Design of directional selection for three-dimensional complex discrete wavelet transform

In this paper, we propose the novel design method of directional selection for three-dimensional complex discrete wavelet transform (3D-CDWT) (hereafter, all abbreviations will be written with capital letters). Previously, the complex discrete wavelet transform has been able to extract directional edges from images using the directional selection property. This can be applied to shape and texture analysis. However the angular range of each directional edge is still unclear and the angular ranges are fixed. Thus, it is difficult to be applied to image processing. Therefore, we firstly clarify the angular range of directional edges by using frequency characteristics. Secondly, we propose a design method for the angular range of directional edges with a desirable angular range. As a result, we can clarify the angular ranges of directional edges and it is possible to obtain the directional edges with arbitrary angular range.