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Mathematical Morphology: introduction - Thibauld Nion (2012)
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Mathematical Morphology: introduction
Mathematical Mathematical MorphologyAn IntroductionThibauld Nion2012
An image: an array of discrete values
127
86
51
63
157
75
92
113
161
69
128
148
150
76
137
143
Image Processing
FilterMeasureTransformDetect...
Linear and Variational Methods
CalculusAnalytic funct.
from methodart.blogspot.com
Control Point
Inspired byPhysics
Mathematical Morphology
Geometry Probability
Inspired byGeology
Foundations: sets and statistical tests
Inside(the object)
Outside(the backround)
Intersection
Inclusion
Example: inclusion and filtering
Keep objects able to contain a given shape(aka structuring element)
Structuring Element
(Random) closed sets
Example: inclusion and filtering
Keep objects able to contain a given shape(aka structuring element)
Structuring Element
(Random) closed sets
Example: inclusion and filtering
Keep objects able to contain a given shape(aka structuring element)
Structuring Element
(Random) closed sets
Example: intersection for description
Run-Length Encoding (RLE) ! Stereology defines area and volume estimators from 1D and 2D measures.
History: Buffon's needle (1733)
History: Buffon's needle (1733)
2.e .L
e
L
History: Name dropping
Buffon (1707-1788) > needle problemCrofton (1826–1915) > Cauchy-Crofton formulaChoquet (1915-2006) > capacities of random closed setsMatheron (1930-2000) & Serra (1940) >Mathematical Morphology
Petrography sample (width 100um) olite, quartz and calcite ,chlorite cement with iron,
Matheron&Serra, ISMM 2000
Mathematical MorphologyHave fun !
from Ella's dad (CC-by)http://www.flickr.com/photos/ellasdad/425813314/