1. Geometric molecular surface modeling using mathematical morphology operators. Journal of Molecular Graphics Volume 13, Issue 6, Pages 331-388 (December 1995) : 331-336. Masato Masuya and Junta Doi Mathematical morphology extracts information about the geometric structure of the object by transforming it through its interaction with another object, a probe.

2. Dilation Here we define P to be a sphere placed in the origin.

3. Erosion

4. Opening

5. Closing

6. X i - atom center R i - atom radius van der Waals surface S v and its interior I v : R w - probe radius Solvent Accessible surface and its interior: Molecular surface and its interior:

7. Cavity and Convex Portion Detection

8. C f = SI m ● R Remove small cavities smaller than a water molecule (R w ): C f filled molecule Cavities: R

9. P r = SI m ○ R Remove small convex parts (R w ):