Filters are fundamental in extracting information from data. For time series and image data that reside on Euclidean domains, filters are the crux of many signal processing and machine learning techniques, including c...
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Filters are fundamental in extracting information from data. For time series and image data that reside on Euclidean domains, filters are the crux of many signal processing and machine learning techniques, including convolutional neural networks. Increasingly, modern data also reside on networks and other irregular domains whose structure is better captured by a graph. To process and learn from such data, graph filters account for the structure of the underlying data domain. In this article, we provide a comprehensive overview of graph filters, including the different filtering categories, design strategies for each type, and trade-offs between different types of graph filters. We discuss how to extend graph filters into filter banks and graph neural networks to enhance the representational power;that is, to model a broader variety of signal classes, data patterns, and relationships. We also showcase the fundamental role of graph filters in signal processing and machine learning applications. Our aim is that this article provides a unifying framework for both beginner and experienced researchers, as well as a common understanding that promotes collaborations at the intersections of signal processing, machine learning, and application domains.
Reed-Xiaoli detector (RXD) is recognized as the benchmark algorithm for image anomaly detection;however, it presents known limitations, namely the dependence over the image following a multivariate Gaussian model, the...
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Reed-Xiaoli detector (RXD) is recognized as the benchmark algorithm for image anomaly detection;however, it presents known limitations, namely the dependence over the image following a multivariate Gaussian model, the estimation and inversion of a high-dimensional covariance matrix, and the inability to effectively include spatial awareness in its evaluation. In this work, a novel graph-based solution to the image anomaly detection problem is proposed;leveraging the graph Fourier transform, we are able to overcome some of RXD's limitations while reducing computational cost at the same time. Tests over both hyperspectral and medical images, using both synthetic and real anomalies, prove the proposed technique is able to obtain significant gains over performance by other algorithms in the state of the art.
In the context of image analysis, the Binary Partition Tree (BPT) is a classical data structure for the hierarchical modelling of images at different scales. BPTs belong both to the families of graph-based models and ...
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In the context of image analysis, the Binary Partition Tree (BPT) is a classical data structure for the hierarchical modelling of images at different scales. BPTs belong both to the families of graph-based models and morphological hierarchies. They constitute an efficient way to define sets of nested partitions of image support, that further provide knowledge-guided reduced research spaces for optimization-based segmentation procedures. Basically, a BPT is built in a mono-feature way, i.e. for one given image, and one given metric, by merging pairs of connected image regions that are similar in the induced feature space. Our goal is to design a new family of BPTs, dealing with the need to directly manage multiple features within its building process, Then, we propose a generalization of the BPT construction framework, allowing one to embed multiple features. The cornerstone of our approach relies on a collaborative strategy used to establish a consensus between different metrics, thus enabling to obtain a unified hierarchical segmentation space. In particular, this provides alternatives to the complex issue of metric construction from several -possibly non-comparable- features. To reach that goal, we first revisit the BPT construction algorithm to describe it in a graph-based-formalism. Then, we present the structural and algorithmic evolutions and impacts when embedding multiple features in BPT construction. Final experiments illustrate how this multi-feature framework can be used to build BPTs from multiple metrics computed through the (potentially multiple) image content(s). (C) 2018 Elsevier Ltd. All rights reserved.
We present an algebraic graph-theoretic approach for quantification of surface morphology. Using this approach, heterogeneous, multi-scaled aspects of surfaces;e.g., semiconductor wafers, are tracked from optical micr...
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We present an algebraic graph-theoretic approach for quantification of surface morphology. Using this approach, heterogeneous, multi-scaled aspects of surfaces;e.g., semiconductor wafers, are tracked from optical micrographs as opposed to reticent profile mapping techniques. Therefore, this approach can facilitate in situ real-time assessment of surface quality. We report two complementary methods for realizing graph-theoretic representation and subsequent quantification of surface morphology variations from optical micrographimages. Experimental investigations with specular finished copper wafers (surface roughness (Sa) approximate to 6nm) obtained using a semiconductor chemical mechanical planarization process suggest that the graph-based topological invariant Fiedler number ((2)) was able to quantify and track variations in surface morphology more effectively compared to other quantifiers reported in literature.
Depth images are often presented at a lower spatial resolution, either due to limitations in the acquisition of the depth or to increase compression efficiency. As a result, upsampling low-resolution depth images to a...
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ISBN:
(纸本)9781479928934
Depth images are often presented at a lower spatial resolution, either due to limitations in the acquisition of the depth or to increase compression efficiency. As a result, upsampling low-resolution depth images to a higher spatial resolution is typically required prior to depth imagebased rendering. In this paper, depth enhancement and upsampling techniques are proposed using a graph-based formulation. In one scheme, the depth is first upsampled using a conventional method, then followed by a graph-based joint bilateral filtering to enhance edges and reduce noise. A second scheme avoids the two-step processing and upsamples the depth directly using the proposed graph-based joint bilateral upsampling. Both filtering and interpolation problems are formulated as regularization problems and the solutions are different from conventional approaches. Further, we also studied operations on different graph structures such as star graph and 8-connected graph. Experimental results show that the proposed methods produce slightly more accurate depth at the full resolution with improved rendering quality of intermediate views.
The paper presents a new graph-based implementation of bilateral filtering. based on the Laplacian mesh smoothing framework, the proposed filter mimics the behaviour of the classical mesh filter while retaining some o...
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The paper presents a new graph-based implementation of bilateral filtering. based on the Laplacian mesh smoothing framework, the proposed filter mimics the behaviour of the classical mesh filter while retaining some of the interesting properties of mesh smoothing. The comparison between the filters is twofold. First of all, the two filters are benchmarked according to their ability to denoise complex synthetic image transitions. The respective performance of the filters are then assessed in a multiresolution denoising scheme for grayscale images, combining wavelet decomposition, shrinkage and bilateral filtering. The results obtained are encouraging and shows that the BMF is a viable alternative to classical bilateral filtering. (C) 2012 Elsevier B.V. All rights reserved.
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