Fuzzy Mathematical Morphology - Medical Image Processing: Advanced Fuzzy Set Theoretic Techniques - page 203

μ E (,)min[,min( . 21 = 1 0407109 08 103091 − . + ,. . − + , . − . + )]

= min[ ,mi 1 n( .,.,.)] 071104 04 = .

μ E (,)min[,min( . 22 = 1 0 907103 08 108091 − . + ,. . − + , . − . + )]

= min[ ,mi 1 n( .,.,.)] 120509 05 = .

μ E (,)min[,min( . 23 = 1 0307108 08 103091 − . + ,. . − + , . − . + )]

= min[ ,mi 1 n( .,,.)] 0610404 = .

μ E (,)min[,min( . 24 = 1 0807103 08 1 − . + ,. . − + )]

= min[ ,min(.,.) 1 1 105 ] = 05 .

The eroded image is

⎡ 05 06 10 05 06

06 07 10 06 03
06 04 05 04 05

. . . . . ⎤

⎢
⎢
⎢

⎥
⎥
⎥

. . . . .

. . . . .

⎣ ⎦

Likewise, for dilation,

μ E (,)max[,max( . 00 = 0 03091 + −= = . )] max[ ,.] 00202 .

μ E (,)max[,max( . 01 = 0 030811091 + −+− . , . )]

= max[ ,max(.,.)] 0 0 109 = 00.

μ E (,)max[,max( . 02 = 0 03071108108 09 1 + −+− . , . ,. . + − )]

= max[ ,max( 0 00080708 ,.,.)] = .

μ E (,)max[,max( 03 = 0 1 07 10808109 09 1 + . − , . + . − ,. . + − )]

= max[ ,max( 0 0070608 08 .,.,.)] = .

μ E (,)max[,max( . 04 = 0 0807108 09 109041 + . − ,. . + − , . + . − )]

= max[ ,ma 0 x( .,.,.)] 050703 07 = .

μ E (,)max[,max( . 10 = 0 04091 03 + −= . )] .