Adaptively Transforming Graph Matching

Wang, Fudong; Xue, Nan; Zhang, Yipeng; Bai, Xiang; Xia, Gui-Song

doi:10.1007/978-3-030-01270-0_38

Cited by 7 publications

(4 citation statements)

References 39 publications

(98 reference statements)

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“…Each partial graph represent with the partial adjacency matrix δ that apply it to any graph Ğ generated by our model and explore similarity between their , for finding best compatibility or a latent vector z* which can minimize differences between input and output graph, to provide more geometric insight on the problem. Process to measure similarities among elements of graphs with probing combination of dependences similar unary, pairwise or high-order [36,37,38] as well as there are Potentials between reference graph and their counterparts similar to [39,40] That follow a function is used for finding dissimilarity or deformation with a convex optimization problem over the set of doubly stochastic matrices.…”

Section: Approachmentioning

confidence: 99%

Graph-Based Method for Anomaly Detection in Functional Brain Network using Variational Autoencoder

Mirakhorli

2019

Preprint

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Functional neuroimaging techniques using resting-state functional MRI (rs-fMRI) have accelerated progress in brain disorders and dysfunction studies. Since, there are the slight differences between healthy and disorder brains, investigation in the complex topology of human brain functional networks is difficult and complicated task with the growth of evaluation criteria. Recently, graph theory and deep learning applications have spread widely to understanding human cognitive functions that are linked to gene expression and related distributed spatial patterns. Irregular graph analysis has been widely applied in many brain recognition domains, these applications might involve both node-centric and graph-centric tasks. In this paper, we discuss about individual Variational Autoencoder and Graph Convolutional Network (GCN) for the region of interest identification areas of brain which do not have normal connection when apply certain tasks. Here, we identified a framework of Graph Auto-Encoder (GAE) with hyper sphere distributer for functional data analysis in brain imaging studies that is underlying non-Euclidean structure, in learning of strong rigid graphs among large scale data. In addition, we distinguish the possible mode correlations in abnormal brain connections.

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Section: Approachmentioning

confidence: 99%

Graph-Based Method for Anomaly Detection in Functional Brain Network using Variational Autoencoder

Mirakhorli

2019

Preprint

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“…Therefore, it is necessary to consider: how to propose a graph matching model to address these variations and enhance the matching performance. To deal with this problem, some works using transformation strategy are proposed such as the variants of iterative closest point [35] [36], Mobius transformation [37] and adaptive transformation [38]. However, the DCM differs from these transformation methods and we make up for their deficiency in the following aspects.…”

Section: Introductionmentioning

confidence: 99%

“…3) The adaptive transformation in [38] is introduced to graph matching from the perspective of functional representation. In which the graph matching is formulated as transformation from one point set to the space spanned by another point set, and the pairwise edge features of graphs are directly represented by unary point features.…”

Section: Introductionmentioning

confidence: 99%

Dual Calibration Mechanism Based L₂, p-Norm for Graph Matching

Huang

et al. 2021

IEEE Trans. Circuits Syst. Video Technol.

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Unbalanced geometric structure caused by variations with deformations, rotations and outliers is a critical issue that hinders correspondence establishment between image pairs in existing graph matching methods. To deal with this problem, in this work, we propose a dual calibration mechanism (DCM) for establishing feature points correspondence in graph matching. In specific, we embed two types of calibration modules in the graph matching, which model the correspondence relationship in point and edge respectively. The point calibration module performs unary alignment over points and the edge calibration module performs local structure alignment over edges. By performing the dual calibration, the feature points correspondence between two images with deformations and rotations variations can be obtained. To enhance the robustness of correspondence establishment, the L2,p-norm is employed as the similarity metric in the proposed model, which is a flexible metric due to setting the different p values. Finally, we incorporate the dual calibration and L2,p-norm based similarity metric into the graph matching model which can be optimized by an effective algorithm, and theoretically prove the convergence of the presented algorithm. Experimental results in the variety of graph matching tasks such as deformations, rotations and outliers evidence the competitive performance of the presented DCM model over the state-of-theart approaches.

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“…Due to the natural linearity of R d , T F can also be represented by a linear representation map P, which is not only a parameterization for GM but also associative with geometric parameters for graphs under geometric deformations. A preliminary version of this work was presented in [19]. nonlinear/complicate Figure 1: FRGM: given two graphs G 1 and G 2 , we construct two function spaces F(V 1 , R) and F(V 2 , R) as representations, where Φ and Ψ are two sets of basis functions that represent the nodes V 1 and V 2 , and F V1 and F V2 are the inner product or metric that represent the edge attributes E 1 and E 2 .…”

Section: Introductionmentioning

confidence: 99%

A Functional Representation for Graph Matching

Wang

Xue

Zhang

et al. 2019

IEEE Trans. Pattern Anal. Mach. Intell.

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Graph matching is an important and persistent problem in computer vision and pattern recognition for finding node-to-node correspondence between graph-structured data. However, as widely used, graph matching that incorporates pairwise constraints can be formulated as a quadratic assignment problem (QAP), which is NP-complete and results in intrinsic computational difficulties. In this paper, we present a functional representation for graph matching (FRGM) that aims to provide more geometric insights on the problem and reduce the space and time complexities of corresponding algorithms. To achieve these goals, we represent a graph endowed with edge attributes by a linear function space equipped with a functional such as inner product or metric, that has an explicit geometric meaning. Consequently, the correspondence between graphs can be represented as a linear representation map of that functional. Specifically, we reformulate the linear functional representation map as a new parameterization for Euclidean graph matching, which is associative with geometric parameters for graphs under rigid or nonrigid deformations. This allows us to estimate the correspondence and geometric deformations simultaneously. The use of the representation of edge attributes rather than the affinity matrix enables us to reduce the space complexity by two orders of magnitudes. Furthermore, we propose an efficient optimization strategy with low time complexity to optimize the objective function. The experimental results on both synthetic and real-world datasets demonstrate that the proposed FRGM can achieve state-of-the-art performance.

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Adaptively Transforming Graph Matching

Cited by 7 publications

References 39 publications

Graph-Based Method for Anomaly Detection in Functional Brain Network using Variational Autoencoder

Graph-Based Method for Anomaly Detection in Functional Brain Network using Variational Autoencoder

Dual Calibration Mechanism Based L₂, p-Norm for Graph Matching

A Functional Representation for Graph Matching

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Adaptively Transforming Graph Matching

Cited by 7 publications

References 39 publications

Graph-Based Method for Anomaly Detection in Functional Brain Network using Variational Autoencoder

Graph-Based Method for Anomaly Detection in Functional Brain Network using Variational Autoencoder

Dual Calibration Mechanism Based L2, p-Norm for Graph Matching

A Functional Representation for Graph Matching

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Dual Calibration Mechanism Based L₂, p-Norm for Graph Matching