The relaxation process is a useful technique for using contextual information to reduce local ambiguity and achieve global consistency in various applications. It is basically a parallel execution model, adjusting the confidence measures of involved entities based on interrelated hypotheses and confidence measures. On the other hand, the neural network is a computational model with massively parallel execution capability. The output of each neuron depends mainly on the information provided by other neurons. Therefore, there exist certain common properties in the relaxation process and the neural network technique. A mapping method that makes the Hopfield neural network perform the relaxation process is proposed. By this method, the neural network technology can be easily adapted to solve the many problems which have already been solved by the relaxation process. An advantage of this is that the relaxation process can be performed in real time since the Hopfield network can be implemented by conventional analog circuits. Experimental results are given to demonstrate the feasibility of the proposed method by performing the image thresholding operation on the proposed neural network.