## 3 Experimental Results
### MLP Architecture Selection  
In order to determine the optimal Multilayer perceptron architecture, the number of layers plays an essential role. In general, the input and output layers are directly related with the nature of the problem to be solved. The main challenge is given to establish the number of hidden layers along with the number of hidden neurons for each of them. To establish the number of hidden layers in the proposed Multilayer perceptron, the range of hidden layers \(h=[1,2,3,4]\) was explored. MLP architectures with more than two hidden layers present low performance in terms of the area under ROC curve and high computational time using the present training set. Consequently, MLP architectures with one and two hidden layers were selected to be analyzed in detail. According to the statistical analysis presented below, the optimal performance of the MLP architecture can be obtained using two hidden layers; therefore, a Multilayer perceptron with a four layers architecture was proposed in the present paper. In addition, the number of hidden neurons for each hidden layer represents one of the main contributions of the present paper, since it has been determined by using a stochastic dominance approach, which is also discussed below. Since the Gaussian matched filter is governed by 4 parameters (\(K\), \(L\), \(T\), \(\sigma\)), and Gabor filters are governed by 3 parameters (\(\tau\), \(l\), \(\kappa\)), these seven parameters have to be determined previously to be used in the artificial neural network. The parameter that govern the directional filters is fixed as \(K=12\) for the GMF, and \(\kappa=45\) for the Gabor filters, because the number of oriented filters is independent from the training set of images, and they are the most common values in literature. Moreover, to select the optimal set of values for the remaining 5 parameters (\(T\), \(L\), and \(\sigma\) for Gaussian matched filter and \(l\), and \(\tau\) for Gabor filters), the training set of 100 X-ray images, and the area under the ROC curve were used to evaluate the filter responses (gray-scale images) for each parameter combination applying an exhaustive full-search procedure over the predefined search space (See Section 2.4). In this procedure, each possible combination of the Gaussian matched filter parameters are taken from the search space and used to perform a single-scale filtering for each image of the training set, which provides a detection response with the same dimension as the input image (\(300\times 300\) pixels). The detection responses obtained with each parameter combination are evaluated in terms of the area under the ROC curve with respect to the ground-truth images. The optimal parameter combination is the one that provides the highest \(A_{z}\) value from the single-scale detection responses. The optimal values of \(L\) and \(T\) for the single-scale Gaussian filtering are used later with each scale of \(\sigma\) when the multiscale analysis is performed in the spatial domain. Moreover, the same procedure was performed in order to determine the optimal \(l\) (elongation) parameter for the Gabor filters. In this case, the optimal elongation parameter found for the single-scale filtering is combined with each scale of \(\tau\) during the multiscale analysis in the frequency domain. After the exhaustive search, the most appropriate set of values for the parameters of the GMF are defined to be \(T=15\) and \(L=13\) pixels, and for the Gabor filters the elongation is defined to be \(l=3\). The multiscale analysis was performed in the range \(\sigma=[1.5,1.6,\ldots,2.5]\) for Gaussian matched filters (11 scales) and using the range \(\tau=[1,3,5,\ldots,19]\) for Gabor filters (10 scales). On the other hand, the selection of the MLP architecture requires a procedure based on a statistical hypothesis test.