MATHEMATICAL 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 ''Z''² (or ''Z''^''d'', for any dimension ''d''), and was later extended to grayscale images and multi-band images.

Contents

Basic operators

External links

Basic operators

★ Erosion of object A by the structural element B is defined by:
::$A\; ominus\; B\; =\; \{z\; |\; (B)\_\{z\}\; subset\; A\}$

★ Dilation of object A by the structural (and symmetrical) element B is defined by:
::$A\; oplus\; B\; =\; \{z\; |\; (B)\_\{z\}\; cap\; A$
eq arnothing}

★ The Opening of A by B is obtained by the erosion of A by B, followed by dilation of the resulting structure by B:
::$A\; circ\; B\; =\; (A\; ominus\; B)\; oplus\; B$

★ The Closing of A by B is obtained by the dilation of A by B, followed by erosion of the resulting structure by B:
::

External links

★ Lectures on Image Processing: A collection of 18 lectures in pdf format from Vanderbilt University. Lectures 16-18 are on Mathematical Morphology, by Alan Peters

★ 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