Multiscale moments-based edge detection

In the paper the geometrical multiscale method of edge location based on custom-built moments has been presented. Custom-built moments were described in the literature as the new concept of moment function design. Unlike the other known moment functions, e.g. power, Zernike or Chebyshev functions, which are defined on circular support, the custom-built moments can be defined on any shape support like, for example, rectangular one. Unfortunately, the method of edge location based on custom-built moments proposed so far is monoscale, what causes that the result of edge detection is either real geometrical or accurate. So, in the method proposed in this paper the multiscalability has been introduced. This approach causes that the results of edge detection are both: compactly geometrical and very accurate. Additionally, the time complexity of the proposed method is O(N² log₂ N) what is far lower than that of many other state-of-the-art geometrical multiresolution methods, especially the one based on wedgelets.