Learning the Conformal Transformation Kernel for Image Recognition

In this paper, we present a multiclass data classifier, denoted by optimal conformal transformation kernel (OCTK), based on learning a specific kernel model, the CTK, and utilize it in two types of image recognition tasks, namely, face recognition and object categorization. We show that the learned CTK can lead to a desirable spatial geometry change in mapping data from the input space to the feature space, so that the local spatial geometry of the heterogeneous regions is magnified to favor a more refined distinguishing, while that of the homogeneous regions is compressed to neglect or suppress the intraclass variations. This nature of the learned CTK is of great benefit in image recognition, since in image recognition we always have to face a challenge that the images to be classified are with a large intraclass diversity and interclass similarity. Experiments on face recognition and object categorization show that the proposed OCTK classifier achieves the best or second best recognition result compared with that of the state-of-the-art classifiers, no matter what kind of feature or feature representation is used. In computational efficiency, the OCTK classifier can perform significantly faster than the linear support vector machine classifier (linear LIBSVM) can.