Hypergraph Spectral Clustering for Point Cloud Segmentation

Zhang, Songyang; Cui, Shuguang; Ding, Zhi

doi:10.1109/lsp.2020.3023587

Cited by 22 publications

(8 citation statements)

References 31 publications

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“…Forming an MLN would often require estimation of distances among nodes and can be time-consuming. Fortunately, we can bypass such complexity and estimate MLN spectrum directly from datasets based on signal properties, e.g., smoothness or stationarity [27]- [30]. In this part, we mainly focus on two scenarios:…”

Section: Direct Spectrum Estimation Over Mlnmentioning

confidence: 99%

Image Processing via Multilayer Graph Spectra

Zhang¹,

Deng²,

Ding³

2021

Preprint

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This work introduces a tensor-based framework of graph signal processing over multilayer networks (M-GSP) to analyze high-dimensional signal interactions. Following Part I's introduction of fundamental definitions and spectrum properties of M-GSP, this second Part focuses on more detailed discussions of implementation and applications of M-GSP. Specifically, we define the concepts of stationary process, convolution, bandlimited signals, and sampling theory over multilayer networks. We also develop fundamentals of filter design and derive approximated methods of spectrum estimation within the proposed framework. For practical applications, we further present several MLN-based methods for signal processing and data analysis. Our experimental results demonstrate significant performance improvement using our M-GSP framework over traditional signal processing solutions.

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Section: Direct Spectrum Estimation Over Mlnmentioning

confidence: 99%

Image Processing via Multilayer Graph Spectra

Zhang¹,

Deng²,

Ding³

2021

Preprint

Self Cite

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“…As a new form of 3D signal expression, point cloud has received widespread attention due to the talent for representing 3D shapes efficiently and being obtained directly and easily by scanning. And it has been adopted in many applications, such as segmentation [1], [2], 3D reconstruction [3], [4], compression [5]- [7], autonomous driving [8]. Particularly, although dense correspondence estimation is a fundamental task in computer vision, which has been investigated widely on other signal formats (e.g.…”

Section: Introductionmentioning

confidence: 99%

Searching Dense Point Correspondences via Permutation Matrix Learning

Zhang

Sun

Dai

et al. 2022

IEEE Signal Process. Lett.

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Although 3D point cloud data has received widespread attentions as a general form of 3D signal expression, applying point clouds to the task of dense correspondence estimation between 3D shapes has not been investigated widely. Furthermore, even in the few existing 3D point cloud-based methods, an important and widely acknowledged principle, i.e. one-toone matching, is usually ignored. In response, this paper presents a novel end-to-end learning-based method to estimate the dense correspondence of 3D point clouds, in which the problem of point matching is formulated as a zero-one assignment problem to achieve a permutation matching matrix to implement the oneto-one principle fundamentally. Note that the classical solutions of this assignment problem are always non-differentiable, which is fatal for deep learning frameworks. Thus we design a special matching module, which solves a doubly stochastic matrix at first and then projects this obtained approximate solution to the desired permutation matrix. Moreover, to guarantee end-to-end learning and the accuracy of the calculated loss, we calculate the loss from the learned permutation matrix but propagate the gradient to the doubly stochastic matrix directly which bypasses the permutation matrix during the backward propagation. Our method can be applied to both non-rigid and rigid 3D point cloud data and extensive experiments show that our method achieves state-of-the-art performance for dense correspondence learning.

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“…Furthermore, by generalizing graph signal processing [19], hypergraph signal processing (HGSP) [21] [20] provides a theoretical foundation for spectral analysis in hypergraph-based point cloud processing. Specifically, stationarity-based hypergraph estimation, in conjunction with hypergraph-based filters, has demonstrated notable successes in processing point clouds for various tasks including segmentation, sampling, and denoising [22], [23].…”

Section: Introductionmentioning

confidence: 99%

An Efficient Hypergraph Approach to Robust Point Cloud Resampling

Deng,

Zhang,

Ding

2021

Preprint

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Efficient processing and feature extraction of largescale point clouds are important in related computer vision and cyber-physical systems. This work investigates point cloud resampling based on hypergraph signal processing (HGSP) to better explore the underlying relationship among different cloud points and to extract contour-enhanced features. Specifically, we design hypergraph spectral filters to capture multi-lateral interactions among the signal nodes of point clouds and to better preserve their surface outlines. Without the need and the computation to first construct the underlying hypergraph, our low complexity approach directly estimates hypergraph spectrum of point clouds by leveraging hypergraph stationary processes from the observed 3D coordinates. Evaluating the proposed resampling methods with several metrics, our test results validate the high efficacy of hypergraph characterization of point clouds and demonstrate the robustness of hypergraph-based resampling under noisy observations.

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Hypergraph Spectral Clustering for Point Cloud Segmentation

Cited by 22 publications

References 31 publications

Image Processing via Multilayer Graph Spectra

Image Processing via Multilayer Graph Spectra

Searching Dense Point Correspondences via Permutation Matrix Learning

An Efficient Hypergraph Approach to Robust Point Cloud Resampling

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