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Academic literature on the topic 'LAPLACIAN MATTE'

Author: Grafiati
Published: 11 September 2023

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Journal articles on the topic "LAPLACIAN MATTE"

1

TAN, GUANGHUA, JUN QI, CHUNMING GAO, JIN CHEN, and LIYUAN ZHUO. "SALIENCY-BASED UNSUPERVISED IMAGE MATTING." International Journal of Pattern Recognition and Artificial Intelligence 28, no. 04 (2014): 1454001. http://dx.doi.org/10.1142/s0218001414540019.

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Spectral matting is the state-of-the-art matting method and can well solve the highly under-conditioned matte problem without manual intervention. However, it suffers from huge computation cost and inaccurate alpha matte. This paper presents a modified spectral matting method which combines saliency detection algorithm to get a higher accuracy of alpha matte with less computational cost. First, the saliency detection algorithm is used to detect general locations of foreground objects. For saliency detection method, original two-stage scheme is replaced by feedback scheme to get a more suitable saliency map for unsupervised image matting. Next, matting components are obtained through a linear transformation of the smallest eigenvectors of the matting Laplacian matrix. Then, the improved saliency map is used for grouping matting components. Finally, the alpha matte is obtained based on matte cost function. Experiments show that the proposed method outperforms the state-of-the-art methods based on spectral matting both in speed and alpha matte accuracy.
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2

Ju, Tingting, Meifeng Dai, Changxi Dai, Yu Sun, Xiangmei Song, and Weiyi Su. "Applications of Laplacian spectrum for the vertex–vertex graph." Modern Physics Letters B 33, no. 17 (2019): 1950184. http://dx.doi.org/10.1142/s0217984919501847.

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Complex networks have attracted a great deal of attention from scientific communities, and have been proven as a useful tool to characterize the topologies and dynamics of real and human-made complex systems. Laplacian spectrum of the considered networks plays an essential role in their network properties, which have a wide range of applications in chemistry and others. Firstly, we define one vertex–vertex graph. Then, we deduce the recursive relationship of its eigenvalues at two successive generations of the normalized Laplacian matrix, and we obtain the Laplacian spectrum for vertex–vertex graph. Finally, we show the applications of the Laplacian spectrum, i.e. first-order network coherence, second-order network coherence, Kirchhoff index, spanning tree, and Laplacian-energy-like.
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3

DING, QINGYAN, WEIGANG SUN, and FANGYUE CHEN. "APPLICATIONS OF LAPLACIAN SPECTRA ON A 3-PRISM GRAPH." Modern Physics Letters B 28, no. 02 (2014): 1450009. http://dx.doi.org/10.1142/s0217984914500092.

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In this paper, we calculate the Laplacian spectra of a 3-prism graph and apply them. This graph is both planar and polyhedral, and belongs to the generalized Petersen graph. Using the regular structures of this graph, we obtain the recurrent relationships for Laplacian matrix between this graph and its initial state — a triangle — and further derive the corresponding relationships for Laplacian eigenvalues between them. By these relationships, we obtain the analytical expressions for the product and the sum of the reciprocals of all nonzero Laplacian eigenvalues. Finally we apply these expressions to calculate the number of spanning trees and mean first-passage time (MFPT) and see that the scaling of MFPT with the network size N is N2, which is larger than those performed on some uniformly recursive trees.
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4

Dai, Meifeng, Tingting Ju, Yongbo Hou, Jianwei Chang, Yu Sun, and Weiyi Su. "Coherence analysis of a family of weighted star-composed networks." International Journal of Modern Physics B 33, no. 23 (2019): 1950264. http://dx.doi.org/10.1142/s0217979219502643.

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Recently, the study of many kinds of weighted networks has received the attention of researchers in the scientific community. In this paper, first, a class of weighted star-composed networks with a weight factor is introduced. We focus on the network consistency in linear dynamical system for a class of weighted star-composed networks. The network consistency can be characterized as network coherence by using the sum of reciprocals of all nonzero Laplacian eigenvalues, which can be obtained by using the relationship of Laplacian eigenvalues at two successive generations. Remarkably, the Laplacian matrix of the class of weighted star-composed networks can be represented by the Kronecker product, then the properties of the Kronecker product can be used to obtain conveniently the corresponding characteristic roots. In the process of finding the sum of reciprocals of all nonzero Laplacian eigenvalues, the key step is to obtain the relationship of Laplacian eigenvalues at two successive generations. Finally, we obtain the main results of the first- and second-order network coherences. The obtained results show that if the weight factor is 1 then the obtained results in this paper coincide with the previous results on binary networks, otherwise the scalings of the first-order network coherence are related to the node number of attaching copy graph, the weight factor and generation number. Surprisingly, the scalings of the first-order network coherence are independent of the node number of initial graph. Consequently, it will open up new perspectives for future research.
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5

KARAMANOS, K., S. I. MISTAKIDIS, T. J. MASSART, and I. S. MISTAKIDIS. "ENTROPY PRODUCTION OF ENTIRELY DIFFUSIONAL LAPLACIAN TRANSFER AND THE POSSIBLE ROLE OF FRAGMENTATION OF THE BOUNDARIES." Fractals 23, no. 03 (2015): 1550026. http://dx.doi.org/10.1142/s0218348x15500267.

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The entropy production and the variational functional of a Laplacian diffusional field around the first four fractal iterations of a linear self-similar tree (von Koch curve) is studied analytically and detailed predictions are stated. In a next stage, these predictions are confronted with results from numerical resolution of the Laplace equation by means of Finite Elements computations. After a brief review of the existing results, the range of distances near the geometric irregularity, the so-called "Near Field", a situation never studied in the past, is treated exhaustively. We notice here that in the Near Field, the usual notion of the active zone approximation introduced by Sapoval et al. [M. Filoche and B. Sapoval, Transfer across random versus deterministic fractal interfaces, Phys. Rev. Lett. 84(25) (2000) 5776;1 B. Sapoval, M. Filoche, K. Karamanos and R. Brizzi, Can one hear the shape of an electrode? I. Numerical study of the active zone in Laplacian transfer, Eur. Phys. J. B. Condens. Matter Complex Syst. 9(4) (1999) 739-753.]2 is strictly inapplicable. The basic new result is that the validity of the active-zone approximation based on irreversible thermodynamics is confirmed in this limit, and this implies a new interpretation of this notion for Laplacian diffusional fields.
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6

He, Jiaojiao, Meifeng Dai, Yue Zong, Jiahui Zou, Yu Sun, and Weiyi Su. "Coherence analysis of a class of weighted tree-like polymer networks." Modern Physics Letters B 32, no. 05 (2018): 1850064. http://dx.doi.org/10.1142/s0217984918500641.

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Complex networks have elicited considerable attention from scientific communities. This paper investigates consensus dynamics in a linear dynamical system with additive stochastic disturbances, which is characterized as network coherence by the Laplacian spectrum. Firstly, we introduce a class of weighted tree-like polymer networks with the weight factor. Then, we deduce the recursive relationship of the eigenvalues of Laplacian matrix at two successive generations. Finally, we calculate the first- and second-order network coherence quantifying as the sum and square sum of reciprocals of all nonzero Laplacian eigenvalues. The obtained results show that the scalings of first-order coherence with network size obey four laws along with the range of the weight factor and the scalings of second-order coherence with network size obey five laws along with the range of the weight factor.
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7

Dai, Changxi, Meifeng Dai, Tingting Ju, Xiangmei Song, Yu Sun, and Weiyi Su. "Eigentime identity of the weighted (m,n)-flower networks." International Journal of Modern Physics B 34, no. 18 (2020): 2050159. http://dx.doi.org/10.1142/s0217979220501593.

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The eigentime identity for random walks on the weighted networks is the expected time for a walker going from a node to another node. Eigentime identity can be studied by the sum of reciprocals of all nonzero Laplacian eigenvalues on the weighted networks. In this paper, we study the weighted [Formula: see text]-flower networks with the weight factor [Formula: see text]. We divide the set of the nonzero Laplacian eigenvalues into three subsets according to the obtained characteristic polynomial. Then we obtain the analytic expression of the eigentime identity [Formula: see text] of the weighted [Formula: see text]-flower networks by using the characteristic polynomial of Laplacian and recurrent structure of Markov spectrum. We take [Formula: see text], [Formula: see text] as example, and show that the leading term of the eigentime identity on the weighted [Formula: see text]-flower networks obey superlinearly, linearly with the network size.
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8

Abanov, Ar, M. Mineev-Weinstein, and A. Zabrodin. "Self-similarity in Laplacian Growth." Physica D: Nonlinear Phenomena 235, no. 1-2 (2007): 62–71. http://dx.doi.org/10.1016/j.physd.2007.04.012.

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9

Alekseev, Oleg. "Martingales of stochastic Laplacian growth." Physica D: Nonlinear Phenomena 412 (November 2020): 132629. http://dx.doi.org/10.1016/j.physd.2020.132629.

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10

Liu, Qun. "Spectral analysis for weighted iterated pentagonal graphs and its applications." Modern Physics Letters B 34, no. 28 (2020): 2050308. http://dx.doi.org/10.1142/s021798492050308x.

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Deterministic weighted networks have been widely used to model real-world complex systems. In this paper, we study the weighted iterated pentagonal networks. From the construction of the network, we derive recursive relations of all eigenvalues and their multiplicities of its normalized Laplacian matrix from the two successive generations of the weighted iterated pentagonal networks. As applications of spectra of the normalized Laplacian matrix, we study the Kemeny’s constant, the multiplicative degree-Kirchhoff index, and the number of weighted spanning trees and derive their exact closed-form expressions for the weighted iterated pentagonal networks.
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