GraphBGS: Background Subtraction via Recovery of Graph Signals

Giraldo, Jhony H.; Bouwmans, Thierry

doi:10.1109/icpr48806.2021.9412999

Cited by 14 publications

(12 citation statements)

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“…In the current work, we extend the definition of Sobolev norms in GSP [6], [30] from static graph signals to a smoothness function for time-varying graph signals, and then we formulate a new reconstruction algorithm. The Sobolev norm was defined by Pesenson [30] as follows:…”

Section: Sobolev Smoothness Of Time-varying Graph Signalsmentioning

confidence: 99%

“…Graph Signal Processing (GSP) is an emerging field that aims to extend the concepts of classical digital signal processing to graphs [1]- [4]. GSP has been used in several applications such as computer vision [5], [6], forecasting [7], sensor networks [8], biological networks [9], image, and 3D point cloud processing [10]- [12]. Similarly, the study of machine learning on graphs [13] has benefited profoundly from GSP; some examples include semi-supervised learning Jhony H. Giraldo, Belmar Garcia-Garcia, and Thierry Bouwmans are with the laboratoire MIA, Mathématiques, Image et Applications, La Rochelle Université, 17000 La Rochelle, France e-mail: jgiral01@univ-lr.fr, belmar 2g@hotmail.com, tbouwman@univ-lr.fr.…”

Section: Introductionmentioning

confidence: 99%

“…In the current work, we build on our previous work [25], and we propose a new algorithm to reconstruct time-varying graph signals from samples. Our algorithm is based on the extension of the Sobolev norm defined in GSP for timevarying graph signals [6], [30]. Therefore, we dub our algorithm as Time-varying Graph signal Reconstruction via Sobolev Smoothness (GraphTRSS).…”

Section: Introductionmentioning

confidence: 99%

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Reconstruction of Time-Varying Graph Signals via Sobolev Smoothness

Giraldo

Mahmood

García-García

et al. 2022

IEEE Trans. on Signal and Inf. Process. over Networks

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Graph Signal Processing (GSP) is an emerging research field that extends the concepts of digital signal processing to graphs. GSP has numerous applications in different areas such as sensor networks, machine learning, and image processing. The sampling and reconstruction of static graph signals have played a central role in GSP. However, many real-world graph signals are inherently time-varying and the smoothness of the temporal differences of such graph signals may be used as a prior assumption. In the current work, we assume that the temporal differences of graph signals are smooth, and we introduce a novel algorithm based on the extension of a Sobolev smoothness function for the reconstruction of time-varying graph signals from discrete samples. We explore some theoretical aspects of the convergence rate of our Time-varying Graph signal Reconstruction via Sobolev Smoothness (GraphTRSS) algorithm by studying the condition number of the Hessian associated with our optimization problem. Our algorithm has the advantage of converging faster than other methods that are based on Laplacian operators without requiring expensive eigenvalue decomposition or matrix inversions. The proposed GraphTRSS is evaluated on several datasets including two COVID-19 datasets and it has outperformed many existing state-of-the-art methods for time-varying graph signal reconstruction. GraphTRSS has also shown excellent performance on two environmental datasets for the recovery of particulate matter and sea surface temperature signals.

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Section: Sobolev Smoothness Of Time-varying Graph Signalsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Reconstruction of Time-Varying Graph Signals via Sobolev Smoothness

Giraldo

Mahmood

García-García

et al. 2022

IEEE Trans. on Signal and Inf. Process. over Networks

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“…There are numerous background modeling algorithms developed in the literature [5], and they can be classified as unsupervised [26,29,37], supervised [1,4,7,23,24], and semisupervised methods [12,13]. Supervised methods allow for more accurate results than unsupervised methods, especially in complex scenarios, but they need typically large training data.…”

Section: Related Workmentioning

confidence: 99%

Efficient and Robust Background Modeling with Dynamic Mode Decomposition

et al. 2022

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A large number of modern video background modeling algorithms deal with computational costly minimization problems that often need parameter adjustments. While in most cases spatial and temporal constraints are added artificially to the minimization process, our approach is to exploit Dynamic Mode Decomposition (DMD), a spectral decomposition technique that naturally extracts spatio-temporal patterns from data. Applied to video data, DMD can compute background models. However, the original DMD algorithm for background modeling is neither efficient nor robust. In this paper, we present an equivalent reformulation with constraints leading to a more suitable decomposition into fore- and background. Due to the reformulation, which uses sparse and low-dimensional structures, an efficient and robust algorithm is derived that computes accurate background models. Moreover, we show how our approach can be extended to RGB data, data with periodic parts, and streaming data enabling a versatile use.

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“…where I is the identity matrix and L is the combinatorial Laplacian matrix of the graph G. Since (L + ϵI) is invertible for ϵ > 0 in undirected graphs [29], the solution of the optimization problem in equation 3 can be given as:…”

Section: F Sobolev For Semi-supervised Learning Algorithmmentioning

confidence: 99%

SemiSegSAR: A Semi-Supervised Segmentation Algorithm for Ship SAR Images

Giraldo

Al-Saad

et al. 2022

IEEE Geosci. Remote Sensing Lett.

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Automatic ship segmentation from high-resolution Synthetic Aperture Radar (SAR) remote sensing images has been a topic of interest that has gradually gained attention over the years due to the abundance of earth observation sensors. Recently, deep learning methods have provided a breakthrough increasing the performance greatly by using large amount of labeled data. Yet, the high cost related to the samples labeling and their scarcity result in significant limitation of their wide use. Therefore, it is crucial to overcome the unlabeled inputs challenge and develop semi-supervised learning approaches to enhance the machine learning models capacity. Our letter proposes a semi-supervised segmentation algorithm for SAR images named SemiSegSAR based on the use of Graph Signal Processing. This method includes instance segmentation; texture and statistical SAR features to represent the nodes of the graph; K-nearest neighbors to construct the graph; and Sobolev minimization algorithm to tackle the problem of semi-supervised semantic segmentation. The proposed algorithm is trained and tested using the publicly available SSDD and HRSID ship detection datasets. Experiments show that SemiSegSAR outperforms the current state-of-the-art semi-supervised and supervised methods while requiring only few labeled data.

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GraphBGS: Background Subtraction via Recovery of Graph Signals

Cited by 14 publications

References 50 publications

Reconstruction of Time-Varying Graph Signals via Sobolev Smoothness

Reconstruction of Time-Varying Graph Signals via Sobolev Smoothness

Efficient and Robust Background Modeling with Dynamic Mode Decomposition

SemiSegSAR: A Semi-Supervised Segmentation Algorithm for Ship SAR Images

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