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IMA Journal of Management Mathematics Advance Access originally published online on March 14, 2007
IMA Journal of Management Mathematics 2007 18(2):207-221; doi:10.1093/imaman/dpm008
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© The authors 2007. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Variable neighbourhood search for colour image quantization

Pierre Hansen1, Jasmina Lazic2 and Nenad Mladenovic3,**

1 GERAD and École des Hautes Études Commerciales, 3000 ch. de la Cote-Sainte-Catherine, Montréal, Canada H3T 2A7, 2 Mathematical Institute, Serbian Academy of Sciences and Arts, Kneza Mihaila 35, 11001 Belgrade, Serbia, 3 School of Information Systems, Computing and Mathematics, Brunel University, Uxbridge, Middlesex UB8 3PH, UK

** Email: nenad.mladenovic{at}brunel.ac.uk


  Abstract

Colour image quantization is a data compression technique that reduces the total set of colours in a digital image to a representative subset. This problem is first expressed as a large M-median one. The advantages of this model over the usual minimum sum-of-squares model are discussed first and then, the heuristic based on variable neighbourhood search metaheuristic is applied to solve it. Computational experience proves that this approach compares favourably with two other recent state-of-the-art heuristics, based on genetic and particle swarm searches.

Keywords: colour image quantization; variable neighbourhood decomposition search; sum-of-squares; clustering problem; M-median problem

Received on April 2006. accepted on 2 February 2007.


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