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Register a new userNeural-IMLS: Learning Implicit Moving Least-Squares for Surface Reconstruction from Unoriented Point clouds
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Added by
Zixiong Wang
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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Surface reconstruction from noisy, non-uniformly, and unoriented point clouds is a fascinating yet difficult problem in computer vision and computer graphics. In this paper, we propose Neural-IMLS, a novel approach that learning noise-resistant signed distance function (SDF) for reconstruction. Instead of explicitly learning priors with the ground-truth signed distance values, our method learns the SDF from raw point clouds directly in a self-supervised fashion by minimizing the loss between the couple of SDFs, one obtained by the implicit moving least-square function (IMLS) and the other by our network. Finally, a watertight and smooth 2-manifold triangle mesh is yielded by running Marching Cubes. We conduct extensive experiments on various benchmarks to demonstrate the performance of Neural-IMLS, especially for point clouds with noise.
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Point set is a flexible and lightweight representation widely used for 3D deep learning. However, their discrete nature prevents them from representing continuous and fine geometry, posing a major issue for learning-based shape generation. In this work, we turn the discrete point sets into smooth surfaces by introducing the well-known implicit moving least-squares (IMLS) surface formulation, which naturally defines locally implicit functions on point sets. We incorporate IMLS surface generation into deep neural networks for inheriting both the flexibility of point sets and the high quality of implicit surfaces. Our IMLSNet predicts an octree structure as a scaffold for generating MLS points where needed and characterizes shape geometry with learned local priors. Furthermore, our implicit function evaluation is independent of the neural network once the MLS points are predicted, thus enabling fast runtime evaluation. Our experiments on 3D object reconstruction demonstrate that IMLSNets outperform state-of-the-art learning-based methods in terms of reconstruction quality and computational efficiency. Extensive ablation tests also validate our network design and loss functions.
Neural shape representations have recently shown to be effective in shape analysis and reconstruction tasks. Existing neural network methods require point coordinates and corresponding normal vectors to learn the implicit level sets of the shape. Normal vectors are often not provided as raw data, therefore, approximation and reorientation are required as pre-processing stages, both of which can introduce noise. In this paper, we propose a divergence guided shape representation learning approach that does not require normal vectors as input. We show that incorporating a soft constraint on the divergence of the distance function favours smooth solutions that reliably orients gradients to match the unknown normal at each point, in some cases even better than approaches that use ground truth normal vectors directly. Additionally, we introduce a novel geometric initialization method for sinusoidal shape representation networks that further improves convergence to the desired solution. We evaluate the effectiveness of our approach on the task of surface reconstruction and show state-of-the-art performance compared to other unoriented methods and on-par performance compared to oriented methods.
The approximation of both geodesic distances and shortest paths on point cloud sampled from an embedded submanifold $mathcal{M}$ of Euclidean space has been a long-standing challenge in computational geometry. Given a sampling resolution parameter $ h $, state-of-the-art discrete methods yield $ O(h) $ provable approximations. In this paper, we investigate the convergence of such approximations made by Manifold Moving Least-Squares (Manifold-MLS), a method that constructs an approximating manifold $mathcal{M}^h$ using information from a given point cloud that was developed by Sober & Levin in 2019. In this paper, we show that provided that $mathcal{M}in C^{k}$ and closed (i.e. $mathcal{M}$ is a compact manifold without boundary) the Riemannian metric of $ mathcal{M}^h $ approximates the Riemannian metric of $ mathcal{M}, $. Explicitly, given points $ p_1, p_2 in mathcal{M}$ with geodesic distance $ rho_{mathcal{M}}(p_1, p_2) $, we show that their corresponding points $ p_1^h, p_2^h in mathcal{M}^h$ have a geodesic distance of $ rho_{mathcal{M}^h}(p_1^h,p_2^h) = rho_{mathcal{M}}(p_1, p_2)(1 + O(h^{k-1})) $ (i.e., the Manifold-MLS is nearly an isometry). We then use this result, as well as the fact that $ mathcal{M}^h $ can be sampled with any desired resolution, to devise a naive algorithm that yields approximate geodesic distances with a rate of convergence $ O(h^{k-1}) $. We show the potential and the robustness to noise of the proposed method on some numerical simulations.
The prevalence of relation networks in computer vision is in stark contrast to underexplored point-based methods. In this paper, we explore the possibilities of local relation operators and survey their feasibility. We propose a scalable and efficient module, called group relation aggregator. The module computes a feature of a group based on the aggregation of the features of the inner-group points weighted by geometric relations and semantic relations. We adopt this module to design our RPNet. We further verify the expandability of RPNet, in terms of both depth and width, on the tasks of classification and segmentation. Surprisingly, empirical results show that wider RPNet fits for classification, while deeper RPNet works better on segmentation. RPNet achieves state-of-the-art for classification and segmentation on challenging benchmarks. We also compare our local aggregator with PointNet++, with around 30% parameters and 50% computation saving. Finally, we conduct experiments to reveal the robustness of RPNet with regard to rigid transformation and noises.
We present an algorithm for approximating a function defined over a $d$-dimensional manifold utilizing only noisy function values at locations sampled from the manifold with noise. To produce the approximation we do not require any knowledge regarding the manifold other than its dimension $d$. We use the Manifold Moving Least-Squares approach of (Sober and Levin 2016) to reconstruct the atlas of charts and the approximation is built on-top of those charts. The resulting approximant is shown to be a function defined over a neighborhood of a manifold, approximating the originally sampled manifold. In other words, given a new point, located near the manifold, the approximation can be evaluated directly on that point. We prove that our construction yields a smooth function, and in case of noiseless samples the approximation order is $mathcal{O}(h^{m+1})$, where $h$ is a local density of sample parameter (i.e., the fill distance) and $m$ is the degree of a local polynomial approximation, used in our algorithm. In addition, the proposed algorithm has linear time complexity with respect to the ambient-spaces dimension. Thus, we are able to avoid the computational complexity, commonly encountered in high dimensional approximations, without having to perform non-linear dimension reduction, which inevitably introduces distortions to the geometry of the data. Additionaly, we show numerical experiments that the proposed approach compares favorably to statistical approaches for regression over manifolds and show its potential.
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