Singularity analysis of higher dimensional signals

Detecting singularities of 2D and 3D signals is important and interesting in various fields. The main concept involves not only the position but also the directions of singularity. And the complexity consists in the fact that one singular point may possess more than one singularity directions. The edge of an image and the directions of singularity can be regarded as a wavefront set in the meaning of microlocal analysis, an abstruse mathematical theory. This paper proposes an easy understanding version of microlocal analysis and applies it to detecting directions of singularity in image processing. Experimental results indicate that singularity and its directions can be searched automatically and successfully.