Mathematical Particulars and Examples
Structuring elements are particular cases of binary images, usually being small and simple. In mathematical morphology, binary images are subsets of an Euclidean space Rd or the integer grid Zd, for some dimension d. Here are some examples of widely used structuring elements (denoted by B):
- Let E=R2; B is an open disk of radius r, centered at the origin.
- Let E=Z2; B is a 3x3 square, that is, B={(-1,-1),(-1,0),(-1,1),(0,-1),(0,0),(0,1),(1,-1),(1,0),(1,1)}.
- Let E=Z2; B is the "cross" given by: B={(-1,0),(0,-1),(0,0),(0,1),(1,0)}.
In the discrete case, a structuring element can also be represented as a set of pixels on a grid, assuming the values 1 (if the pixel belongs to the structuring element) or 0 (otherwise).
When used by a hit-or-miss transform, usually the structuring element is a composite of two disjoint sets (two simple structuring elements), one associated to the foreground, and one associated to the background of the image to be probed. In this case, an alternative representation of the composite structuring element is as a set of pixels which are either set (1, associated to the foreground), not set (0, associated to the background) or "don't care".
Read more about this topic: Structuring Element
Famous quotes containing the words mathematical, particulars and/or examples:
“The circumstances of human society are too complicated to be submitted to the rigour of mathematical calculation.”
—Marquis De Custine (1790–1857)
“Two things of opposite natures seem to depend
On one another, as a man depends
On a woman, day on night, the imagined
On the real. This is the origin of change.
Winter and spring, cold copulars, embrace
And forth the particulars of rapture come.”
—Wallace Stevens (1879–1955)
“In the examples that I here bring in of what I have [read], heard, done or said, I have refrained from daring to alter even the smallest and most indifferent circumstances. My conscience falsifies not an iota; for my knowledge I cannot answer.”
—Michel de Montaigne (1533–1592)