Generalized histogram intersection kernel for image recognition

Histogram intersection (HI) kernel has been recently introduced for image recognition tasks. The HI kernel is proved to be positive definite and thus can be used in support vector machine (SVM) based recognition. Experimentally, it also leads to good recognition performances. However, its derivation applies only for binary strings such as color histograms computed on equally sized images. In this paper, we propose a new kernel, which we named generalized histogram intersection (GHI) kernel, since it applies in a much larger variety of contexts. First, an original derivation of the positive definiteness of the GHI kernel is proposed in the general case. As a consequence, vectors of real values can be used, and the images no longer need to have the same size. Second, a hyper-parameter is added, compared to the HI kernel, which allows us to better tune the kernel model to particular databases. We present experiments which prove that the GHI kernel outperforms the simple HI kernel in a simple recognition task. Comparisons with other well-known kernels are also provided.