arXiv subjects

Antonio Ortega

Publications and source records attributed to Antonio Ortega.

At least 55 records · Page 3Linked to original sources

arXiv2024

Full reference point cloud quality assessment using support vector regression

Point clouds are a general format for representing realistic 3D objects in diverse 3D applications. Since point clouds have large data sizes, developing efficient point cloud compression methods is crucial. However, excessive compression leads to various distortions, which deteriorates the point cloud quality perceived by end users. Thus, establishing reliable point cloud quality assessment (PCQA) methods is essential as a benchmark to develop efficient compression methods. This paper presents an accurate full-reference point cloud quality assessment (FR-PCQA) method called full-reference quality assessment using support vector regression (FRSVR) for various types of degradations such as compression distortion, Gaussian noise, and down-sampling. The proposed method demonstrates accurate PCQA by integrating five FR-based metrics covering various types of errors (e.g., considering geometric distortion, color distortion, and point count) using support vector regression (SVR). Moreover, the proposed method achieves a superior trade-off between accuracy and calculation speed because it includes only the calculation of these five simple metrics and SVR, which can perform fast prediction. Experimental results with three types of open datasets show that the proposed method is more accurate than conventional FR-PCQA methods. In addition, the proposed method is faster than state-of-the-art methods that utilize complicated features such as curvature and multi-scale features. Thus, the proposed method provides excellent performance in terms of the accuracy of PCQA and processing speed. Our method is available from https://github.com/STAC-USC/FRSVR-PCQA.

cs.CV↗

arXiv2024

Fast graph-based denoising for point cloud color information

Point clouds are utilized in various 3D applications such as cross-reality (XR) and realistic 3D displays. In some applications, e.g., for live streaming using a 3D point cloud, real-time point cloud denoising methods are required to enhance the visual quality. However, conventional high-precision denoising methods cannot be executed in real time for large-scale point clouds owing to the complexity of graph constructions with K nearest neighbors and noise level estimation. This paper proposes a fast graph-based denoising (FGBD) for a large-scale point cloud. First, high-speed graph construction is achieved by scanning a point cloud in various directions and searching adjacent neighborhoods on the scanning lines. Second, we propose a fast noise level estimation method using eigenvalues of the covariance matrix on a graph. Finally, we also propose a new low-cost filter selection method to enhance denoising accuracy to compensate for the degradation caused by the acceleration algorithms. In our experiments, we succeeded in reducing the processing time dramatically while maintaining accuracy relative to conventional denoising methods. Denoising was performed at 30fps, with frames containing approximately 1 million points.

cs.CV↗

arXiv2024

Full-reference Point Cloud Quality Assessment Using Spectral Graph Wavelets

Point clouds in 3D applications frequently experience quality degradation during processing, e.g., scanning and compression. Reliable point cloud quality assessment (PCQA) is important for developing compression algorithms with good bitrate-quality trade-offs and techniques for quality improvement (e.g., denoising). This paper introduces a full-reference (FR) PCQA method utilizing spectral graph wavelets (SGWs). First, we propose novel SGW-based PCQA metrics that compare SGW coefficients of coordinate and color signals between reference and distorted point clouds. Second, we achieve accurate PCQA by integrating several conventional FR metrics and our SGW-based metrics using support vector regression. To our knowledge, this is the first study to introduce SGWs for PCQA. Experimental results demonstrate the proposed PCQA metric is more accurately correlated with subjective quality scores compared to conventional PCQA metrics.

cs.CV↗

arXiv2024

Adaptive Online Learning of Separable Path Graph Transforms for Intra-prediction

Current video coding standards, including H.264/AVC, HEVC, and VVC, employ discrete cosine transform (DCT), discrete sine transform (DST), and secondary to Karhunen-Loeve transforms (KLTs) decorrelate the intra-prediction residuals. However, the efficiency of these transforms in decorrelation can be limited when the signal has a non-smooth and non-periodic structure, such as those occurring in textures with intricate patterns. This paper introduces a novel adaptive separable path graph-based transform (GBT) that can provide better decorrelation than the DCT for intra-predicted texture data. The proposed GBT is learned in an online scenario with sequential K-means clustering, which groups similar blocks during encoding and decoding to adaptively learn the GBT for the current block from previously reconstructed areas with similar characteristics. A signaling overhead is added to the bitstream of each coding block to indicate the usage of the proposed graph-based transform. We assess the performance of this method combined with H.264/AVC intra-coding tools and demonstrate that it can significantly outperform H.264/AVC DCT for intra-predicted texture data.

eess.IV↗

arXiv2024

Lossy Compression of Adjacency Matrices by Graph Filter Banks

This paper proposes a compression framework for adjacency matrices of weighted graphs based on graph filter banks. Adjacency matrices are widely used mathematical representations of graphs and are used in various applications in signal processing, machine learning, and data mining. In many problems of interest, these adjacency matrices can be large, so efficient compression methods are crucial. In this paper, we propose a lossy compression of weighted adjacency matrices, where the binary adjacency information is encoded losslessly (so the topological information of the graph is preserved) while the edge weights are compressed lossily. For the edge weight compression, the target graph is converted into a line graph, whose nodes correspond to the edges of the original graph, and where the original edge weights are regarded as a graph signal on the line graph. We then transform the edge weights on the line graph with a graph filter bank for sparse representation. Experiments on synthetic data validate the effectiveness of the proposed method by comparing it with existing lossy matrix compression methods.

eess.SP↗

arXiv2024

Irregularity-Aware Bandlimited Approximation for Graph Signal Interpolation

In most work to date, graph signal sampling and reconstruction algorithms are intrinsically tied to graph properties, assuming bandlimitedness and optimal sampling set choices. However, practical scenarios often defy these assumptions, leading to suboptimal performance. In the context of sampling and reconstruction, graph irregularities lead to varying contributions from sampled nodes for interpolation and differing levels of reliability for interpolated nodes. The existing GFT-based methods in the literature make bandlimited signal approximations without considering graph irregularities and the relative significance of nodes, resulting in suboptimal reconstruction performance under various mismatch conditions. In this paper, we leverage the GFT equipped with a specific inner product to address graph irregularities and account for the relative importance of nodes during the bandlimited signal approximation and interpolation process. Empirical evidence demonstrates that the proposed method outperforms other GFT-based approaches for bandlimited signal interpolation in challenging scenarios, such as sampling sets selected independently of the underlying graph, low sampling rates, and high noise levels.

eess.SP↗

arXiv2024

Optimizing $k$ in $k$NN Graphs with Graph Learning Perspective

In this paper, we propose a method, based on graph signal processing, to optimize the choice of $k$ in $k$-nearest neighbor graphs ($k$NNGs). $k$NN is one of the most popular approaches and is widely used in machine learning and signal processing. The parameter $k$ represents the number of neighbors that are connected to the target node; however, its appropriate selection is still a challenging problem. Therefore, most $k$NNGs use ad hoc selection methods for $k$. In the proposed method, we assume that a different $k$ can be chosen for each node. We formulate a discrete optimization problem to seek the best $k$ with a constraint on the sum of distances of the connected nodes. The optimal $k$ values are efficiently obtained without solving a complex optimization. Furthermore, we reveal that the proposed method is closely related to existing graph learning methods. In experiments on real datasets, we demonstrate that the $k$NNGs obtained with our method are sparse and can determine an appropriate variable number of edges per node. We validate the effectiveness of the proposed method for point cloud denoising, comparing our denoising performance with achievable graph construction methods that can be scaled to typical point cloud sizes (e.g., thousands of nodes).

cs.LG↗

arXiv2024

Frequency analysis and filter design for directed graphs with polar decomposition

In this study, we challenge the traditional approach of frequency analysis on directed graphs, which typically relies on a single measure of signal variation such as total variation. We argue that the inherent directionality in directed graphs necessitates a multifaceted analytical approach that incorporates multiple signal variations definitions. Our methodology leverages the polar decomposition to define two distinct variations, each associated with different matrices derived from this decomposition. This approach provides a novel interpretation in the node domain and reveals aspects of graph signals that may be overlooked with a singular measure of variation. Additionally, we develop graph filters specifically designed to smooth graph signals in accordance with our proposed variations. These filters allow for bypassing costly filtering operations associated with the original graph through effective cascading. We demonstrate the efficacy of our methodology using an M-block cyclic graph example, validating our claims and showcasing the advantages of our multifaceted approach in analyzing signals on directed graphs.

eess.SP↗

arXiv2023

Nowcasting Temporal Trends Using Indirect Surveys

Indirect surveys, in which respondents provide information about other people they know, have been proposed for estimating (nowcasting) the size of a \emph{hidden population} where privacy is important or the hidden population is hard to reach. Examples include estimating casualties in an earthquake, conditions among female sex workers, and the prevalence of drug use and infectious diseases. The Network Scale-up Method (NSUM) is the classical approach to developing estimates from indirect surveys, but it was designed for one-shot surveys. Further, it requires certain assumptions and asking for or estimating the number of individuals in each respondent's network. In recent years, surveys have been increasingly deployed online and can collect data continuously (e.g., COVID-19 surveys on Facebook during much of the pandemic). Conventional NSUM can be applied to these scenarios by analyzing the data independently at each point in time, but this misses the opportunity of leveraging the temporal dimension. We propose to use the responses from indirect surveys collected over time and develop analytical tools (i) to prove that indirect surveys can provide better estimates for the trends of the hidden population over time, as compared to direct surveys and (ii) to identify appropriate temporal aggregations to improve the estimates. We demonstrate through extensive simulations that our approach outperforms traditional NSUM and direct surveying methods. We also empirically demonstrate the superiority of our approach on a real indirect survey dataset of COVID-19 cases.

cs.SI↗

arXiv2023

Towards a geometric understanding of Spatio Temporal Graph Convolution Networks

Spatiotemporal graph convolutional networks (STGCNs) have emerged as a desirable model for skeleton-based human action recognition. Despite achieving state-of-the-art performance, there is a limited understanding of the representations learned by these models, which hinders their application in critical and real-world settings. While layerwise analysis of CNN models has been studied in the literature, to the best of our knowledge, there exists no study on the layerwise explainability of the embeddings learned on spatiotemporal data using STGCNs. In this paper, we first propose to use a local Dataset Graph (DS-Graph) obtained from the feature representation of input data at each layer to develop an understanding of the layer-wise embedding geometry of the STGCN. To do so, we develop a window-based dynamic time warping (DTW) method to compute the distance between data sequences with varying temporal lengths. To validate our findings, we have developed a layer-specific Spatiotemporal Graph Gradient-weighted Class Activation Mapping (L-STG-GradCAM) technique tailored for spatiotemporal data. This approach enables us to visually analyze and interpret each layer within the STGCN network. We characterize the functions learned by each layer of the STGCN using the label smoothness of the representation and visualize them using our L-STG-GradCAM approach. Our proposed method is generic and can yield valuable insights for STGCN architectures in different applications. However, this paper focuses on the human activity recognition task as a representative application. Our experiments show that STGCN models learn representations that capture general human motion in their initial layers while discriminating different actions only in later layers. This justifies experimental observations showing that fine-tuning deeper layers works well for transfer between related tasks.

eess.IV↗

arXiv2023

The faces of Convolution: from the Fourier theory to algebraic signal processing

In this expository article, we provide a self-contained overview of the notion of convolution embedded in different theories: from the classical Fourier theory to the theory of algebraic signal processing. We discuss their relations and differences. Toward the end, we provide an opinion on whether there is a consistent approach to convolution that unifies seemingly different approaches by different theories.

eess.SP↗

arXiv2023

Study of Manifold Geometry using Multiscale Non-Negative Kernel Graphs

Modern machine learning systems are increasingly trained on large amounts of data embedded in high-dimensional spaces. Often this is done without analyzing the structure of the dataset. In this work, we propose a framework to study the geometric structure of the data. We make use of our recently introduced non-negative kernel (NNK) regression graphs to estimate the point density, intrinsic dimension, and the linearity of the data manifold (curvature). We further generalize the graph construction and geometric estimation to multiple scale by iteratively merging neighborhoods in the input data. Our experiments demonstrate the effectiveness of our proposed approach over other baselines in estimating the local geometry of the data manifolds on synthetic and real datasets.

cs.LG↗

arXiv2023

Neighborhood and Graph Constructions using Non-Negative Kernel Regression

Data-driven neighborhood definitions and graph constructions are often used in machine learning and signal processing applications. k-nearest neighbor~(kNN) and $ε$-neighborhood methods are among the most common methods used for neighborhood selection, due to their computational simplicity. However, the choice of parameters associated with these methods, such as k and $ε$, is still ad hoc. We make two main contributions in this paper. First, we present an alternative view of neighborhood selection, where we show that neighborhood construction is equivalent to a sparse signal approximation problem. Second, we propose an algorithm, non-negative kernel regression~(NNK), for obtaining neighborhoods that lead to better sparse representation. NNK draws similarities to the orthogonal matching pursuit approach to signal representation and possesses desirable geometric and theoretical properties. Experiments demonstrate (i) the robustness of the NNK algorithm for neighborhood and graph construction, (ii) its ability to adapt the number of neighbors to the data properties, and (iii) its superior performance in local neighborhood and graph-based machine learning tasks.

cs.LG↗

arXiv2023

Signal Variation Metrics and Graph Fourier Transforms for Directed Graphs

In this paper we consider the problem of constructing graph Fourier transforms (GFTs) for directed graphs (digraphs), with a focus on developing multiple GFT designs that can capture different types of variation over the digraph node-domain. Specifically, for any given digraph we propose three GFT designs based on the polar decomposition. Our method is closely related to existing polar decomposition based GFT designs, but with added interpretability in the digraph node-domain. Each of our proposed digraph GFTs has a clear node domain variation interpretation, so that one or more of the GFTs can be used to extract different insights from available graph signals. We demonstrate the benefits of our approach experimentally using M-block cyclic graphs, showing that the diffusion of signals on the graph leads to changes in the spectrum obtained from our proposed GFTs, but cannot be observed with the conventional GFT definition.

eess.SP↗

arXiv2023

Graph Signal Processing over a Probability Space of Shift Operators

Graph signal processing (GSP) uses a shift operator to define a Fourier basis for the set of graph signals. The shift operator is often chosen to capture the graph topology. However, in many applications, the graph topology may be unknown a priori, its structure uncertain, or generated randomly from a predefined set for each observation. Each graph topology gives rise to a different shift operator. In this paper, we develop a GSP framework over a probability space of shift operators. We develop the corresponding notions of Fourier transform, MFC filters, and band-pass filters, which subsumes classical GSP theory as the special case where the probability space consists of a single shift operator. We show that an MFC filter under this framework is the expectation of random convolution filters in classical GSP, while the notion of bandlimitedness requires additional wiggle room from being simply a fixed point of a band-pass filter. We develop a mechanism that facilitates mapping from one space of shift operators to another, which allows our framework to be applied to a rich set of scenarios. We demonstrate how the theory can be applied by using both synthetic and real datasets.

eess.SP↗

arXiv2023

Graph Signal Processing: History, Development, Impact, and Outlook

Graph signal processing (GSP) generalizes signal processing (SP) tasks to signals living on non-Euclidean domains whose structure can be captured by a weighted graph. Graphs are versatile, able to model irregular interactions, easy to interpret, and endowed with a corpus of mathematical results, rendering them natural candidates to serve as the basis for a theory of processing signals in more irregular domains. In this article, we provide an overview of the evolution of GSP, from its origins to the challenges ahead. The first half is devoted to reviewing the history of GSP and explaining how it gave rise to an encompassing framework that shares multiple similarities with SP. A key message is that GSP has been critical to develop novel and technically sound tools, theory, and algorithms that, by leveraging analogies with and the insights of digital SP, provide new ways to analyze, process, and learn from graph signals. In the second half, we shift focus to review the impact of GSP on other disciplines. First, we look at the use of GSP in data science problems, including graph learning and graph-based deep learning. Second, we discuss the impact of GSP on applications, including neuroscience and image and video processing. We conclude with a brief discussion of the emerging and future directions of GSP.

eess.SP↗

arXiv2023

Joint Graph and Vertex Importance Learning

In this paper, we explore the topic of graph learning from the perspective of the Irregularity-Aware Graph Fourier Transform, with the goal of learning the graph signal space inner product to better model data. We propose a novel method to learn a graph with smaller edge weight upper bounds compared to combinatorial Laplacian approaches. Experimentally, our approach yields much sparser graphs compared to a combinatorial Laplacian approach, with a more interpretable model.

eess.SP↗

arXiv2023

Towards bandwidth estimation for graph signal reconstruction

In numerous graph signal processing applications, data is often missing for a variety of reasons, and predicting the missing data is essential. In this paper, we consider data on graphs modeled as bandlimited graph signals. Predicting or reconstructing the unknown signal values for such a model requires an estimate of the signal bandwidth. In this paper, we address the problem of estimating the reconstruction errors, minimizing which would thereby provide an estimate of the signal bandwidth. In doing so, we design a cross-validation approach needed for stable graph signal reconstruction and propose a method for estimating the reconstruction errors for different choices of signal bandwidth. Using this technique, we are able to estimate the reconstruction error on a variety of real-world graphs.

eess.SP↗