Hausdorff Kernel for 3D Object Acquisition and Detection

Learning one class at a time can be seen as an effective solution to classification problems in which only the positive examples are easily identifiable. A kernel method to accomplish this goal consists of a representation stage - which computes the smallest sphere in feature space enclosing the positive examples - and a classification stage - which uses the obtained sphere as a decision surface to determine the positivity of new examples. In this paper we describe a kernel well suited to represent, identify, and recognize 3D objects from unconstrained images. The kernel we introduce, based on Hausdorff distance, is tailored to deal with grey-level image matching. The effectiveness of the proposed method is demonstrated on several data sets of faces and objects of artistic relevance, like statues.