Optim Lett DOI 10.1007/s11590-016-1031-7 ORIGINAL PAPER A DC optimization-based clustering technique for edge detection W. Khalaf 1 · A. Astorino 2 · P. D’Alessandro 3 · M. Gaudioso 4 Received: 27 July 2015 / Accepted: 30 March 2016 © Springer-Verlag Berlin Heidelberg 2016 Abstract We introduce a method for edge detection which is based on clustering the pixels representing any given digital image into two sets (the edge pixels and the non-edge ones). The process is based on associating to each pixel an appropriate vector representing the differences in brightness w.r.t. the surrounding pixels. Clustering is driven by the norms of such vectors, thus it takes place in R, which allows us to use a (simple) DC (Difference of Convex) optimization algorithm to get the clusters. A novel thinning technique, based on calculation of the edge phase angles, refines the classification obtained by the clustering algorithm. The results of some numerical experiments are also provided. Keywords Classification · Clustering · DC optimization · Edge detection The work has been partially supported by Project PON 01_01180 “Neurostar”. B M. Gaudioso gaudioso@deis.unical.it; gaudioso@dimes.unical.it W. Khalaf walaakhalaf@yahoo.com; walaa@deis.unical.it A. Astorino astorino@icar.cnr.it P. D’Alessandro pietrodalessandro@gmail.com 1 Computer and Software Engineering Department, College of Engineering, AlMystansiriya University, Baghdad, Iraq 2 Istituto di Calcolo e Reti ad Alte Prestazioni - C.N.R., 87036 Rende (CS), Italy 3 ICT Sud, 87036 Rende (CS), Italy 4 D.I.M.E.S., Università della Calabria, 87036 Rende (CS), Italy 123