7.1 Morfologi untuk
Pengolahan Citra :
Thickening, Skeleton
Thickening
Thickening
-the morphological dual of thinning
-Denote by
The structuring element with the same form as those
shown in thinning, but with all 1’s and 0’s interchanged.
Thickening
However a separate algorithm for thickening is seldom used in
practices, instead, the usual procedure is to thin the background,
and then complement the result.
Give A, get C=Ac, thin C, and then get Cc.
This procedure
may result in some
disconnected
points, usually it
follows by a simple
postprocessing step
to them.
Skeletons
Skeletons
Skeletons
-Define in terms of erosions and openings
-Denote by:
Sk(A)=(AkB)- (AkB) ◦B
A  B  ( A B)  B
(A kB)=(…(A B) B) …) B)
K=max{k|(A B)   }
S ( A)   Sk ( A)
k 0
K is the last iterative step before A erodes to an empty set.
Also, A can be reconstructed from these subsets:
K
A   ( S k ( A)  kB)
k 0
(Sk ( A)  kB)  ((...( Sk ( A)  B)  B)  ...)  B
Skeletons
Error in the book:
Chinese edition page 442
or English edition page 545
Skeletons
Binary fingerprint image
Skeleton image
MATLAB code: y=bwmorph(x,’skel’,inf);
Skeletons.m
Summary
Dilation, Erosion,
Opening, Closing,
Skeletons, Boundary
extraction
Convex hull
Region filling
Thinning,
Thickening
Pruning
Summary
Summary
Summary
Summary
Daftar Pustaka
• Kadir, Abdul, Susanto,A., “Pengolahan Citra, Teori Dan
Aplikasi”, Andi, Yogyakarta, 2013.