I am struggling to implement a mathematical morphology toolset in an image processing package. I base my implementation on what I saw in MATLAB, and on several papers on the subject.
There seems to be abundant literature on morphological operation optimization through structuring element (strel) decomposition. For instance, one can get a tremendous speed bonus by using two orthogonal lines instead of a square as structuring element for dilation. Several papers give methods for optimization through strel decomposition:
- Rolf Adams, "Radial Decomposition of Discs and Spheres," CVGIP: Graphical Models and Image Processing, vol. 55, no. 5, September 1993, pp. 325-332.
- Rein van den Boomgard and Richard van Balen, Methods for Fast Morphological Image Transforms Using Bitmapped Binary Images, CVGIP: Models and Image Processing, vol. 54, no. 3, May 1992, pp. 252-254
However, all these publications are about 2D structuring elements. I could not find much on 3D decompositions.
Do you have any clues on how to decompose:
- a 3D sphere. Not a ball that is used in 2D grayscale morphology, but an actual flat 3D sphere;
- a 3D diamond?