Is there a difference between 8 adjacency and m adjacency of pixels other than its definition?

Question

The definition of 8-adjacency and m-adjacency are clear. But is there a case where two pixels p and q can be 8-adjacent, but not m-adjacent. I have given the definition of 8-adjacent and m-adjacent below:

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

m-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 N4(p) N4(q) has no pixels whose values are from V.

Adnah

Answer 1

There is a clear mathematical defition for these adjacencies. So no, there can be no difference other than that definition.

m adjacendy is used to resolve abiguities in 8-adjacency. m-adjacency is a special case of 8-adjacency. So yes there are cases where 2 pixels are 8-adjacent but not m-adjacent. Otherwise if they were the same, you wouldn't need a separate m-adjacency right?

May pixels p and q have the value 1 (from V).

Then in both examples p and q are 8-adjacent.

0 0 0
0 p 0
q 0 0

0 0 0
0 p 0
q 1 0 

But only in the first one they are m-adjacent.

Nogood

Answer 2

This is the definition 8-adjacency: two pixels p and q with values from V are 8-adjacent if q is in the set N8(p).

m-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 N4(p) N4(q) has no pixels whose values are from V.

In our case here set N4(p) N4(q) has pixels hose values are from V. So it is not 8-adjacency.

Cinchonism

As it’s currently written, your answer is unclear. Please edit to add additional details that will help others understand how this addresses the question asked. You can find more information on how to write good answers in the help center. – Psychophysiology