上海大孝 SHIANCH AI JLAO IONG LNTVERSTY 2 Erosion and dilation Erosion With a and B as sets in Z, the erosion of a by B is defined as AOB=ZB)CA AOB=zB)nAc=0 Set b: a structural elements other banes: Shrink, Reduce
9.2 Erosion and Dilation • Erosion A ⊖ B = {z|(B)z ⊆ A} With A and B as sets in Z2 , the erosion of A by B is defined as • Set B: A structural elements • Other banes: Shrink, Reduce A ⊖ B = {z|(B)z ∩ Ac = ∅}
上海大孝 SHIANCH AI JLAO IONG LNTVERSTY 9.2 Erosion and dilation 一-一-----------1 a b c de d Figure 9.4 B (a set A aeB (b Square d/8 4 d structuring element B d/2 c) Erosion of A by B. shown shaded d)Elongated d/2 aeB structuring element B 113d411 (e) Erosion of a by B d/8 d/8 using this element
9.2 Erosion and Dilation Figure 9.4 (a) Set A. (b) Square structuring element, B. (c) Erosion of A by B, shown shaded. (d) Elongated structuring element. (e) Erosion of A by B using this element
上海大孝 SHIANCH AI JLAO IONG LNTVERSTY 2 Erosion and dilation a d Figure 9. 5 Using erosion to remove image components (aA486x486 binary image of a wire-bond mask (b)(d)Image eroded using square structuring elements of sizes11×11.15×15,and 4545, respectively. The elements of the ses were all 1s
9.2 Erosion and Dilation Figure 9.5 Using erosion to remove image components. (a) A 486×486 binary image of a wire-bond mask. (b)-(d) Image eroded using square structuring elements of sizes 11×11, 15×15, and 45×45, respectively. The elements of the SEs were all 1s
上海大孝 SHIANCH AI JLAO IONG LNTVERSTY 2 Erosion and dilation Dilation With a and b as sets in Z2, the dilation of a by b is defined as AB={z(B)-0A≠Q AB={z(B2∩4]c Set B: a structural elements Relation to Convolution mask Flipping Overlapping Other names: Grow, Expand
9.2 Erosion and Dilation • Dilation With A and B as sets in Z2 , the dilation of A by B is defined as • Set B: A structural elements • Relation to Convolution mask: ▪ Flipping ▪ Overlapping • Other names: Grow, Expand { |[( ) ] } ˆ A B z B A A = z { |( ) } ˆ A B z B A = z
上海大孝 SHIANCH AI JLAO IONG LNTVERSTY 2 Erosion and dilation a b c d/4 de d d/4 Figure 9.6 B=B a)set A A⊕B b) square structuring d/8 d element the dot denotes the origin) d/2 1/4 c) Dilation of a by B, shown shaded d)Elongated structuring element (e) Dilation of A using this B= B d/2 element A⊕B d/8 d/8
9.2 Erosion and Dilation Figure 9.6 (a) Set A. (b) Square structuring element (the dot denotes the origin). (c) Dilation of A by B, shown shaded. (d) Elongated structuring element. (e) Dilation of A using this element