Graph Signal Processing for Geometric Data and Beyond: Theory and Applications

@article{Hu2021GraphSP,
  title={Graph Signal Processing for Geometric Data and Beyond: Theory and Applications},
  author={Wei Hu and Jiahao Pang and Xianming Liu and Dong Tian and Chia-Wen Lin and Anthony Vetro},
  journal={ArXiv},
  year={2021},
  volume={abs/2008.01918}
}
Geometric data acquired from real-world scenes, e.g., 2D depth images, 3D point clouds, and 4D dynamic point clouds, have found a wide range of applications including immersive telepresence, autonomous driving, surveillance, etc. Due to irregular sampling patterns of most geometric data, traditional image/video processing methodologies are limited, while Graph Signal Processing (GSP)---a fast-developing field in the signal processing community---enables processing signals that reside on… 

Figures and Tables from this paper

Point Cloud Attacks in Graph Spectral Domain: When 3D Geometry Meets Graph Signal Processing
TLDR
This work proposes point cloud attacks from a new perspective—the graph spectral domain attack, aiming to perturb graph transform coefficients in the spectral domain that corresponds to varying certain geometric structure, and introduces a low-frequency constraint to limit perturbations within imperceptible high- frequencies.
Dynamic Point Cloud Denoising via Gradient Fields
TLDR
This paper proposes a novel gradient-field-based dynamic point cloud denoising method, exploiting the temporal correspondence via the estimation of gradient—a fundamental problem in dynamic point clouds processing and analysis.
VIPDA: A Visually Driven Point Cloud Denoising Algorithm Based on Anisotropic Point Cloud Filtering
TLDR
A novel visually driven point cloud denoising algorithm (VIPDA) inspired by visually driven filtering approaches that outperforms the others in terms of the signal-to-noise ratio (SNR) and compares with state-of-the-art methods.
Exploring the Devil in Graph Spectral Domain for 3D Point Cloud Attacks
TLDR
This work proposes point cloud attacks from a new perspective—Graph Spectral Domain Attack (GSDA), aiming to perturb transform coefficients in the graph spectral domain that corresponds to varying certain geometric structure, and demonstrates the effectiveness of the proposed GSDA in terms of both imperceptibility and attack success rates under a variety of defense strategies.
Adaptive Sign Algorithm for Graph Signal Processing
Deep Point Set Resampling via Gradient Fields
TLDR
A novel paradigm of point set resampling for restoration, which learns continuous gradient fields of point clouds that converge points towards the underlying surface that guarantees the continuity of the model for solvable optimization is proposed.
Laplacian Constrained Precision Matrix Estimation: Existence and High Dimensional Consistency
  • E. Pavez
  • Computer Science, Mathematics
    AISTATS
  • 2022
TLDR
This paper obtains a necessary and sufficient condition for existence of this estimator, that con-sists on checking whether a certain data dependent graph is connected, and proves consistency in the high dimensional setting under the symmetrized Stein loss.
Generic Reversible Visible Watermarking via Regularized Graph Fourier Transform Coding
TLDR
This work proposes regularized Graph Fourier Transform (GFT) coding, where the difference image is smoothed via the graph Laplacian regularizer for more efficient compression and then encoded by multi-resolution GFTs in an approximately optimal manner.
SCTN: Sparse Convolution-Transformer Network for Scene Flow Estimation
TLDR
This work proposes a novel architecture named Sparse Convolution-Transformer Network (SCTN) that equips the sparse convolution with the transformer, and shows that the learned relation-based contextual information is rich and helpful for matching corresponding points, benefiting scene flow estimation.
Unsupervised Learning of Geometric Sampling Invariant Representations for 3D Point Clouds
TLDR
This work proposes a novel unsupervised learning of geometric sampling invariant representations, aiming to learn intrinsic feature representations of point clouds on graphs based on that the geometry of one object can be sampled in various patterns and densities into different forms of point Clouds.
...
...

References

SHOWING 1-10 OF 155 REFERENCES
Feature Graph Learning for 3D Point Cloud Denoising
TLDR
This work alternately optimize the diagonal and off-diagonal entries of a Mahalanobis distance matrix and constrain the Schur complement of sub-matrix to be positive definite (PD) via linear inequalities derived from the Gershgorin circle theorem.
Dynamic Graph CNN for Learning on Point Clouds
TLDR
This work proposes a new neural network module suitable for CNN-based high-level tasks on point clouds, including classification and segmentation called EdgeConv, which acts on graphs dynamically computed in each layer of the network.
Multiresolution Graph Fourier Transform for Compression of Piecewise Smooth Images
TLDR
Experimental results show that the proposed multiresolution-GFT scheme outperforms H.264 intra by 6.8 dB on average in peak signal-to-noise ratio at the same bit rate.
Wavelets on Graphs via Spectral Graph Theory
Graph Laplacians and their Convergence on Random Neighborhood Graphs
TLDR
This paper determines the pointwise limit of three different graph Laplacians used in the literature as the sample size increases and the neighborhood size approaches zero and shows that for a uniform measure on the submanifold all graph LaPLacians have the same limit up to constants.
3D Point Cloud Denoising Using Graph Laplacian Regularization of a Low Dimensional Manifold Model
TLDR
This paper extends a previously proposed low-dimensional manifold model for the image patches to surface patches in the point cloud, and seeks self-similar patches to denoise them simultaneously using the patch manifold prior, and proposes a new discrete patch distance measure to quantify the similarity between two same-sized surface patches for graph construction that is robust to noise.
Graph-Based Blind Image Deblurring From a Single Photograph
TLDR
This paper argues that a skeleton image—a proxy that retains the strong gradients of the target but smooths out the details—can be used to accurately estimate the blur kernel and has a unique bi-modal edge weight distribution, and designs a reweighted graph total variation (RGTV) prior that can efficiently promote a bi- modal edge Weight distribution given a blurry patch.
Graph-Based Compression of Dynamic 3D Point Cloud Sequences
TLDR
This is the first paper that exploits both the spatial correlation inside each frame and the temporal correlation between the frames (through the motion estimation) to compress the color and the geometry of 3D point cloud sequences in an efficient way.
An Analysis of the Convergence of Graph Laplacians
TLDR
A kernel-free framework is introduced to analyze graph constructions with shrinking neighborhoods in general and apply it to analyze locally linear embedding (LLE) and how desirable properties such as a convergent spectrum and sparseness can be achieved by choosing the appropriate graph construction.
Fast Resampling of Three-Dimensional Point Clouds via Graphs
TLDR
This work uses a general feature-extraction operator to represent application-dependent features and proposes a general reconstruction error to evaluate the quality of resampling; by minimizing the error, it obtains a general form of optimal resamplings distribution.
...
...