Spectral-based mesh segmentation

Mejía, Daniel; Ruiz-Salguero, Oscar; Cadavid, Carlos A.

doi:10.1007/s12008-016-0300-0

Cited by 13 publications

(16 citation statements)

References 39 publications

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“…The sparsity of a graph is equal to the minimum sparsity of a cut. It then follows that the cut which exhibits minimum sparsity and the minimum normalized cut in (33) produce the same set E.…”

Section: Other Forms Of the Normalized Cutmentioning

confidence: 98%

“…A more general form of the normalized cut may also involve vertex weights when designing the size of subsets E and H. By defining, respectively, the volumes of these sets as V E = n∈E D nn and V H = n∈H D nn , and using these volumes instead of the number of vertices N E and N H in the definition of the normalized cut in (33), we arrive at [59] CutV…”

Section: Volume Normalized Minimum Cutmentioning

confidence: 99%

“…In this way, graphs are perfectly well equipped to exploit the fundamental relations among both the measured data and the underlying graph topology; this inherent ability to incorporate physically relevant data properties has made GSP and GML key technologies in the emerging field of Big Data Analytics (BDA). Indeed, in applications defined on irregular data domains, Graph Data Analytics (GDA) has been proven to offer a quantum step forward from the classical time (or space) series analyses [27,28,29,30,31,32,33,34,35], including the following aspects…”

Section: Introductionmentioning

confidence: 99%

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Graph Signal Processing -- Part I: Graphs, Graph Spectra, and Spectral Clustering

Stanković¹,

Mandic²,

Daković³

et al. 2019

Preprint

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The area of Data Analytics on graphs promises a paradigm shift as we approach information processing of classes of data, which are typically acquired on irregular but structured domains (social networks, various ad-hoc sensor networks). Yet, despite its long history, current approaches mostly focus on the optimization of graphs themselves, rather than on directly inferring learning strategies, such as detection, estimation, statistical and probabilistic inference, clustering and separation from signals and data acquired on graphs. To fill this void, we first revisit graph topologies from a Data Analytics point of view, and establish a taxonomy of graph networks through a linear algebraic formalism of graph topology (vertices, connections, directivity). This serves as a basis for spectral analysis of graphs, whereby the eigenvalues and eigenvectors of graph Laplacian and adjacency matrices are shown to convey physical meaning related to both graph topology and higher-order graph properties, such as cuts, walks, paths, and neighborhoods. Through a number of carefully chosen examples, we demonstrate that the isomorphic nature of graphs enables the basic properties and descriptors to be preserved throughout the data analytics process, even in the case of reordering of graph vertices, where classical approaches fail. Next, to illustrate estimation strategies performed on graph signals, spectral analysis of graphs is introduced through eigenanalysis of mathematical descriptors of graphs and in a generic way. Finally, a framework for vertex clustering and graph segmentation is established based on graph spectral representation (eigenanalysis) which illustrates the power of graphs in various data association tasks. The supporting examples demonstrate the promise of Graph Data Analytics in modeling structural and functional/semantic inferences. At the same time, Part I serves as a basis for Part II and Part III which deal with theory, methods and applications of processing Data on Graphs and Graph Topology Learning from data.

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Section: Other Forms Of the Normalized Cutmentioning

confidence: 98%

Section: Volume Normalized Minimum Cutmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Graph Signal Processing -- Part I: Graphs, Graph Spectra, and Spectral Clustering

Stanković¹,

Mandic²,

Daković³

et al. 2019

Preprint

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“…The smoothness of graph signals is used in graph topology learning [22], vertex ordering, and graph clustering [23]. Since u 1 , corresponding to 1 = 0, is constant, the vertex ordering can be done using the next smoothest eigenvector u 2 (called the Fiedler vector).…”

Section: Graph Signal and Spectrummentioning

confidence: 99%

Local Smoothness of Graph Signals

Daković

Stanković

Sejdić

2019

Mathematical Problems in Engineering

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Analysis of vertex-varying spectral content of signals on graphs challenges the assumption of vertex invariance and requires the introduction of vertex-frequency representations as a new tool for graph signal analysis. Local smoothness, an important parameter of vertex-varying graph signals, is introduced and defined in this paper. Basic properties of this parameter are given. By using the local smoothness, an ideal vertex-frequency distribution is introduced. The local smoothness estimation is performed based on several forms of the vertex-frequency distributions, including the graph spectrogram, the graph Rihaczek distribution, and a vertex-frequency distribution with reduced interferences. The presented theory is illustrated through numerical examples.

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“…e approaches can be broadly classified into three categories: (1) Region-based: based on features of models (e.g., surface), divide the model into different and nonoverlaping regions using methods such as the region growing method [11,12] and the watershed algorithm [13,14]. (2) Graph-based: it generally represents the model in terms of an undirected graph (dual graph [3] and attributed adjacent graph [15]) and segmented by graph cuts [16], normalized cuts [17], and spectral theory [18]. (3) e extracted features of the model are clustered, and the points or surfaces of a model having similar property can be obtained according to the clustering result [3,19,20].…”

Section: Related Workmentioning

confidence: 99%

CAD Model Segmentation Algorithm Using the Fusion of PERT and Spectral Technology

Wei

2019

Mathematical Problems in Engineering

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For complex CAD models, model segmentation technology is an important support for model retrieval and reuse. In this article, we first propose a novel CAD model segmentation method that uses the fusion of the program/project evaluation and review technique (PERT) and the Laplacian spectrum theory. By means of PERT, spectral theory, and the CAD models’ geometrical and topological information, we transform the b-rep model faces into two-dimensional coordinate points corresponding to the nodes of the attributed adjacent graph (AAG). The k-means approach with the Silhouette coefficient was employed to conduct unsupervised learning of the coordinate points. The experimental results demonstrate that (1) the proposed approach can effectively transform the b-rep model into a two-dimensional coordinate point set; (2) the k-means algorithm can efficiently cluster points to achieve segmentation; and (3) in view of human cognition, the segmentation results are more reasonable. It can effectively divide the point set into several groups to achieve the model segmentation.

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Spectral-based mesh segmentation

Cited by 13 publications

References 39 publications

Graph Signal Processing -- Part I: Graphs, Graph Spectra, and Spectral Clustering

Graph Signal Processing -- Part I: Graphs, Graph Spectra, and Spectral Clustering

Local Smoothness of Graph Signals

CAD Model Segmentation Algorithm Using the Fusion of PERT and Spectral Technology

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