Improving segmentation velocity using an evolutionary method Diego Oliva a,b,⇑ , Valentín Osuna-Enciso c , Erik Cuevas b , Gonzalo Pajares a , Marco Pérez-Cisneros b,c , Daniel Zaldívar b a Dpto. Ingeniería del Software e Inteligencia Artificial, Facultad Informática, Universidad Complutense de Madrid, 28040 Madrid, Spain b Departamento de Electrónica, Universidad de Guadalajara, CUCEI, Av. Revolución 1500, Guadalajara, Jal, Mexico c Departamento de Ingenierías, Universidad de Guadalajara, CUTONALA, Sede Provisional Casa de la Cultura – Administración: Calle Morelos 180, Tonalá, Jalisco, Mexico article info Article history: Available online 9 April 2015 Keywords: Image processing Segmentation Evolutionary algorithms Tsallis entropy Electro-magnetism optimization abstract Image segmentation plays an important role in image processing and computer vision. It is often used to classify an image into separate regions, which ideally correspond to different real-world objects. Several segmentation methods have been proposed in the literature, being thresholding techniques the most popular. In such techniques, it is selected a set of proper threshold values that optimize a determined functional criterion, so that each pixel is assigned to a determined class according to its corresponding threshold points. One interesting functional criterion is the Tsallis entropy, which gives excellent results in bi-level thresholding. However, when it is applied to multilevel thresholding, its evaluation becomes computationally expensive, since each threshold point adds restrictions, multimodality and complexity to its functional formulation. Therefore, in the process of finding the appropriate threshold values, it is desired to limit the number of evaluations of the objective function (Tsallis entropy). Under such circumstances, most of the optimization algorithms do not seem to be suited to face such problems as they usually require many evaluations before delivering an acceptable result. On the other hand, the Electromagnetism-Like algorithm is an evolutionary optimization approach which emulates the attraction–repulsion mechanism among charges for evolving the individuals of a population. This tech- nique exhibits interesting search capabilities whereas maintains a low number of function evaluations. In this paper, a new algorithm for multilevel segmentation based on the Electromagnetism-Like algorithm is proposed. In the approach, the optimization algorithm based on the electromagnetism theory is used to find the optimal threshold values by maximizing the Tsallis entropy. Experimental results over several images demonstrate that the proposed approach is able to improve the convergence velocity, compared with similar methods such as Cuckoo search, and Particle Swarm Optimization. Ó 2015 Elsevier Ltd. All rights reserved. 1. Introduction Segmentation is one of the basic steps of an image analysis system, and consists in separating objects from each other, by considering characteristics contained in a digital image. It has been applied to feature extraction (Kong, Deng, & Dai, 2015), object identification and classification (Cao, Li, Du, Zhang, & Zheng, 2014), surveillance (Bhandari, Singh, Kumar, & Singh, 2014), among other areas. In order to obtain homogeneous regions of pix- els, a common method is using the histogram’s information with a thresholding approach (Sarkar & Das, 2013).This method is consid- ered the easiest one in segmentation, and it works taking threshold values which separate adequately the distinct regions of pixels in the image being processed. In general, there are two thresholding approaches, namely bi-level and multilevel. In bi-level threshold- ing (BT), it is only needed a threshold value to separate the two objects of an image (e.g. foreground and background). For real life images, BT does not provide appropriate results. On the other hand, multilevel thresholding (MT) divides the pixels in more than two homogeneous classes and it needs several threshold values (Akay, 2012; Maitra & Chatterjee, 2008). Threshold methods are divided in parametric and nonparametric (Akay, 2012; Xia, Song, & He, 2015). In parametric approaches, it is necessary estimating the parameters of a probability density function capable of modeling each class. Such an approach is time consuming and computationally expensive. A nonparametric technique employs a given criteria (between-class variance, entropy and error rate http://dx.doi.org/10.1016/j.eswa.2015.03.028 0957-4174/Ó 2015 Elsevier Ltd. All rights reserved. ⇑ Corresponding author at: Dpto. Ingeniería del Software e Inteligencia Artificial, Facultad Informática, Universidad Complutense de Madrid, 28040 Madrid, Spain. Tel.: +52 33 1378 5900x27714. E-mail addresses: doliva@ucm.es, diego.oliva@cucei.udg.mx (D. Oliva), valentin. osuna@cutonala.udg.mx (V. Osuna-Enciso), erik.cuevas@cucei.udg.mx (E. Cuevas), pajares@ucm.es (G. Pajares), marco.perez@cucei.udg.mx, marco.perez@cutonala. udg.mx (M. Pérez-Cisneros), daniel.zaldivar@cucei.udg.mx (D. Zaldívar). Expert Systems with Applications 42 (2015) 5874–5886 Contents lists available at ScienceDirect Expert Systems with Applications journal homepage: www.elsevier.com/locate/eswa