstructed surface is a good smooth approximation of the noisy point set. Our method projects the noisy points onto the surface and alternately reconstructs and projects the point set. We use the iterative Poisson surface reconstruction (iPSR) to support unoriented surface reconstruction. Our method iteratively performs iPSR and acts as an outer loop of iPSR. Considering that the octree depth significantly affects the reconstruction results, we propose an adaptive depth selection strategy to ensure an appropriate depth choice. To manage the oversmoothing phenomenon near the sharp features, we propose a λ\lambda-projection method, which means to project the noisy points onto the surface with an individual control coefficient λi\lambda_{i} for each point. The coefficients are determined through a Voronoi-based feature detection method. Experimental results show that our method achieves high performance in point cloud denoising and unoriented surface reconstruction within different noise scales, and exhibits well-rounded performance in various types of inputs. The source code is available at~\url{https://github.com/Submanifold/AlterUpdate}.Comment: Accepted by Computers & Graphics from CAD/Graphics 202

    Neural-Singular-Hessian: Implicit Neural Representation of Unoriented Point Clouds by Enforcing Singular Hessian

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    Neural implicit representation is a promising approach for reconstructing surfaces from point clouds. Existing methods combine various regularization terms, such as the Eikonal and Laplacian energy terms, to enforce the learned neural function to possess the properties of a Signed Distance Function (SDF). However, inferring the actual topology and geometry of the underlying surface from poor-quality unoriented point clouds remains challenging. In accordance with Differential Geometry, the Hessian of the SDF is singular for points within the differential thin-shell space surrounding the surface. Our approach enforces the Hessian of the neural implicit function to have a zero determinant for points near the surface. This technique aligns the gradients for a near-surface point and its on-surface projection point, producing a rough but faithful shape within just a few iterations. By annealing the weight of the singular-Hessian term, our approach ultimately produces a high-fidelity reconstruction result. Extensive experimental results demonstrate that our approach effectively suppresses ghost geometry and recovers details from unoriented point clouds with better expressiveness than existing fitting-based methods

    CircNet: Meshing 3D Point Clouds with Circumcenter Detection

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    Reconstructing 3D point clouds into triangle meshes is a key problem in computational geometry and surface reconstruction. Point cloud triangulation solves this problem by providing edge information to the input points. Since no vertex interpolation is involved, it is beneficial to preserve sharp details on the surface. Taking advantage of learning-based techniques in triangulation, existing methods enumerate the complete combinations of candidate triangles, which is both complex and inefficient. In this paper, we leverage the duality between a triangle and its circumcenter, and introduce a deep neural network that detects the circumcenters to achieve point cloud triangulation. Specifically, we introduce multiple anchor priors to divide the neighborhood space of each point. The neural network then learns to predict the presences and locations of circumcenters under the guidance of those anchors. We extract the triangles dual to the detected circumcenters to form a primitive mesh, from which an edge-manifold mesh is produced via simple post-processing. Unlike existing learning-based triangulation methods, the proposed method bypasses an exhaustive enumeration of triangle combinations and local surface parameterization. We validate the efficiency, generalization, and robustness of our method on prominent datasets of both watertight and open surfaces. The code and trained models are provided at https://github.com/Ruitao-L/CircNet.Comment: accepted to ICLR202

    Neural Gradient Learning and Optimization for Oriented Point Normal Estimation

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    We propose Neural Gradient Learning (NGL), a deep learning approach to learn gradient vectors with consistent orientation from 3D point clouds for normal estimation. It has excellent gradient approximation properties for the underlying geometry of the data. We utilize a simple neural network to parameterize the objective function to produce gradients at points using a global implicit representation. However, the derived gradients usually drift away from the ground-truth oriented normals due to the lack of local detail descriptions. Therefore, we introduce Gradient Vector Optimization (GVO) to learn an angular distance field based on local plane geometry to refine the coarse gradient vectors. Finally, we formulate our method with a two-phase pipeline of coarse estimation followed by refinement. Moreover, we integrate two weighting functions, i.e., anisotropic kernel and inlier score, into the optimization to improve the robust and detail-preserving performance. Our method efficiently conducts global gradient approximation while achieving better accuracy and generalization ability of local feature description. This leads to a state-of-the-art normal estimator that is robust to noise, outliers and point density variations. Extensive evaluations show that our method outperforms previous works in both unoriented and oriented normal estimation on widely used benchmarks. The source code and pre-trained models are available at https://github.com/LeoQLi/NGLO.Comment: accepted by SIGGRAPH Asia 202

    What's the Situation with Intelligent Mesh Generation: A Survey and Perspectives

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    Intelligent Mesh Generation (IMG) represents a novel and promising field of research, utilizing machine learning techniques to generate meshes. Despite its relative infancy, IMG has significantly broadened the adaptability and practicality of mesh generation techniques, delivering numerous breakthroughs and unveiling potential future pathways. However, a noticeable void exists in the contemporary literature concerning comprehensive surveys of IMG methods. This paper endeavors to fill this gap by providing a systematic and thorough survey of the current IMG landscape. With a focus on 113 preliminary IMG methods, we undertake a meticulous analysis from various angles, encompassing core algorithm techniques and their application scope, agent learning objectives, data types, targeted challenges, as well as advantages and limitations. We have curated and categorized the literature, proposing three unique taxonomies based on key techniques, output mesh unit elements, and relevant input data types. This paper also underscores several promising future research directions and challenges in IMG. To augment reader accessibility, a dedicated IMG project page is available at \url{https://github.com/xzb030/IMG_Survey}

    Phase transition for the vacant set of random walk and random interlacements

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    We consider the set of points visited by the random walk on the discrete torus (Z/NZ)d(\mathbb{Z}/N\mathbb{Z})^d, for d≥3d \geq 3, at times of order uNduN^d, for a parameter u>0u>0 in the large-NN limit. We prove that the vacant set left by the walk undergoes a phase transition across a non-degenerate critical value u∗=u∗(d)u_* = u_*(d), as follows. For all u<u∗u< u_*, the vacant set contains a giant connected component with high probability, which has a non-vanishing asymptotic density and satisfies a certain local uniqueness property. In stark contrast, for all u>u∗u> u_* the vacant set scatters into tiny connected components. Our results further imply that the threshold u∗u_* precisely equals the critical value, introduced by Sznitman in arXiv:0704.2560, which characterizes the percolation transition of the corresponding local limit, the vacant set of random interlacements on Zd\mathbb{Z}^d. Our findings also yield the analogous infinite-volume result, i.e. the long purported equality of three critical parameters uˉ\bar u, u∗u_* and u∗∗u_{**} naturally associated to the vacant set of random interlacements.Comment: 94 pages, 2 figure
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