Microlocal analysis of edge flatness through directional multiscale representations
| Autor: | Kanghui Guo, Demetrio Labate |
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| Rok vydání: | 2016 |
| Předmět: |
Local flatness
Applied Mathematics Flatness (systems theory) 010102 general mathematics Mathematical analysis Microlocal analysis Boundary (topology) 02 engineering and technology 01 natural sciences Edge detection Computational Mathematics Wavelet Shearlet 0202 electrical engineering electronic engineering information engineering 020201 artificial intelligence & image processing 0101 mathematics Scaling Mathematics |
| Zdroj: | Advances in Computational Mathematics. 43:295-318 |
| ISSN: | 1572-9044 1019-7168 |
| DOI: | 10.1007/s10444-016-9486-8 |
| Popis: | Edges and surface boundaries are often the most relevant features in images and multidimensional data. It is well known that multiscale methods including wavelets and their more sophisticated multidimensional siblings offer a powerful tool for the analysis and detection of such sets. Among such methods, the continuous shearlet transform has been especially successful. This method combines anisotropic scaling and directional sensitivity controlled by shear transformations in order to precisely identify not only the location of edges and boundary points but also edge orientation and corner points. In this paper, we show that this framework can be made even more flexible by controlling the scaling parameter of the anisotropic dilation matrix and considering non-parabolic scaling. We prove that, using `higher-than-parabolic' scaling, the modified shearlet transform is also able to estimate the degree of local flatness of an edge or surface boundary, providing more detailed information about the geometry of edge and boundary points. |
| Databáze: | OpenAIRE |
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