Texture Classification with the PQ Kernel

Computer vision researchers have developed various learning methods based on the bag of words model for image related tasks, including image categorization, image retrieval and texture classification. In this model, images are represented as histograms of visual words (or textons) from a vocabulary that is obtained by clustering local image descriptors. Next, a classifier is trained on the data. Most often, the learning method is a kernel-based one. Various kernels can be plugged in to the kernel method. Popular choices, besides the linear kernel, are the intersection, the Hellinger’s, the χ2 and the Jensen-Shannon kernels. Recent object recognition results indicate that the novel PQ kernel seems to improve the accuracy over most of the state of the art kernels. The PQ kernel is inspired from a set of rank correlation statistics specific for ordinal data, that are based on counting concordant and discordant pairs among two variables. In this paper, the PQ kernel is used for the first time for the task of texture classification. The PQ kernel is computed in O(n logn) time using an efficient algorithm based on merge sort. The algorithm leverages the use of the PQ kernel for large vocabularies. Texture classification experiments are conducted to compare the PQ kernel with other state of the art kernels on two benchmark data sets of texture images. The PQ kernel has the best accuracy on both data sets. In terms of time, the PQ kernel becomes comparable with the state of the art Jensen-Shannon kernel. In conclusion, the PQ kernel can be used to obtain a better pairwise similarity between histograms, which, in turn, improves the texture classification accuracy.