Enhanced Hoppeld Network for Morphologic Image Processing

Hoppeld networks are neural architectures remarkable by architectural simplicity and exibility in usage. There are many areas in which Hoppeld networks have been successfully applied, including associative memories, pattern recognition and artiicial intelligence. This paper proposes a novel application of Hoppeld networks in image processing, as morphologic lters, and illustrates the concept with a comprehensive example of a morphologic lter used for feature extraction. 1 The enhanced Hoppeld network The massive parallelism of neural networks and the resulting computational power make them a very attractive prospect for image processing applications. Especially ltering operations require large amounts of computations and could beneet the most from the possibilities of neural architectures. Among the many diierent architectures, Hoppeld networks stand out because of their simplicity and versatility. This paper explains how Hoppeld networks can be used in the design of morphologic lters in general and shows a detailed example of such a morphologic lter, specialized in feature extraction. Researchers who have attempted to use the Hop-eld network to solve speciic problems 5], trying to exploit the excellent computational qualities of the network | massive parallelism and very simple structure | have found that the most diicult problem is to determine the weights of the network 1]. The dif-culties arise mostly because the only way the evolution of the network can be controlled is through the minimization of the Liapunov energy function 2, 3, 4]. The simplicity of the network has therefore some disadvantages along with its many advantages. It is diicult, if not impossible, to describe a complex problem in the very restrictive terms of a single function 6] because for many practical problems there are several variables involved. Each variable is a function of the state of the network and the solution consists of an acceptable set of values of those functions. To control the evolution of the state of the network and to decide whether the state represents an acceptable solution, a new layer is added to the Hoppeld network (Figure 1). In a Hoppeld network, the processing stops when convergence is attained. Therefore, the state of the network representing the solution needs to be equivalent to a minimum of the Liapunov energy function. Most of the times this is diicult to realize. The added layer observes the state of the network at all moments and decides whether the state of the network represents a solution. The advantage is in that …