Analysis of Singularities and Edge Detection using the Shearlet Transform

The continuous curvelet and shearlet transforms have recently been shown to be much more effective than the traditional wavelet transform in dealing with the set of discontinuities of functions and distributions. In particular, the continuous shearlet transform has the ability to provide a very precise geometrical characterization of general discontinuity curves occurring in images. In this paper, we show that these properties are useful to design improved algorithms for the analysis and detection of edges. 1