Nonlocal PDEs-Based Morphology on Weighted Graphs for Image and Data Processing

Ta, Vinh-Thong; Elmoataz, Abderrahim; Lézoray, Olivier

doi:10.1109/tip.2010.2101610

Cited by 54 publications

(9 citation statements)

References 54 publications

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“…Let us recall some weighted partial difference operators on graphs that are essential in our paper. We refer to [21,23,38,20], for more detailed description of these operators.…”

Section: Notations and Preliminariesmentioning

confidence: 99%

Nonlocal Perimeters and Curvature Flows on Graphs with Applications in Image Processing and High-Dimensional Data Classification

Bouchairi

Elmoataz

Fadili

2023

SIAM J. Imaging Sci.

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In this paper, we revisit the notion of perimeter on graphs, introduced in [19], and we extend it to so-called inner and outer perimeters. We will also extend the notion of total variation on graphs. Thanks to the co-area formula, we show that discrete total variations can be expressed through these perimeters. Then, we propose a novel class of curvature operators on graphs that unifies both local and nonlocal mean curvature on an Euclidean domain. This leads us to translate and adapt the notion of the mean curvature flow on graphs as well as the level set mean curvature, which can be seen as approximate schemes. Finally, we exemplify the usefulness of these methods in image processing, 3D point cloud processing, and high dimensional data classification.

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“…Let us recall some weighted partial difference operators on graphs that are essential in our paper. We refer to [21,23,38,20], for more detailed description of these operators.…”

Section: Notations and Preliminariesmentioning

confidence: 99%

Nonlocal Perimeters and Curvature Flows on Graphs with Applications in Image Processing and High-Dimensional Data Classification

Bouchairi

Elmoataz

Fadili

2023

SIAM J. Imaging Sci.

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“…In order to achieve the joint enhancement of structural features and sparse features in SAR imagery, two split variables Z 1 and Z 2 representing the structure and sparsity and their corresponding dual variables S 1 and S 2 are incorporated and updated as in (43). Therefore, the purpose of the global optimization stage is to achieve the coordination of multitask by updating the primal variable X in (43).…”

Section: Cooperative Optimization Of Xmentioning

confidence: 99%

“…Specifically, the morphology introduces topological and geometric continuous space concepts on both continuous and discrete spaces, such as size, shape, convexity, and connectivity. Classical MM employs invariant structure elements to construct spatially-invariant operators and regards the structure elements as probes to traverse the imaging scenes/targets [38], [39], [40], [41], [42], [43], [44], [45], [46]. Therefore, by incorporating the blocking of structure elements, MM theory is capable of realizing the structural feature enhancement and effectively improving the elaborated imagery.…”

mentioning

confidence: 99%

Enhanced SAR Imagery by Autoblocking Approach Using Morphology Amoeba in ADMM Manner

Huan,

Song,

Dai

et al. 2023

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

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For conventional structure-guaranteed synthetic aperture radar (SAR) imagery problems, some of them are modeled as 1 / 2 mixed norm regularization, and some are modeled as a group of least absolute shrinkage and selection operator. However, due to the inflexible prior based on the Euclidean distance blocking, the target of interests and the background noise are easily attributed into the same block, which will consequently be retained or removed simultaneously. Therefore, it is difficult to distinguish the target with rich structures in a complicated environment. In this article, to realize the elaborated structure feature enhancement of interested targets in the echoed SAR data, a novel morphological autoblocking-alternating direction method of multipliers (MAB-ADMM) SAR imaging algorithm is proposed with a hybrid Frobenius and morphology F / M norm regularization. To realize the flexible blocking, an autoblocking mechanism is constructed by spatially-variant morphological amoeba (SVMA) in the F / M mixed norm. In the autoblocking mechanism, the geodesic distance of SVMA is utilized to accurately and flexibly fit the target structure and guarantee the elaborated structure. Moreover, in the proposed MAB-ADMM algorithm, the flexibly blocking structure feature and intrablock sparse feature are jointly optimized by the F / M and 1 norm. In the experiments, both simulated and raw SAR data collected by an airborne SAR are applied to qualitatively evaluate the proposed algorithm. Comparisons with conventional methods are carried out to reveal the superiority of the proposed algorithm. Moreover, the phase transition diagram is shown to verify the proposed algorithm in terms of quantitative aspects.

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“…Opening the morphological operations could smooth bright regions of the image corresponding to the size of the used structuring element. So, opening can be very useful to extract the scene in the background of non-uniform illumination [21]. The opening operation on low frequency coefficients SC a by structuring element d, denoted by SC a • d, is defined as follow:…”

Section: Non-uniform Illumination Correctionmentioning

confidence: 99%

Adaptive enhancement for infrared image using shearlet frame

Fan¹,

Du-yan²,

Gao³

et al. 2016

J. Opt.

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An infrared imaging sensor is sensitive to the variation of imaging environment, which may affect the image quality and blur the edges in an infrared image. Therefore, it is necessary to enhance the infrared image. To improve the image contrast and adaptively enhance image structures, such as edges and details, this paper proposes a novel infrared image enhancement algorithm in the shearlet transform domain. To avoid over-enhancing strong edges and amplifying noise in plateau regions, we linearly enhance the details on the high frequency components based on their structure information, and improve the global image contrast by non-uniform illumination correction on the low frequency component. Then we convert the processed low and high components into the spatial domain to obtain the final enhanced image. Experimental results show that the proposed algorithm could enhance the infrared image details well and produce few noise regions, which is very helpful for target detection and recognition.

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Nonlocal PDEs-Based Morphology on Weighted Graphs for Image and Data Processing

Cited by 54 publications

References 54 publications

Nonlocal Perimeters and Curvature Flows on Graphs with Applications in Image Processing and High-Dimensional Data Classification

Nonlocal Perimeters and Curvature Flows on Graphs with Applications in Image Processing and High-Dimensional Data Classification

Enhanced SAR Imagery by Autoblocking Approach Using Morphology Amoeba in ADMM Manner

Adaptive enhancement for infrared image using shearlet frame

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