This paper presents a two-stage neural system to determine the contact points between a three-fingered gripper and an object of arbitrary shape. In the first stage, a CCD camera captures the image of the object and such an image is transformed into a two-dimensional outline through a nearest neighbour algorithm. In the second phase, two neural networks, functioning in cascade, select three contact points in the outline. A competitive Hopfield neural network defines an approximate polygon considering a reduced number of boundary points of the original outline. Then, a supervised neural network, either a multi-layer perceptron or a radial basis function (RBF) network, find the contact points. The experiments suggest that the RBF network trained by the global ridge regression method is suitable for on-line applications and presents the best overall performance in terms of accuracy and robustness to noise. Moreover, this method is able to find correctly the contact points for objects of arbitrary shapes.