Made to measure morphological filters Fernand Meyer Center of mathematical morphology MinesParisTech France Non edge preserving filters The adjunction erosiondilation Openingsclosings The simplest filters ID: 770906
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Made to measure morphological filters Fernand Meyer Center of mathematical morphology Mines-ParisTech France
Non edge preserving filters The adjunction erosion/dilation Openings/closings The simplest filters Alternate sequential filters
Erosions and dilations of increasing sizes
Erosions of increasing size Regional minima get larger New maxima may appear. Most maxima vanish, others get larger.
Dilations of increasing size New minima may appear. Most mainima vanish, others get larger. Regional maxima get larger, some coalesce, others disappear.
Increasing erosions Increasing dilations Erosion = minimal value in a window darker image Dilation = maximal value in a window brighter image INCREASING WINDOW + STRONGER EFFECT
combining an erosion and a dilation in sequence , in order to get openings or closings.
A dilation Brighter An erosion Darker = opening Darker Followed by
openings of increasing size Each reg. min. of a large closing contains a reg. Min. of each smaller opening Regional maxima get larger, some coalesce, others disappear.
A dilation Brighter An erosion Darker = closing Brighter Followed by
openings of increasing size Regional minima get larger, some coalesce, others disappear. Each reg. max. of a large closing contains a reg. Max. of each smaller closing
Open-close, close-open, Open-close-open, close-open-close
A closing Brighter An opening Darker = morphological filter Similar grey tone Followed by
A closing Brighter An opening Darker = morphological filter Similar grey tone Followed by
Opening followed by closing of increasing sizes Regional minima Regional maxima
Closing followed by opening of increasing sizes Regional minima Regional maxima
Opening followed by closing of increasing sizes Closing followed by opening of increasing sizes The two are not comparable
Open close open of increasing sizes Close-open-close open-close-open Close open close of increasing sizes
Closing followed by opening followed by closing of increasing sizes Regional minima Regional maxima
A small closing followed by a small opening = small effects A large closing followed by a large opening = too crude Alternate sequential filter = sequence of increasing pairs of an opening followed by a closing
Alternate sequential filter starting with an opening of increasing sizes Regional minima Regional maxima
Alternate sequential filter starting with a closing of increasing sizes Regional minima Regional maxima
Partial conclusion Non edge preserving filters simplify the images but the displacement of the contours is annoying in many cases and in particular if the filter precedes image segmentation We will now introduce edge preserving filters : Razings Floodings Levelings