Behavioural study of median associative memory under true-colour image patterns Roberto A. Va´ zquez a , Humberto Sossa b,n a Intelligent Systems Group, Faculty of Engineering – Universidad La Salle, Benjamı ´n Franklin 47 Col. Condesa CP 06140, Me ´xico D.F., Mexico b Centro de Investigacio´n en Computacio´n – IPN, Av. Juan de Dios Batı ´z, esq. Miguel Otho´n de Mendiza´bal, Mexico City 07738, Mexico article info Article history: Received 2 November 2009 Received in revised form 23 March 2011 Accepted 4 April 2011 Communicated by W. Yu Available online 31 May 2011 Keywords: Associative memories Median associative memories Pattern recall Pattern restoration abstract Median associative memories (MED-AMs) are a special type of associative memory that substitutes the maximum and minimum operators of a morphological associative memory with the median operator. This associative model has been applied to restore grey scale images and provided a better performance than morphological associative memories when the patterns are altered with mixed noise. Despite their power, MED-AMs have not been adopted in problems related with true-colour patterns. In this paper, we describe how MED-AMs can be applied to problems involving true-colour patterns. Furthermore, a complete study of the behaviour of this associative model in the restoration of true-colour images is performed using a benchmark of 16,000 images altered by different noise types. & 2011 Elsevier B.V. All rights reserved. 1. Introduction The concept of associative memory AM emerges from psycholo- gical theories of human and animal learning [19–21]. These devices store information by learning correlations among different stimuli. When a stimulus is presented as a memory cue, the associated one is retrieved in consequence. This means that the two stimuli have become associated with each other in the memory. An AM can be seen as a particular type of neural network designed to recall output patterns in terms of input patterns that can appear altered by some kind of noise. Several AMs have been proposed lately. For example, Steinbuch [1] suggested an associative memory based on a switching matrix. Anderson [2] presented a simple neural network generating an interactive memory. Kohonen [3] replaced the lernmatrix of Steinbuch by a correlation matrix. The output in these models is produced in a single feedforward compu- tation where correlation or Hebbian learning is used to synthesise the synaptic weight matrix. Another type of associative memory was proposed by Hopfield [4]. This model is different from other previous models in that it computes its output recursively in time until the system becomes stable. There are other types of associative mem- ories that are not necessarily represented by a matrix such as [13,15,16]; however, this paper will be devoted to those represented with a matrix. Recently, morphological, median and fuzzy associative memories were proposed; refer for example to [5–12,22]. Although the performance obtained with these models is pretty acceptable, they also have to satisfy several constrains, which limit their applicability in complex problems. Most of these AMs have several constraints. Among these we could mention their storage capacity (limited), the pattern types (only binary, bipolar, integer or real patterns), noise robustness (additive, subtractive, mixed, Gaussian noise, deformations, etc.). In 1998, Ritter et al. [8] proposed the concept of morphological associative memories (MAMs), which exhibit optimal absolute storage capacity and one-step convergence. Basically, the authors substituted the outer product by max and min operations. This type of associative model has been applied to different pattern recognition problems including face localisation and reconstruc- tion of grey scale [9] and true-colour images [17]; however, they are not robust to mixed noise. Another interesting approach was introduced by Sossa et al. [12] in their work ‘‘A new associative memory to recall real-valued patterns’’. In this model, the authors substituted the max–min operator by the med operator. By using this new operator the median associative model (MED-AM) was capable of dealing with patterns, which include additive and subtractive noise at the same time. In addition, in [7,14], the authors described some useful techniques for increasing model accuracy. Despite the power of this model, it has not been applied to problems involving true-colour patterns, nor has a deep study of this associative model under true- colour image pattern been performed. Bearing this in mind, this paper describes how a MED-AM can be applied to problems that involve true-colour patterns. Furthermore, a complete study of the behaviour of this associative model in the Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/neucom Neurocomputing 0925-2312/$ - see front matter & 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.neucom.2011.04.013 n Correspondence to: Centro de Investigacio´ n en Computacio´ n – IPN, Av. Juan de Dios Ba´ tiz s/n, Esquina con Miguel Otho´ n de Mendiza´ bal, Colonia Nueva Industrial Vallejo, CP 07700, Me´ xico D.F., Mexico. E-mail addresses: ravem@lasallistas.org.mx (R.A. Va´ zquez), hsossa@cic.ipn.mx (H. Sossa). Neurocomputing 74 (2011) 2985–2997