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Register a new userBeyond Farthest Point Sampling in Point-Wise Analysis
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Yiqun Lin
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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Sampling, grouping, and aggregation are three important components in the multi-scale analysis of point clouds. In this paper, we present a novel data-driven sampler learning strategy for point-wise analysis tasks. Unlike the widely used sampling technique, Farthest Point Sampling (FPS), we propose to learn sampling and downstream applications jointly. Our key insight is that uniform sampling methods like FPS are not always optimal for different tasks: sampling more points around boundary areas can make the point-wise classification easier for segmentation. Towards the end, we propose a novel sampler learning strategy that learns sampling point displacement supervised by task-related ground truth information and can be trained jointly with the underlying tasks. We further demonstrate our methods in various point-wise analysis architectures, including semantic part segmentation, point cloud completion, and keypoint detection. Our experiments show that jointly learning of the sampler and task brings remarkable improvement over previous baseline methods.
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Augmentation can benefit point cloud learning due to the limited availability of large-scale public datasets. This paper proposes a mix-up augmentation approach, PointManifoldCut, which replaces the neural network embedded points, rather than the Euclidean space coordinates. This approach takes the advantage that points at the higher levels of the neural network are already trained to embed its neighbors relations and mixing these representation will not mingle the relation between itself and its label. This allows to regularize the parameter space as the other augmentation methods but without worrying about the proper label of the replaced points. The experiments show that our proposed approach provides a competitive performance on point cloud classification and segmentation when it is combined with the cutting-edge vanilla point cloud networks. The result shows a consistent performance boosting compared to other state-of-the-art point cloud augmentation method, such as PointMixup and PointCutMix. The code of this paper is available at: https://github.com/fun0515/PointManifoldCut.
Let $P$ be a simple polygon with $n$ vertices. For any two points in $P$, the geodesic distance between them is the length of the shortest path that connects them among all paths contained in $P$. Given a set $S$ of $m$ sites being a subset of the vertices of $P$, we present a randomized algorithm to compute the geodesic farthest-point Voronoi diagram of $S$ in $P$ running in expected $O(n + m)$ time. That is, a partition of $P$ into cells, at most one cell per site, such that every point in a cell has the same farthest site with respect to the geodesic distance. In particular, this algorithm can be extended to run in expected $O(n + mlog m)$ time when $S$ is an arbitrary set of $m$ sites contained in $P$, thereby solving the open problem posed by Mitchell in Chapter 27 of the Handbook of Computational Geometry.
Features that are equivariant to a larger group of symmetries have been shown to be more discriminative and powerful in recent studies. However, higher-order equivariant features often come with an exponentially-growing computational cost. Furthermore, it remains relatively less explored how rotation-equivariant features can be leveraged to tackle 3D shape alignment tasks. While many past approaches have been based on either non-equivariant or invariant descriptors to align 3D shapes, we argue that such tasks may benefit greatly from an equivariant framework. In this paper, we propose an effective and practical SE(3) (3D translation and rotation) equivariant network for point cloud analysis that addresses both problems. First, we present SE(3) separable point convolution, a novel framework that breaks down the 6D convolution into two separable convolutional operators alternatively performed in the 3D Euclidean and SO(3) spaces. This significantly reduces the computational cost without compromising the performance. Second, we introduce an attention layer to effectively harness the expressiveness of the equivariant features. While jointly trained with the network, the attention layer implicitly derives the intrinsic local frame in the feature space and generates attention vectors that can be integrated into different alignment tasks. We evaluate our approach through extensive studies and visual interpretations. The empirical results demonstrate that our proposed model outperforms strong baselines in a variety of benchmarks
Recently, 3D deep learning models have been shown to be susceptible to adversarial attacks like their 2D counterparts. Most of the state-of-the-art (SOTA) 3D adversarial attacks perform perturbation to 3D point clouds. To reproduce these attacks in pseudo physical scenario, a generated adversarial 3D point cloud need to be reconstructed to mesh, which leads to a significant drop in its adversarial effect. In this paper, we propose a strong 3D adversarial attack named Mesh Attack to address this problem by directly performing perturbation on mesh of a 3D object. Specifically, in each iteration of our method, the mesh is first sampled to point cloud by a differentiable sample module. Then a point cloud classifier is used to back-propagate a combined loss to update the mesh vertices. The combined loss includes an adversarial loss to mislead the point cloud classifier and three mesh losses to regularize the mesh to be smooth. Extensive experiments demonstrate that the proposed scheme outperforms SOTA 3D attacks by a significant margin in the pseudo physical scenario. We also achieved SOTA performance under various defenses. Moreover, to the best of our knowledge, our Mesh Attack is the first attempt of adversarial attack on mesh classifier. Our code is available at: {footnotesize{url{https://github.com/cuge1995/Mesh-Attack}}}.
Given a set of point sites in a simple polygon, the geodesic farthest-point Voronoi diagram partitions the polygon into cells, at most one cell per site, such that every point in a cell has the same farthest site with respect to the geodesic metric. We present an $O(nloglog n+mlog m)$- time algorithm to compute the geodesic farthest-point Voronoi diagram of $m$ point sites in a simple $n$-gon. This improves the previously best known algorithm by Aronov et al. [Discrete Comput. Geom. 9(3):217-255, 1993]. In the case that all point sites are on the boundary of the simple polygon, we can compute the geodesic farthest-point Voronoi diagram in $O((n + m) log log n)$ time.
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