Distributed framework matching
This paper studies the problem of distributed framework matching (FM), which originates from the assignment task in multi-robot coordination and the matching task in pattern recognition. The objective of distributed FM is to distributively seek a correspondence which minimizes some metrics descri...
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Main Authors: | , , |
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Other Authors: | |
Format: | Article |
Language: | English |
Published: |
2022
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Subjects: | |
Online Access: | https://hdl.handle.net/10356/162586 |
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Institution: | Nanyang Technological University |
Language: | English |
Summary: | This paper studies the problem of distributed framework matching (FM), which originates from the assignment task
in multi-robot coordination and the matching task in pattern
recognition. The objective of distributed FM is to distributively
seek a correspondence which minimizes some metrics describing
the disagreement between two frameworks (i.e., graphs and their
embeddings). In view of the type of the underlying graph in the
framework, two formulations, undirected framework matching
(UFM) and directed framework matching (DFM), and their
convex relaxations, relaxed UFM (RUFM) and relaxed DFM
(RDFM), are presented. UFM is converted into a graph matching
(GM) problem with the adjacency matrix being replaced by a
matrix constructed from the undirected framework under certain
graphical conditions, and can be solved distributively. Sufficient
conditions for the equivalence between UFM and RUFM, and
the perturbation admitting exact recovery of correspondence are
established. On the other hand, DFM embeds the configuration
of the directed framework via another type of matrix, whose
computation is distributed, and can deal with the case of two
frameworks with different sizes of node sets. A distributed
optimization algorithm for solving RDFM is proposed and its
convergence results are established which allows DFM to be
solved in a fully distributed manner. Simulation examples on
both synthetic data and real world datasets demonstrate the
applicability and efficacy of our theoretical results in formation
control and object matching problems. |
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