数字图像处理英语课件chapter2

Example of adjacency
Suppose V={1}
Ambiguity
(a)
(c)
Figure 2. (a) Arrangement of pixels; (b) pixels that are 8-adjacent (shown as dashed) to the center pixel; (c ) m-adjacency.
• Identifying criterion (for connectivity):
– If they are neighbors, and – If their gray levels satisfy a specified criterion of similarity. – Example: Binary Image
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Digital Image Processing, 2nd ed.
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Path (curve)
• A path from pixel p with coordinate (x, y) to pixel q with coordinate (s, t)
For a pixel p at (x, y) , there are 4 horizontal and vertical neighbors: (x+1,y), (x-1,y), (x,y+1), (x,y-1), and 4 diagonal neighbors of p (x+1,y+1),(x+1,y-1),(x-1,y+1,(x-1,y-1), (ND(p)) This set of pixels , N8(p), is called the 8-neighbors of p.
• Connected Component of S:
– For any pixel p in S, the set of pixels that are connected to it in S is called connected component of S
• Connected set:
– If S only has one connected component, then set S is called a connected set.
© 2009 Lianxi Yuan
Digital Image Processing, 2nd ed.
www.hrbeu.edu.cn
Example of region
1 1 1
1 1
1
1 1
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1 1
Figure 3. Two regions (of 1s) that are adjacent if 8-adjecency is used
• Two pixels may be 4-neighbors • But they are said to be connected only if they have the same value.
© 2009 Lianxi Yuan
Digital Image Processing, 2nd ed.
– Be a sequence of distinct pixels with coordinates
• (x0,y0), (x1, y1), … (xn,yn) – where (x0, y0)= (x, y) ; (xn, yn)=(s, t) – Pixel (xi, yi) and (xi-1,yi-1) are adjacent for i in [1,n] – n is the length of the path
– All the points in Ru is called the foreground of the image – All the points in (Ru)c are called the background of the image
© 2009 Lianxi Yuan
Digital Image Processing, 2nd ed.
© 2009 Lianxi Yuan
Digital Image Processing, 2nd ed.
www.hrbeu.edu.cn
Example 1 of boundary
The point circled is not a member of border of the 1valued region if 4-connectivity is used between the region and its background.
Digital Image Processing, 2nd ed.
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Chapter Two
Some Basic Relationship Between Pixels
© 2009 Lianxi Yuan
Digital Image Processing, 2nd ed.
– If (x0,y0) =(xn, yn) , the path is a closed path.
• Define 4-, 8-, or m-paths (see example above)
© 2009 Lianxi Yuan
Digital Image Processing, 2nd ed.
www.hrbeu.edu.cn
Adjacency
Let V be the set of gray-level values • 4-adjacency. – Two pixels p and q with gray-level values from V are 4-adjacency if q is in the set N4(p) • 8-adjacency. – Two pixels p and q with values from V are 8adjacency if q is in the set N8(p)
• to Eliminate the ambiguities that arise when 8-adjacency is used
A intersection B (A∩B)
© 2009 Lianxi Yuan
Digital Image Processing, 2nd ed.
www.hrbeu.edu.cn
www.hrbeu.edu.cn
Connect
• Let S represent a subset of pixels in an image. • Two pixels p and q are said to be connected in S
– if there exists a path between them consisting entirely of pixels in S.
0
1 1 1
0 0
0 0
Digital Image Processing, 2nd ed.
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Region (cont.)
• Suppose that an image contains K disjoint regions, Rk, k=1,2,…,K, none of which touches the image border. • Let Ru denote the union of all the K regions and let (Ru)c denote its complement.
0 0 0 0 0 0
0 1 1 1 1 0
0 1 1 1 1 0
0 0 0 1 1 0
0 0 0 0 0 0
Boundary(cont’)
• The preceding definition is referred to as the inner border of the region to distinguish it from its outer border, which is the corresponding border in the background. • Such algorithm usually are formulated to follow the outer boundary in order to guarantee that the result will form a closed path.
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Boundary
• The boundary (border, contour) of a region R is the set of points that are adjacent to points in the complement of R. • The border of a region is the set of pixels in the region that have at least one background neighbor (another definition).
( x 1, y 1), ( x 1, y 1), ( x 1, y 1), ( x 1, y 1)
© 2009 Lianxi Yuan
Digital Image Processing, 2nd ed.
www.hrbeu.edu.cn
Neighbors of a Pixel(cont’)
Figure 4. The circled point is part of the boundary of the 1valued pixels only if 8-adjecency between the region and background is used
© 2009 Lianxi Yuan
p p
Figure1. diagram of N4(p) and N8(p)
© 2009 Lianxi Yuan
Digital Image Processing, 2nd ed.
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Connectivity
• Connectivity between pixels:
– To simplify concept (regions and boundaries)
© 2009 Lianxi Yuan
Digital Image Processing, 2nd ed.
www.hrbeu.edu.cn
Adjacency (cont’)
Let V be the set of gray-level values • m-adjacency (mixed adjacency): If – q is in N4(p) , or q is in ND(p) – and the set N4(p)∩N4(q) has no pixels whose values are from V – being a modification of 8-adjacency
© 2009 Lianxi Yuan
Digital Image Processing, 2nd ed.
www.hrbeu.edu.cn
Region
Let R be a subset of pixels in an image. • Region: if R is a connected set. • Two regions, Ri and Rj are said to be adjacent if their union forms a connected set. • Regions that are not adjacent are said to be disjoint • 4- and 8-adjacency are considered when referring to regions
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Neighbors of a Pixel
Suppose an image f(x,y), and use lowercase letters to represent a pixel. For any pixel p at (x, y) , there are 4 horizontal and vertical neighbors: ( x, y 1),( x, y 1),( x 1, y),( x 1, y) This set of pixels denoted by N4(p) , is called the 4neighbors of p. The four diagonal neighbors of p , ND(p), have coordinates: