Direct modeling of image keypoints distribution through copula-based image signatures

Local Image Descriptors (LID) aggregation models such as Bag of Words and Fisher Vectors represent an image based on the distribution of its LIDs given a global model, e.g. a
visual codebook or a Gaussian Mixture. Inspired by Copula theory, in this paper we propose a LID-based feature that represents directly the behavior of the image LID distribution, without requiring to compute a global model. Following the definition of Copula, we represent the distribution of the image LIDs by describing, on one side, its marginals, and on the other side, a Copula function. The Copula defines the dependencies between the marginals and their mapping to a multivariate probability distribution function. We test the resulting feature for scene recognition and video retrieval (Trecvid data), showing that our
approach outperforms, in both tasks, the Bag of Words and the Fisher Vectors Model.