||Local features have repeatedly shown their effectiveness for object recognition during the last years, and they have consequently become the preferred descriptor for this type of problems. The solution of the correspondence problem is traditionally approached with exact or approximate techniques. In this paper we are interested in methods that solve the correspondence problem via the definition of a kernel function that makes it possible to use local features as input to a support vector machine. We single out the match kernel, an exact approach, and the pyramid match kernel, that uses instead an approximate strategy. We present a thorough experimental evaluation of the two methods on three different databases. Results show that the exact method performs consistently better than the approximate one, especially for the object identification task, when training on a decreasing number of images. Based on these findings and on the computational cost of each approach, we suggest some criteria for choosing between the two kernels given the application at hand.