Detection and description of scale invariant 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. In this paper we address the problem of detecting and describing blob-like features in the shearlets framework. We derive a measure which is very effective for blob detection and closely related to the Laplacian of Gaussian. We demonstrate the measure satisfies the perfect scale invariance property in the continuous case. In the discrete setting, we derive algorithms for blob detection and feature point description. Finally, we report an experimental evidence that our method is very suitable to deal with compressed and noisy images, thanks to the sparsity property of shearlets