Modeling the impact of keypoint detection errors on local descriptor similarity

Abstract

This paper presents a mathematical analysis of the impact of key-point detection errors on the similarity of local image descriptors that are based on histogram of gradients. First, we derive a closed-form expression for the 𝐿p distance between two descriptors, for general translation, scale and orientation detection errors. Second, we introduce a detailed analysis for the special case where translation errors dominate, using the 𝐿2 distance. We show that the individual components which form the squared 𝐿2 distance can be approximated using Gamma distributions whose parameters are computed in closed-form by our model. We obtain approximate closed-form expressions for the expected squared 𝐿2 distances when translation errors are fixed or uniformly distributed. Finally, these models are validated using image patches extracted from two standard image retrieval datasets, by comparing the predicted distributions to the ground-truth.