An efficient Self-Organizing Active Contour model for image segmentation Mohammed M. Abdelsamea a , Giorgio Gnecco a,n , Mohamed Medhat Gaber b a IMT Institute for Advanced Studies, Lucca, Italy b Robert Gordon University, Aberdeen, UK article info Article history: Received 16 December 2013 Received in revised form 2 June 2014 Accepted 24 July 2014 Communicated by M. Bianchini Available online 6 August 2014 Keywords: Region-based segmentation Variational level set method Active contours Self-organizing neurons Region-based prior knowledge abstract Active Contour Models (ACMs) constitute a powerful energy-based minimization framework for image segmentation, based on the evolution of an active contour. Among ACMs, supervised ACMs are able to exploit the information extracted from supervised examples to guide the contour evolution. However, their applicability is limited by the accuracy of the probability models they use. As a consequence, effectiveness and efficiency of supervised ACMs are among their main real challenges, especially when handling images containing regions characterized by intensity inhomogeneity. In this paper, to deal with such kinds of images, we propose a new supervised ACM, named Self-Organizing Active Contour (SOAC) model, which combines a variational level set method (a specific kind of ACM) with the weights of the neurons of two Self-Organizing Maps (SOMs). Its main contribution is the development of a new ACM energy functional optimized in such a way that the topological structure of the underlying image intensity distribution is preserved – using the two SOMs – in a parallel-processing and local way. The model has a supervised component since training pixels associated with different regions are assigned to different SOMs. Experimental results show the superior efficiency and effectiveness of SOAC versus several existing ACMs. & 2014 Elsevier B.V. All rights reserved. 1. Introduction Image segmentation is the problem of partitioning the domain Ω of an image I(x), where x A Ω is the pixel location within the image, into different subsets Ω i , for i belonging to an index set I , where each subset has a different characterization in terms of color, intensity, texture, and/or other features used as similarity criteria. Segmentation is a fundamental component of image processing, which plays a significant role in computer vision, object recognition, and object tracking. Image segmentation can also be expressed as a contour extraction problem [1]. Active Contour Models (ACMs) constitute a powerful energy-based approach to segmentation. Such models usually deal with the segmentation problem as a functional (also called infinite-dimen- sional) optimization problem, which tries to partition a given image into regions on the basis of the maximization/minimization of a suitable energy functional. Starting from an initial contour, the optimization of the functional is performed iteratively, evolving the current contour with the aim of approximating better and better the actual object boundary (hence the term “active contour” models, which is used also for models that evolve the contour but are not based on the explicit minimization of a functional). Among ACMs, those based on variational level set methods [2] are particularly interesting, as they represent the current contour as the zero level set of a function, instead of a parametric curve. For this reason, they are able to model arbitrarily complex shapes, and to handle topological changes of the object boundary, such as merging and splitting. ACMs also allow the integration of boundary and regional information within the energy framework, and also information coming from a learning process [3]. A challenge for current ACMs consists in handling images with complex fore- ground/background intensity distributions (e.g., containing objects characterized by many different intensities), and intensity inho- mogeneity (e.g., when there are no visible intensity changes around the true object boundary). Such a challenge is exacerbated when the amount of overlap between the foreground/background intensity distributions is hard to be estimated. An effective solu- tion to deal with this issue is to incorporate prior knowledge in the image segmentation framework, e.g., by learning how to model the complexity of object shape and intensity distributions, when training examples are available. In general, ACMs can be classified into three categories: edge- based, region-based, and hybrid models. Edge-based models make use of an edge-detector (in general, the gradient of the image intensity), to stop the evolution of the contour on the true Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/neucom Neurocomputing http://dx.doi.org/10.1016/j.neucom.2014.07.052 0925-2312/& 2014 Elsevier B.V. All rights reserved. n Corresponding author. E-mail addresses: mohammed.abdelsamea@imtlucca.it (M.M. Abdelsamea), giorgio.gnecco@imtlucca.it (G. Gnecco), m.gaber1@rgu.ac.uk (M.M. Gaber). Neurocomputing 149 (2015) 820–835