GENOCOP Algorithm and Hierarchical Grid Transformation for Image Warping of Two-Dimensional Gel Electrophoretic Maps

  • Elisa RobottiEmail author
  • Emilio MarengoEmail author
  • Marco Demartini
Part of the Methods in Molecular Biology book series (MIMB, volume 1384)


Hierarchical grid transformation is a powerful hierarchical approach to 2-D map warping, able to model both global and local deformations. The algorithm can be stopped when a desired degree of accuracy in the images alignment is obtained. The deformed image is warped and aligned to the target image using a grid where the number of nodes increases in each step of the algorithm. The numerical optimization of the position of the nodes of the grid can be efficiently solved by genetic algorithms, ensuring the achievement of the optimal position of the nodes with a low computational cost with respect to other methods. Here, the optimization of the position of the nodes is carried out by GENOCOP (genetic algorithm for numerical optimization of constrained problems), refined by the following conjugate gradient optimization step. The modeling of the warped space is then achieved by a spline model where some constraints are introduced in the choice of the nodes that are moved. The whole procedure can be intended as an evolutionary method that models the deformation of the gel map at different levels of detail.

Key words

Hierarchical grid transformation GENOCOP Warping 2-D maps Genetic algorithm 



The authors gratefully acknowledge the collaboration of Dr. Alberto Zamò (Policlinico G. B. Rossi, University of Verona) who provided the biological samples used to produce the electrophoretic 2-D maps used in this study. The contents of this chapter are reproduced and adapted from [26] with permission from The Royal Society of Chemistry.


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of Sciences and Technological InnovationUniversity of Piemonte OrientaleAlessandriaItaly

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