Descriptor Learning Using Convex Optimisation

Karen Simonyan, Andrea Vedaldi, Andrew Zisserman

Abstract: The objective of this work is to learn descriptors suitable for the sparse feature detectors used in viewpoint invariant matching. We make a number of novel contributions towards this goal: first, it is shown that learning the pooling regions for the descriptor can be formulated as a convex optimisation problem selecting the regions using sparsity; second, it is shown that dimensionality reduction can also be formulated as a convex optimisation problem, using the nuclear norm to reduce dimensionality. Both of these problems use large margin discriminative learning methods. The third contribution is a new method of obtaining the positive and negative training data in a weakly supervised manner. And, finally, we employ a state-of-the-art stochastic optimizer that is efficient and well matched to the non-smooth cost functions proposed here. It is demonstrated that the new learning methods improve over the state of the art in descriptor learning for large scale matching, Brown et al. [2], and large scale object retrieval, Philbin et al. [10].