Image Processing Reference
In-Depth Information
Fig. 3.5. An example of a 3D difference filter derived by arranging two 2D Lapla-
cians. A 3D directional filter is obtained from 2D omnidirectional ones.
( a )
( b )
Fig. 3.6. The combination of 2D Sobel filters for deriving 3D filters: ( a )Juxtaposi-
tion of three 2D filters; ( b ) difference of two 2D directional filters. Both are obtained
from 2D directional filters and are directional as 3D filters.
( a )
( b )
Fig. 3.7. The extension of a 2D Sobel filter to a 3D Sobel filter: ( a )2DSobelfilter;
( b )3DSobelfilter.
(ii) (2D, directional)
(3D, omnidirectional)
(iii) (2D, omnidirectional)
(3D, directional)
(3D, omnidirectional)
(iv) (2D, omnidirectional)
(3D, omnidirectional)
Remark 3.11. Large numbers of 2D filters have been developed for various
applications and have been studied theoretically and experimentally. Most
of their structures and properties are extended straightforward to 3D image
 
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