Pixel Relations

1
Pixel Relations
2
Neighboring, Adjacency

• N4(p) 4-neighbors
• ND(p) 4-diagonal neighbors
• N8(p) N4(p)? ND(p) 8-neighbors

• Adjacency
• V a set of gray levels s.t. if a pixels gray
  level in V, it will be used to establish
  adjacency.
• 4-adjacency
• 8-adjacency
• m-adjacency

p


p

q s
p
r
q s
p
r
3
Path, Connectivity, Region

• Path
• a path from p (s,t) to q (x,y) is a set
  adjacent points
• P(p,q) (s,t), , (xi, yi), , (x, y)
• If (s, t) (x, y), P is a closed path.
• p and q are connected in S if P(p,q) ? S. The set
  q P(p,q) ? S is a Connected Component of p ? S.

• S is a connected set if it has only one connected
  component. S is also called a Region.
• The boundary of a region R p p ? R, exists q
  ? R, q ? N(p)
• If R is entire image, its boundary is the first
  and last rows and columns of pixels.

4
Distance Metrics

• Normed distance
• Given pixels p, q, r, a function D(p,q) is a
  distance function if
• Euclidean distance
• L2 norm

• City-block distance
• L1 norm
• Chessboard distance
• L? norm