Research on Rejection Capabilities of Paper Currency Recognition System with the Neural Network Employing Gaussian Function
Baiqing Sun · Kochi University of Technology Academic Resource Repository (Kochi University of Technology) · 2006
In this research, in order to improve rejection capabilities of currency recognition systems for unknown currency patterns on premise of guaranteeing their recognition capabilities for known currency patterns, a new paper currency recognition system based on neural networks is proposed. The neural network is a three-layer feedforward neural network (FNN), in which a Gaussian function is employed as the activation function in hidden layer and output layer. The recognition system is composed of two parts. The first is preprocessing, including detecting edges, compressing data dimensionalities, and extracting digital features. The second one is recognition, in which the core is a neural network classifier, in which the ridge-like Gaussian activation function is used. It makes the classifier have the potential of rejecting unknown currency pattern. Outputs of the classier are evaluated according with a certain criterion, and hence the input currencies are judged whether be rejected or not, and which pattern belongs to. In the procedure of preprocessing, in order to reduce dimensionality of paper currencies to be recognized effectively, pixels of currency images are grouped in some blocks, each of which are replaced with a single effective pixel whose gray-scale value is given by the average of the gray-scale values of the original pixels in the block. After that, in order to further compress dimensionality of the network and improve robustness of the system, slab values are applied to represent digital features of the paper currency image. In this procedure, for acquiring more features of a currency image, a mask set is utilized. It involves several mask patterns, each of which differs from the others and covers a different area of the currency image. Because many mask patterns can be obtained depending on different combinations of the blocks, many corresponding slab values are generated to be representative of the digital features of these currencies. In our recognition system, the slab values of a currency image are the input vector of the neural network. In the procedure of recognition, the slab values representing features of the currency are inputted the neural network employing the proposed Gaussian activation function, which is different with not only the simple radial basis function but also the Gaussian bars function. It is a ridge-like function in multi-dimensional space. Its activation is stretch out to infinity along the ridge, but is restricted by the width parameter on the orthogonal direction of the ridge. Its active range lies on the value of the width parameter. The directions, distributions and active ranges are controlled by corresponding weights, biases and widths, respectively. Hence the network with this activation function has more potential to improve rejection capabilities on promise of ensuring recognition capabilities of the system. The experiments about the influences of the parameters of the Gaussian function to performances of the system are designed and executed. The corresponding results are analyzed. It can be found from these results that the performances of the system are very sensitive to variations of the width parameter. During the training procedure, in order to obtain satisfying performances, several learning algorithms are employed to optimizing the parameters. The improved back propagation algorithm is used to optimize the weights and biases of the network. The sequential gradient algorithm fitting for the proposed network are derived, and applied to optimize the width parameters. At the same time, it is found in this experiment that the different sequences of training currency samples influence the rejection capabilities of the system remarkably as using the sequential version of the gradient descent algorithm, and the reasons leading to this phenomenon are analyzed. In order to search the appropriate width parameters in larger region and avoid the problem of local minima, a new hybrid-learning algorithm is also proposed. The algorithm is used to optimize the widths of the Gaussian function. The algorithm consists of two steps, one is searching local minima near start point by employing the sequential gradient descent method with a momentum term, because the sequential gradient descent algorithm is a stochastic searching method and is possible to escape the iterative search from local minima. If the iterative search still cannot shake off bindings of local minima by employing this first step solely, the second step of this algorithm is then activated. First, a random vector is mixed in increment terms of the width parameters to replace that momentum term, then coefficients of the random vector and the gradient term are optimized simultaneously using the downhill simplex method. In this case, derivative calculation is unnecessary, and the span and directions of the iteration search have more possibilities. It hence can explore optimal parameters in a larger range and extricate the search from local minima more quickly and easily. The results of the experiments show that using the proposed algorithm, the iteration search span and directions of increments of the widths have more combinations, it can extricate the search from local minima more quickly and easily and explore optimal solutions of widths in a larger range. Moreover, the proposed recognition system using the algorithm is insensitive for the change of initial range of width parameters, and it can improve the rejection capabilities for unknown currency patterns on promise of guaranteeing the recognition capabilities for known currency patterns.