A new approach to shortest paths on networks based on the quantum bosonic mechanism

IEEE Trans. on Image Process.

Bouwmans

et al. 2017

124

Background estimation and foreground segmentation are important steps in many high-level vision tasks. Many existing methods estimate background as a low-rank component and foreground as a sparse matrix without incorporating the structural information. Therefore, these algorithms exhibit degraded performance in the presence of dynamic backgrounds, photometric variations, jitter, shadows, and large occlusions. We observe that these backgrounds often span multiple manifolds. Therefore, constraints that ensure continuity on those manifolds will result in better background estimation. Hence, we propose to incorporate the spatial and temporal sparse subspace clustering into the robust principal component analysis (RPCA) framework. To that end, we compute a spatial and temporal graph for a given sequence using motion-aware correlation coefficient. The information captured by both graphs is utilized by estimating the proximity matrices using both the normalized Euclidean and geodesic distances. The low-rank component must be able to efficiently partition the spatiotemporal graphs using these Laplacian matrices. Embedded with the RPCA objective function, these Laplacian matrices constrain the background model to be spatially and temporally consistent, both on linear and nonlinear manifolds. The solution of the proposed objective function is computed by using the linearized alternating direction method with adaptive penalty optimization scheme. Experiments are performed on challenging sequences from five publicly available datasets and are compared with the 23 existing state-of-the-art methods. The results demonstrate excellent performance of the proposed algorithm for both the background estimation and foreground segmentation.

Section: E Geodesic Distance Based Proximity Matricesmentioning

confidence: 99%

Section: H Proposed Ladmap Optimizationmentioning

confidence: 99%

See 1 more Smart Citation

Background–Foreground Modeling Based on Spatiotemporal Sparse Subspace Clustering

Javed

IEEE Trans. on Image Process.

Bouwmans

et al. 2017

124

“…Pettie and Ramachandran [43] have proposed an algorithm for the all-pairs geodesic distance problem having the time complexity of O(mn log α(m, n)), where α(m, n) is a very slowly growing inverse-Ackermann function, m is the number of edges, and n is the number of vertices. Recently Jiang et al [25] has proposed Quantum Bosonic Shortest Path Searching (QBSPS). For the all-pairs shortest-path problem in a random scale-free network with n vertices, QBSPS runs in O(µ(n) ln ln n) time [25].…”

Section: Complexity Analysis Of the Proposed Algorithmmentioning

confidence: 99%

“…Recently Jiang et al [25] has proposed Quantum Bosonic Shortest Path Searching (QBSPS). For the all-pairs shortest-path problem in a random scale-free network with n vertices, QBSPS runs in O(µ(n) ln ln n) time [25].…”

Section: Complexity Analysis Of the Proposed Algorithmmentioning

confidence: 99%

Using Geodesic Space Density Gradients for Network Community Detection

IEEE Trans. Knowl. Data Eng.

Small²,

Al-Maadeed

et al. 2017

Using geodesic space density gradients for network community detection. IEEE Transactions on Knowledge and Data Engineering, 294 (4). pp. 921-935. Permanent WRAP URL:http://wrap.warwick.ac.uk/84012 Copyright and reuse:The Warwick Research Archive Portal (WRAP) makes this work by researchers of the University of Warwick available open access under the following conditions. Copyright © and all moral rights to the version of the paper presented here belong to the individual author(s) and/or other copyright owners. To the extent reasonable and practicable the material made available in WRAP has been checked for eligibility before being made available.Copies of full items can be used for personal research or study, educational, or not-for profit purposes without prior permission or charge. Provided that the authors, title and full bibliographic details are credited, a hyperlink and/or URL is given for the original metadata page and the content is not changed in any way.Publisher's statement: "© 2017 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting /republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works." A note on versions:The version presented here may differ from the published version or, version of record, if you wish to cite this item you are advised to consult the publisher's version. Please see the 'permanent WRAP URL' above for details on accessing the published version and note that access may require a subscription.For more information, please contact the WRAP Team at: wrap@warwick.ac.uk 1 Using Geodesic Space Density Gradients for Network Community DetectionArif Mahmood, Michael Small, Somaya Ali Al-Maadeed, and Nasir Rajpoot Abstract-Many real world complex systems naturally map to network data structures instead of geometric spaces because the only available information is the presence or absence of a link between two entities in the system. To enable data mining techniques to solve problems in the network domain, the nodes need to be mapped to a geometric space. We propose this mapping by representing each network node with its geodesic distances from all other nodes. The space spanned by the geodesic distance vectors is the geodesic space of that network. Position of different nodes in the geodesic space encode the network structure. In this space, considering a continuous density field induced by each node, density at a specific point is the summation of density fields induced by all nodes. We drift each node in the direction of positive density gradient using an iterative algorithm till each node reaches a local maximum. Due to the network structure captured by this space, the nodes that drift to the same region of space belong to the same communities in the original network. We use the direction of movement and final position of each...

Cellular community detection for tissue phenotyping in colorectal cancer histology images

Javed

Fraz

et al. 2020

Medical Image Analysis

137