Artificial Ant Colonies in Digital Image Habitats – A Mass Behaviour Effect Study on Pattern Recognition

Some recent studies have pointed that , the self-organization of neurons into brain-like structures, and the self-organization of ants into a swarm are similar in many respects. If possible to implement, these features could lead to important developments in pattern recognition systems, where perceptive capabilities can emerge and evolve from the interaction of many simple local rules. The principle of the method is inspired by the work of Chialvo and Millonas who developed the first numerical simulation in which swarm cognitive map formation could be explained. From this point, an extended model is presented in order to deal with digital image habitats, in which artificial ants could be able to react to the environment and perceive it. Evolution of pheromone fields point that artificial ant colonies could react and adapt appropriately to any type of digital habitat. 1. From Natural to Digital Habitats In “Godel, Escher, Bach”, Douglas Hofstadter explores the difference between an ant colony as a whole and the individual that compose it. According to Hofstadter, the behaviour of the whole colony is far more sophisticated and of very different character than the behaviour of the individual ants. A colony’s collective behaviour exceeds the sum of its individual member’s actions (so-called emergence) and is most easily observed when studying their foraging activity. Most species of ants forage collectively using chemical recruitment strategies, termed pheromone trails, to lead their fellow nest-mates to food sources. This analogy with the way that real and natural ant colonies work and migrate, has suggested the definition in 1991/92 of a new computational paradigm, which is called the Ant System by Marco Dorigo [8]. In these studies there is no precommitment to any particular representational scheme: the desired behaviour is specified, but there is minimal specification of the mechanism required to generate that behaviour, i.e. global behaviour evolves from the many relations of multiple simple behaviours. Since then several studies were conducted to apply this recent paradigm – or analogous ones in real case problems, with successful results. The new heuristic has the following desirable characteristics: (1) It is versatile, in that it can be applied to similar versions of the same problem; (2) It is Robust. It can be applied with only minimal changes to other problems (e.g. combinatorial optimisation problems such as the quadratic assignment problem QAP, travelling salesman problem TSP, or the job-shop scheduling problem JSP);. and (3) It is a population based approach. This last property is interesting since it allows the exploitation of positive feedback as a search mechanism (the collective behaviour that emerges is a form of autocatalytic “snow ball” effect that reinforces itself behaviour, where the more the ants follow a trail, the more attractive that trail becomes for being followed). It also makes the system amenable to parallel implementations (though, only the intrinsically parallel and distributed nature of these systems are considered in this work). However, none of these new paradigms has been applied to Pattern Recognition problems (and namely to the sub-problem of image segmentation). The application of these heuristics on image segmentation looks very promising, since segmentation can be looked as a clustering and combinatorial problem [19, 20], and grey level image itself as a topographic map (where the image is the ant colony habit). Moreover, and as reported by some studies, the self-organisation of neurones into brain-like structures, and the self-organisation of ants into a swarm are similar in many respects. The present paper is based on Chialvo and Millonas work [4], which is probably, one of the simplest (local, memoryless, homogeneous and isotropic) models which leads to trail forming, where the formation trails and networks of ant traffic are not imposed by any special boundary conditions, lattice topology, or additional behavioural rules. The next section is dedicated to explain how this model operate in a finite square lattice, while the remaining sections will be devoted to extend their work to digital image lattices, where the respective grey level intensities will be considered in each ant perception of his neighbourhood. The main goal is to achieve a global perception of one image as the emergent sum of local perceptions of the whole colony. 2. The Chialvo and Millonas Swarm Cognitive Map Model As described by Chialvo and Millonas in [4], the state of an individual ant can be expressed by its position r, and orientation θ. Since the response at a given time is assumed to be independent of the previous history of the individual, it is sufficient to specify a transition probability from one place and orientation (r,θ) to the next (r,θ) an instant later. In previous works [16,17] transition rules were derived and generalized from noisy response functions, which in turn were found to reproduce a number of experimental results with real ants. The response function can effectively be translated into a two-parameter transition rule between the cells by use of a pheromone weigthing function: This equation measures the relative probabilities of moving to a cite r (in our context, to a pixel) with pheromone density σ(r) as discussed in [16,17]. The parameter β is associated with the osmotropotaxic sensitivity, recognised by Wilson [25] as one of two fundamental different types of ants sense-data processing. Osmotropotaxis, is related to a kind of instantaneous pheromonal gradient following, while the other, klinotaxis, to a sequential method (though only the former will be considered in the present work as in [4]). Also it can be seen as a physiological inversenoise parameter or gain. In practical terms, this parameter controls the degree of randomness with wich each ant follows the gradient of pheromone. As putted by both authors, for low values of β the pheromone concentration does not greatly affect its choice, while high values cause it to follow pheromone gradient with more certainty. On the other hand, 1/δ is the sensory capacity, which describes the fact that each ant’s ability to sense pheromone decreases somewhat at high concentrations. In addition to the former equation, there is a weigthing factor w(∆θ), where ∆θ is the change in direction at each time step, i.e. measures the magnitude of the difference in orientation. This weighting factor ensures that very sharp turns are much less likely than turns through smaller angles; thus each ant in the colony have a probabilistic bias in the forward direction. For instance, if we consider that one agent is coming from the north direction (fig. 1a), south-west (fig. 1b), or north-east (fig.1c), the following values w(∆θ) will be considered: ( ) β δσ σ σ       + + = 1 1 W