电子残发女学光电科学与工程学院 SCHOOL OF OPTOELECTRONIC SCIENCE AND ENGINEERING OF UESTC 2.Dilation Operations 4®B={8.n1*@ B and 4 overlap by at least one element. A⊕B={[(@)nA]=A B is viewed as a Problems conin mask. 9.11-9.12 ☑=Empty set Nonlinear /linear operation 4=Object to be dilated B Structuring element ★Dilation means“extend
2. Dilation Operations ( ) ˆ z A B z B A = = Empty set A = Object to be dilated B = Structuring element ★ Dilation means “extend” ( ) ˆ z A B z B A A = and A overlap by at least one element. B ˆ B is viewed as a convolution mask. Problems 9.11-9.12 Nonlinear /linear operation
电子科发女学光电科学与工程学院 SCHOOL OF OPTOELECTRONIC SCIENCE AND ENGINEERING OF UESTC 2.Dilation Operations B B Original image (A) ▣Intersect pixel Center pixel
B Original image (A) B ˆ Intersect pixel Center pixel 2. Dilation Operations
电子科线女学光电科学与工程学院 SCHOOL OF OPTOELECTRONIC SCIENCE AND ENGINEERING OF UESTC 2.Dilation Operations Result of Dilation Boundary of the "center pixels" where B. intersects A
Result of Dilation Boundary of the “center pixels” where intersects A ( ) B z ˆ 2. Dilation Operations
电子科线女学光电科学与工程学院 SCHOOL OF OPTOELECTRONIC SCIENCE AND ENGINEERING OF UESTC 2.Dilation Operations a b c de d/4 FIGURE 9.6 (a)Set A. ·a4 (b)Square B=B structuring ele- A⊕B ment (the dot de- A notes the origin). d d/8 d/8 (c)Dilation of A by B,shown shaded. d/2 (d)Elongated d/4 structuring ele- ment.(e)Dilation of A using this element.The d d dotted border in (c)and (e)is the boundary of set A. B=B shown only for d/2 reference A⊕B d/8 d d/8
2. Dilation Operations
电子科线女学光电科学与工程学院 SCHOOL OF OPTOELECTRONIC SCIENCE AND ENGINEERING OF UESTC Example:Application of Dilation a c b Historically,certain computer Historically,certain computer programs were written using programs were written using FIGURE 9.7 (a)Sample text of only two digits rather than only two digits rather than poor resolution four to define the applicable four to define the applicable with broken year.Accordingly,the year.Accordingly,the characters (see company's software may company's software may magnified view). (b)Structuring recognize a date using "00" recognize a date using "00" element. as 1900 rather than the yer as 1900 rather than the year (c)Dilation of(a) 2000. 2000. by (b).Broken segments were joined. 01 "Repair"broken characters
Example: Application of Dilation ★ “Repair” broken characters