i. In a digital image, the relationship between pixels can be known with the help of adjacency.

ii. A pixel p, at coordinates (x, y) has four horizontal and vertical neighbors whose coordinates are given by $(x + 1, y), (x - 1, y), (x, y + 1), (x, y - 1)$

iii. This set of pixels, called the 4-neighbors of p, is denoted by N4(p). Each pixel is a unit distance from (x, y), and some of the neighbor locations of p lie out-side the digital image

iv. The four diagonal neighbors of p have coordinates $(x 1, y + 1), (x + 1, y - 1), (x 1, y + 1), (x -1, y - 1)$ and are denoted by ND(p). These points, together with the 4-neighbors, are called the 8-neighbors of p, denoted by N8(p).

v. Now there are three types of adjacencies :

(a) 4-adjacency:Duo pixels p and q with values from V are 4-adjacent if q is in the set N4(p).

(b)8-adjacency. Two pixels p and q with values from V are 8-adjacent if q is in the set N8(p).

(c) m-adjacency (mixed adjacency). Two pixels p and q with values from V are m-adjacent if (i) q is in N4(p), or (ii) q is in ND(p) and the set

N 4( p) N 4(q) has no pixels whose values are from V.

vi. Mixed adjacency is a modification of 8-adjacency. It is introduced to eliminate the ambiguities that often arise when 8-adjacency is used.

vii. For example, consider the pixel arrangement shown in Fig. 1(a) for V = {1 }. The three pixels at the top of Fig. 1(b) show multiple (ambiguous) 8-adjacency, as indicated by the dashed lines. This ambiguity is removed by using m-adjacency, as shown in Fig. 1(c).

Fig. 1

viii. Thus in this manner, mixed adjutancy is introduced, to eliminate the ambiguities that often arise when 8-adjecancy is used.