Traditional classification approaches generalize poorly on image classification tasks, because of the high dimensionality of the feature space. This paper shows that support vector machines (SVM's) can generalize well on difficult image classification problems where the only features are high dimensional histograms. Heavy-tailed RBF kernels of the form K(x, y) = e(-rho)Sigma(i)/xia-yia/b with a x(i)(a) improves the performance of linear SVM's to such an extend that it makes them, for this problem, a valid alternative to RBF kernels.