Object Detection in Images: Run-Time Complexity and Parameter Selection of Support Vector Machines

In this paper 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. In fact 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 (ROC) 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. 1. Object detection and classification The problem of object detection in images is the problem of detecting three dimensional objects in the scene by using the image projected by the object on the sensing plane of a standard camera. Face detection is one of the most interesting applications of object detection in images [10]. An other interesting application, which is getting particular attention from referee associations, sport press and supporters [9, 7, 5], concerns the problem of detecting goals during a football match by using images acquired by a standard TV camera. For an appropriate position of the camera with respect to the football ground, the problem of goal detection can be reduced to the problem of detecting the ball in images of the goalmouth [2]. The problem of object detection can be seen as a learning from examples problem in which the examples are particular views of the object we are interested to detect. In particular, object detection can be seen as a classification problem, because our ultimate goal is to determine a separating surface, optimal under certain conditions, which is able to separate object views from image patterns that are not instances of the object. So in this perspective the data to classify are image patches represented by vectors which, in general, live in spaces with a very high number of dimensions, for example equal to the number of pixels in the patch. Moreover the detection of objects in images requires an exhaustive search of the current image, that is all the patches with a given dimension has to be classified in the image. The size of the data to classify and the need of scanning exhaustively the image for looking for the candidate object show that the problem of object detection in images is a time consuming task and so some strategy for reducing the complexity of the classifier has to be taken into account for handling real contexts.