Neighborhood-preserving translations on graphs

Grelier, Nicolas; Pasdeloup, Bastien; Vialatte, J; Gripon, Vincent

doi:10.1109/globalsip.2016.7905874

Cited by 9 publications

(9 citation statements)

References 7 publications

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“…GSP [ 7 ] is a mathematical framework that aims at extending harmonic analysis to irregular domains described using similarity graphs. As such, it is possible to define tools such as translations [ 15 ], convolutions [ 16 ], filtering [ 17 ] and wavelets [ 18 ] taking into account the complex structure of the inputs. GSP has successfully been applied to domains ranging from neuroimaging [ 19 ] to deep learning [ 16 , 20 , 21 ].…”

Section: Proposed Methodsmentioning

confidence: 99%

Improved Visual Localization via Graph Filtering

et al. 2021

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Vision-based localization is the problem of inferring the pose of the camera given a single image. One commonly used approach relies on image retrieval where the query input is compared against a database of localized support examples and its pose is inferred with the help of the retrieved items. This assumes that images taken from the same places consist of the same landmarks and thus would have similar feature representations. These representations can learn to be robust to different variations in capture conditions like time of the day or weather. In this work, we introduce a framework which aims at enhancing the performance of such retrieval-based localization methods. It consists in taking into account additional information available, such as GPS coordinates or temporal proximity in the acquisition of the images. More precisely, our method consists in constructing a graph based on this additional information that is later used to improve reliability of the retrieval process by filtering the feature representations of support and/or query images. We show that the proposed method is able to significantly improve the localization accuracy on two large scale datasets, as well as the mean average precision in classical image retrieval scenarios.

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Section: Proposed Methodsmentioning

confidence: 99%

Improved Visual Localization via Graph Filtering

et al. 2021

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“…Theorem 8 Let Γ = Cay(G; S) be the Cayley graph of a finite group G of order N with S closed under conjugation, and equipped with the eigenbasis φ π i,j given by Equation (18). Assume g is constant over every representation of G, i.e., for every π ∈ G and i, j = 1, .…”

Section: More General Translations On Cayley Graphsmentioning

confidence: 99%

“…the translation operator introduced by Shuman, Ricaud, and Vandergheynst [37]. Inspired by classical (commutative) Fourier analysis, they define the notions of convolution, modulation, and translation via the graph Fourier transform; 2. the linear isometric shift operator introduced by Girault, Gonçalves, and Fleury [15]; 3. the energy-preserving shift operator introduced by Gavili and Zhang [12]; 4. translation induced by the adjacency matrix of the graph, as proposed by Sandryhaila and Moura [32]; 5. translation induced by pointwise multiplication with personalized PageRank vectors defined by Tepper and Sapiro [41], and; 6. the neighborhood preserving translation defined by Pasdeloup et al [18,30].…”

Section: Introductionmentioning

confidence: 99%

Gabor-type frames for signal processing on graphs

Ghandehari¹,

Guillot²,

Hollingsworth³

2020

Preprint

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In the past decade, significant progress has been made to generalize classical tools from Fourier analysis to analyze and process signals defined on networks. In this paper, we propose a new framework for constructing Gabor-type frames for signals on graphs. Our approach uses general and flexible families of linear operators acting as translations. Compared to previous work in the literature, our methods yield the sharp bounds for the associated frames, in a broad setting that generalizes several existing constructions. We also examine how Gabor-type frames behave for signals defined on Cayley graphs by exploiting the representation theory of the underlying group. We explore how natural classes of translations can be constructed for Cayley graphs, and how the choice of an eigenbasis can significantly impact the properties of the resulting translation operators and frames on the graph.

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“…GSP: graph signal processing [6] is a mathematical framework that aims at extending harmonic analysis to irregular domains described using similarity graphs. As such, it is possible to define tools such as translations [12], convolutions [13], filtering [14] and wavelets [15] taking into account the complex structure of the inputs. GSP has successfully been applied to domains ranging from neuroimaging [16] to deep learning [13], [17], [18].…”

Section: Related Workmentioning

confidence: 99%

Improved Visual Localization via Graph Smoothing

Lassance,

Latif,

Garg

et al. 2019

Preprint

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Vision based localization is the problem of inferring the pose of the camera given a single image. One solution to this problem is to learn a deep neural network to infer the pose of a query image after learning on a dataset of images with known poses. Another more commonly used approach rely on image retrieval where the query image is compared against the database of images and its pose is inferred with the help of the retrieved images. The latter approach assumes that images taken from the same places consists of the same landmarks and, thus would have similar feature representations. These representation can be learned using full supervision to be robust to different variations in capture conditions like time of the day and weather. In this work, we introduce a framework to enhance the performance of these retrieval based localization methods by taking into account the additional information including GPS coordinates and temporal neighbourhood of the images provided by the acquisition process in addition to the descriptor similarity of pairs of images in the reference or query database which is used traditionally for localization. Our method constructs a graph based on this additional information and use it for robust retrieval by smoothing the feature representation of reference and/or query images. We show that the proposed method is able to significantly improve the localization accuracy on two large scale datasets over the baselines.

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Neighborhood-preserving translations on graphs

Cited by 9 publications

References 7 publications

Improved Visual Localization via Graph Filtering

Improved Visual Localization via Graph Filtering

Gabor-type frames for signal processing on graphs

Improved Visual Localization via Graph Smoothing

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