Topic
Geometric data analysis
About: Geometric data analysis is a research topic. Over the lifetime, 1156 publications have been published within this topic receiving 31627 citations.
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21 Jul 2017
TL;DR: This paper designs a novel type of neural network that directly consumes point clouds, which well respects the permutation invariance of points in the input and provides a unified architecture for applications ranging from object classification, part segmentation, to scene semantic parsing.
Abstract: Point cloud is an important type of geometric data structure. Due to its irregular format, most researchers transform such data to regular 3D voxel grids or collections of images. This, however, renders data unnecessarily voluminous and causes issues. In this paper, we design a novel type of neural network that directly consumes point clouds, which well respects the permutation invariance of points in the input. Our network, named PointNet, provides a unified architecture for applications ranging from object classification, part segmentation, to scene semantic parsing. Though simple, PointNet is highly efficient and effective. Empirically, it shows strong performance on par or even better than state of the art. Theoretically, we provide analysis towards understanding of what the network has learnt and why the network is robust with respect to input perturbation and corruption.
9,457 citations
TL;DR: In many applications, such geometric data are large and complex (in the case of social networks, on the scale of billions) and are natural targets for machine-learning techniques as mentioned in this paper.
Abstract: Many scientific fields study data with an underlying structure that is non-Euclidean. Some examples include social networks in computational social sciences, sensor networks in communications, functional networks in brain imaging, regulatory networks in genetics, and meshed surfaces in computer graphics. In many applications, such geometric data are large and complex (in the case of social networks, on the scale of billions) and are natural targets for machine-learning techniques. In particular, we would like to use deep neural networks, which have recently proven to be powerful tools for a broad range of problems from computer vision, natural-language processing, and audio analysis. However, these tools have been most successful on data with an underlying Euclidean or grid-like structure and in cases where the invariances of these structures are built into networks used to model them.
2,565 citations
TL;DR: This paper briefly update the discussion in that paper and summarize the advances in the ten years since the paper by Rohlf and Marcus (1993) and speculate on future directions in morphometric analysis.
Abstract: The analysis of shape is a fundamental part of much biological research. As the field of statistics developed, so have the sophistication of the analysis of these types of data. This lead to multivariate morphometrics in which suites of measurements were analyzed together using canonical variates analysis, principal components analysis, and related methods. In the 1980s, a fundamental change began in the nature of the data gathered and analyzed. This change focused on the coordinates of landmarks and the geometric information about their relative positions. As a by-product of such an approach, results of multivariate analyses could be visualized as configurations of landmarks back in the original space of the organism rather than only as statistical scatter plots. This new approach, called “geometric morphometrics”, had benefits that lead Rohlf and Marcus (1993) to proclaim a “revolution” in morphometrics. In this paper, we briefly update the discussion in that paper and summarize the advances in the ten years since the paper by Rohlf and Marcus. We also speculate on future directions in morphometric analysis.
1,910 citations
Book•
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01 Jan 1985
TL;DR: This text accurately treats the parametric geometry of curves, surfaces and solids, the construction of geometric models and the analytical techniques that can be used and applications.
Abstract: From the Publisher:
The first comprehensive and complete coverage of geometric modeling. This text accurately treats the parametric geometry of curves, surfaces and solids, the construction of geometric models and the analytical techniques that can be used and applications. Extensive use is made of end-of-chapter problems.
1,323 citations
Posted Content•
TL;DR: PointNet as discussed by the authors proposes a novel type of neural network that directly consumes point clouds and well respects the permutation invariance of points in the input, which provides a unified architecture for applications ranging from object classification, part segmentation, to scene semantic parsing.
Abstract: Point cloud is an important type of geometric data structure. Due to its irregular format, most researchers transform such data to regular 3D voxel grids or collections of images. This, however, renders data unnecessarily voluminous and causes issues. In this paper, we design a novel type of neural network that directly consumes point clouds and well respects the permutation invariance of points in the input. Our network, named PointNet, provides a unified architecture for applications ranging from object classification, part segmentation, to scene semantic parsing. Though simple, PointNet is highly efficient and effective. Empirically, it shows strong performance on par or even better than state of the art. Theoretically, we provide analysis towards understanding of what the network has learnt and why the network is robust with respect to input perturbation and corruption.
1,156 citations