Scale Invariant and Noise Robust Interest Points with Shearlets

Shearlets are a relatively new directional multi-scale framework for signal analysis, which have been shown effective to enhance signal discontinuities, such as edges and corners at multiple scales even in the presence of a large quantity of noise. In this paper, we consider blob-like features in the shearlets framework. We derive a measure, which is very effective for blob detection, and, based on this measure, we propose a blob detector and a keypoint description, whose combination outperforms the state-of-the-art algorithms with noisy and compressed images. We also demonstrate that the measure satisfies the perfect scale invariance property in the continuous case. We evaluate the robustness of our algorithm to different types of noise, including blur, compression artifacts, and Gaussian noise. Furthermore, we carry on a comparative analysis on benchmark data, referring, in particular, to tolerance to noise and image compression.