Graph Laplacian for image anomaly detection

Verdoja, Francesco; Grangetto, Marco

doi:10.1007/s00138-020-01059-4

Cited by 33 publications

(25 citation statements)

References 69 publications

(116 reference statements)

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“…In this section, we compare the proposed GLRD_TFE algorithm with a series of classical or widely used anomaly detection algorithms, such as GRX [5], LRX [6], KLRX [7], LAD [25], CRD [11], BJSRD [12], and LRASR [15]. All the experiments are conducted on a PC with Intel Core i5-9300H 2.40 GHz and 16 GB RAM.…”

Section: Experimental Results and Analysismentioning

confidence: 99%

“…In addition, as an unsupervised problem, making the assumption of known clustering number K is often unrealistic, especially for some HSI data with complex background structures. In our paper, inspired by [25], a graph Laplacian matrix-based method (GLM) is proposed for dictionary construction. It has big advantages of maintaining the principal structure and capturing the local information.…”

Section: Dictionary Construction Based On Graph Laplacian Matrixmentioning

confidence: 99%

“…Consequently, a weight matrix W can be obtained where W(a, b) = w a,b . According to [25], a combinatorial graph Laplacian matrix L is supposed to be captured first in order to compute the optimal decorrelating transform leveraging on spectral graph theory. Specifically, the graph Laplacian matrix L = D -W. D is called the degree matrix that is also a diagonal matrix and computed as follows:…”

Section: Dictionary Construction Based On Graph Laplacian Matrixmentioning

confidence: 99%

“…Some researchers explored approaches on generic graphs [24], but those cannot be straightforwardly extended to images. Verdoja [25] constructed connected graphs both spatially and spectrally, and compared them with the RX method to reduce the calculation cost and improve the efficiency. Zhao [26] designed a predicted connected component graph to find potential anomalies first, and then they designed the second type of graph (elp-graph) in a manifold space to determine the robust background and keep credible anomalies in the potential anomaly dataset away.…”

Section: Introductionmentioning

confidence: 99%

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Hyperspectral Anomaly Detection via Graph Dictionary-Based Low Rank Decomposition with Texture Feature Extraction

et al. 2020

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The accuracy of anomaly detection in hyperspectral images (HSIs) faces great challenges due to the high dimensionality, redundancy of data, and correlation of spectral bands. In this paper, to further improve the detection accuracy, we propose a novel anomaly detection method based on texture feature extraction and a graph dictionary-based low rank decomposition (LRD). First, instead of using traditional clustering methods for the dictionary, the proposed method employs the graph theory and designs a graph Laplacian matrix-based dictionary for LRD. The robust information of the background matrix in the LRD model is retained, and both the low rank matrix and the sparse matrix are well separated while preserving the correlation of background pixels. To further improve the detection performance, we explore and extract texture features from HSIs and integrate with the low-rank model to obtain the sparse components by decomposition. The detection results from feature maps are generated in order to suppress background components similar to anomalies in the sparse matrix and increase the strength of real anomalies. Experiments were run on one synthetic dataset and three real datasets to evaluate the performance. The results show that the performance of the proposed method yields competitive results in terms of average area under the curve (AUC) for receiver operating characteristic (ROC), i.e., 0.9845, 0.9962, 0.9699, and 0.9900 for different datasets, respectively. Compared with seven other state-of-the-art algorithms, our method yielded the highest average AUC for ROC in all datasets.

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Section: Experimental Results and Analysismentioning

confidence: 99%

Section: Dictionary Construction Based On Graph Laplacian Matrixmentioning

confidence: 99%

Section: Dictionary Construction Based On Graph Laplacian Matrixmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Hyperspectral Anomaly Detection via Graph Dictionary-Based Low Rank Decomposition with Texture Feature Extraction

et al. 2020

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“…The synthetic dataset applied in the experiment is provided by Verdoja et al [43]. In this synthesized dataset, the background image is cropped from the Salinas scene.…”

Section: A Hyperspectral Datasets Description 1) Synthetic Datasetmentioning

confidence: 99%

Visual Attention and Background Subtraction With Adaptive Weight for Hyperspectral Anomaly Detection

Xiang

Song

Qin

et al. 2021

IEEE J. Sel. Top. Appl. Earth Observations Remote Sensing

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Anomaly detection (AD) in hyperspectral target detection is of particular interest because no prior knowledge of ground object spectra is required. However, it is difficult to utilize the salient features of hyperspectral image (HSI) and mitigate the effects of noise in hyperspectral AD, which greatly limits the detection performance. Here we report a strategy to implement hyperspectral AD by visual attention model and background subtraction with adaptive weight. Through band selection method, the most discriminating bands are selected as the input images for subsequent processing. Then, the hyperspectral visual attention model (HVAM) is introduced, for the first time, into hyperspectral AD for extracting the salient feature map of the input images. Furthermore, the background subtraction process that can reduce the background and noise in the salient feature map is developed via curvature filter. Using this operation, the initial anomaly area map is obtained. Finally, incorporating with the spectral information, an adaptive weight map is applied to the initial anomaly area map to further suppress the background. In the experiment, the proposed method is compared with seven other state-of-the-art methods on synthetic and real-world HSI. Most importantly, the results demonstrate that the proposed method is effective and performs better than alternative methods. We believe that this method can open a new avenue of visual processing methods for hyperspectral AD. IndexTerms-Anomaly detection (AD), hyperspectral visual attention model (HVAM), background subtraction, curvature filter, hyperspectral image (HSI).

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Invited Paper: Detection of False Data Injection Attacks in Power Systems Using a Secured-Sensors and Graph-Based Method

Morgenstern,

Dabush,

Kim

et al. 2023

Lecture Notes in Computer Science

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Graph Laplacian for image anomaly detection

Cited by 33 publications

References 69 publications

Hyperspectral Anomaly Detection via Graph Dictionary-Based Low Rank Decomposition with Texture Feature Extraction

Hyperspectral Anomaly Detection via Graph Dictionary-Based Low Rank Decomposition with Texture Feature Extraction

Visual Attention and Background Subtraction With Adaptive Weight for Hyperspectral Anomaly Detection

Invited Paper: Detection of False Data Injection Attacks in Power Systems Using a Secured-Sensors and Graph-Based Method

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