Singh, AV and Chaudhury, KN (2020) On Uniquely Registrable Networks. In: IEEE Transactions on Network Science and Engineering, 7 (3). pp. 1327-1336.
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Abstract
Consider a network with N nodes in d-dimensional Euclidean space, and M subsets of these nodes P1,, PM. Assume that the nodes in a given Pi are observed in a local coordinate system. The registration problem is to compute the coordinates of the N nodes in a global coordinate system, given the information about P1, PM and the corresponding local coordinates. The network is said to be uniquely registrable if the global coordinates can be computed uniquely (modulo Euclidean transforms). We formulate a necessary and sufficient condition for a network to be uniquely registrable in terms of rigidity of the body graph of the network. A particularly simple characterization of unique registrability is obtained for planar networks. Furthermore, we show that k-vertex-connectivity of the body graph is equivalent to quasi k-connectivity of the bipartite correspondence graph of the network. Along with results from rigidity theory, this helps us resolve a recent conjecture due to Sanyal et al. (R. Sanyal, M. Jaiswal, and K. N. Chaudhury, 'On a registration-based approach to sensor network localization,' IEEE Trans. Signal Process., vol. 65, no. 20, pp. 5357-5367, Oct. 2017.) that quasi three-connectivity of the correspondence graph is both necessary and sufficient for unique registrability in two dimensions. We present counterexamples demonstrating that while quasi (d+1)-connectivity is necessary for unique registrability in any dimension, it fails to be sufficient in three and higher dimensions. © 2013 IEEE.
| Item Type: | Journal Article |
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| Publication: | IEEE Transactions on Network Science and Engineering |
| Publisher: | IEEE Computer Society |
| Additional Information: | The copyright of this article belongs to IEEE Computer Society |
| Keywords: | Sensor networks; Signal processing, Euclidean transforms; Global coordinate systems; Global coordinates; Higher dimensions; K-vertex connectivity; Local coordinate system; Registration problems; Sensor network localization, Rigidity |
| Department/Centre: | Division of Electrical Sciences > Electrical Engineering |
| Date Deposited: | 21 Dec 2020 11:47 |
| Last Modified: | 21 Dec 2020 11:47 |
| URI: | http://eprints.iisc.ac.in/id/eprint/66685 |
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