Mathematical morphology
From Wikipedia, the free encyclopedia
For other uses, see Morphology.
Mathematical morphology (MM) is a theoretical model for digital images built upon lattice theory and topology. It is the foundation of morphological image processing, which is based on shift-invariant (translation invariant) operators based principally on Minkowski addition.
Mathematical morphology was originally developed for binary images, viewed as subsets of the integer grid Z2 (or Zd, for any dimension d), and was later extended to grayscale images and multi-band images.
[edit] Basic operators
- Erosion of object A by the structural element B is defined by:
- Dilation of object A by the structural (and symmetrical) element B is defined by:
- The Opening of A by B is obtained by the erosion of A by B, followed by dilation of the resulting structure by B:
- The Closing of A by B is obtained by the dilation of A by B, followed by erosion of the resulting structure by B:
[edit] External links
- Center of Mathematical Morphology, Paris School of Mines
- History of Mathematical Morphology, by Jean Serra
- Morphology Digest, a newsletter on mathematical morphology, by Pierre Soille
- Mathematical Morphology; from Computer Vision lectures, by Robyn Owens
