Object detection in images: run-time complexity and parameter selection of support vector machines

We address two aspects related to the exploitation of support vector machines (SVM) for classification in real application domains, such as the detection of objects in images. The first one concerns the reduction of the run-time complexity of a reference classifier without increasing its generalization error. We show that the complexity in test phase can be reduced by training SVM classifiers on a new set of features obtained by using principal component analysis (PCA). Moreover due to the small number of features involved, we explicitly map the new input space in the feature space induced by the adopted kernel function. Since the classifier is simply a hyperplane in the feature space, then the classification of a new pattern involves only the computation of a dot product between the normal to the hyperplane and the pattern. The second issue concerns the problem of parameter selection. In particular we show that the receiver operating characteristic curves, measured on a suitable validation set, are effective for selecting, among the classifiers the machine implements, the one having performances similar to the reference classifier. We address these two issues for the particular application of detecting goals during a football match.