Basic relations :

Neighbors

jth Column

0 1 2……………………..…N-1

0

1

ith 2

row .

.

.

. f (i,j)

.

.

N-1

j

j

j-1 j j+1

i-1

8 - neighbors

4 - neighbors

i 4 -connected

i

i+1

N8 , N4

Pixel Relations :

1. Neighbors

j-1 j j+1

b

c

p

a

d

i-1

i

i+1

4-neighbors

( i , j-1 ) ( i , j+1 )

( i-1, j ) ( i+1 , j )

8-neighbors +

( i-1,j-1 ) ( i-1,j+1 )

( i+1,j-1) ( i+1,j+1 )

1

1

0

4-adjacency

8-adjacency

0

1

0

m-adjacency

1

0

0

Digital path

p₁ p₂……p_n

connected

ò ( x₁, y₁ ) , ( x₂, y₂ ) , ………( x_n , y_n)

* path length

* closed path

* connected components

* region boundary

DISTANCE MEASURES

1) Euclidian

1) p(x,y) d >= 0

q(s,t) D( p,q) = D(q,p)

D( p,r) = D(p,s) + D(s,r)

De = Ö ( x-s )² + ( y-t )²

D₄ : city block

D₄(p,q) = ïx-s ï + ïy-tï

2

2 1 2

2 1 0 1 2

2 1 2

2

D₈(p,q) = max( ïx-s ï, ïy-tï )

2 2 2 2 2

2 1 1 1 2

2 1 0 1 2

2 1 1 1 2

2 2 2 2 2

Image Operations :

Point Operations

Local Operations

Global Operations

Linear Operations :

H( a f + b g) = a H(f) + b H(g)

1= dr . p_r(r)

ds

ds = p_r(r).dr

r

S(r) = ò p_r(w)dw

0

Cumulative Distribution Fn. :

S= T(r)

r

T(r) = ò p_r(w)dw

0

p_r(r) = -2r +2 0 £ r £ 1

r r r

T(r) = ò (-2w + 2) dw = -2 w² / 2 ï+ 2w ï

0 0 0

S = T(r) = - r² + 2r

r = T^-1 (s)

s = -r² + 2r

-r² + 2r –s = 0

r = [ -2 + Ö (2)² – {4(-1) * (-s)} ] / 2(-1)