Neural network architectures have been proposed as new computer architectures and a Hopfield neural network has been shown to find good solutions very fast in solving complex optimization problems. It should be noted, however, that a Hopfield neural network with fixed neural gains only guarantees to find local optimum solutions, not the global optimum solution. Image segmentation, like other engineering problems, can be formalized as an optimization problem and implemented using neural network architectures if an appropriate optimization function is defined. To achieve a good image segmentation, the global or the nearly global optimum solutions of the appropriate optimization function need to be found. In this paper, we propose a new neural network architecture for image segmentation, `an annealed Hopfield neural network,' which incorporates an annealing schedule for the neural gains. We implemented image segmentation using this annealed Hopfield neural network with an optimization function proposed by Blake and Zisserman and achieved good image segmentation in detecting horizontal and vertical boundaries. Later, we proposed an extended optimization function to achieve better performance on detecting sharp corners and diagonally oriented boundaries. Finally, simulation results on synthetic and real images are shown and compared with general-purpose mean field annealing technique.