BACKGROUND: This paper analyzes the effect of the mean-square error principle on the optimization process using a Special Case of Hopfield Neural Network (SCHNN). METHODS: The segmentation of multidimensional medical and colour images can be formulated as an energy function composed of two terms: the sum of squared errors, and a noise term used to avoid the network to be stacked in early local minimum points of the energy landscape. RESULTS: Here, we show that the sum of weighted error, higher than simple squared error, leads the SCHNN classifier to reach faster a local minimum closer to the global minimum with the assurance of acceptable segmentation results. CONCLUSIONS: The proposed segmentation method is used to segment 20 pathological liver colour images, and is shown to be efficient and very effective to be implemented for use in clinics.