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Mathematical Morphology: introduction - Thibauld Nion (2012)
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Mathematical Morphology: Pixels and probabilities
Mathematical Mathematical MorphologyPixels and ProbabilitiesThibauld Nion2012
Buffon's needle (1733)
What probabilty for the fallen needle to crossthe line between two strips ?
Back to basics: throwing a point.
Probability fora point to fall inthe white area ?
Back to basics: throwing a point.
Probability fora point to fall inthe white area ?
Back to basics: throwing a point.
Probability fora point to fall inthe white area ?
Back to basics: throwing a point.
Probability fora point to fall inthe white area ?
Count the numberof white pixels and divide by image's area.
Back to basics: throwing a point.
Count the numberof white pixels and divide by image's area.
Remember the erosion ?
Given a S.E. B find the region ofthe studied set A, where B can be translated and still fit in A.
Erosion as a measure
Probability for the S.E. B to fall inside A.
Remember the dilation ?
Given a S.E. B find the region ofthe whole space, where B can be translated and intersect A.
Dilation as a measure
Probabilityfor the S.E. B to intersect A.
Erosion curve as a signature
P
SE side length
P
0
Erosion curve as a signature
P
SE side length
0
P
0
Erosion curve as a signature
P
SE side length
0
0
Erosion curve as a signature
P
SE side length
0
Shape sensitive signatures
P
SE side length
0
Shape sensitive signatures
P
SE side length
0
Getting back to an old friend
Erosion by a bi-pointand varying the separationbetween the points.
Getting back to an old friend
Getting back to an old friend
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Getting back to an old friend
Getting back to an old friend
Applications
Statistics on objects shapes
Classification
Fricout Gabriel. Propriétés morphologiques et optiques des surfaces rugueuses. Thèse de Doctorat en Morphologie Mathématique. ENSMP, 5 novembre 2004. 235 p. http://pastel.archives-ouvertes.fr/pastel-00001102
Mathematical MorphologyHave fun !
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