MATLAB: How to calculate gradient between the currently processed point (x,y) and its neighboring point in one of eight compass direction.

Question

Dear All,

i'm working for make iterative threshold technique. This technique is first modified with calculating gradient between currently proccessed point (x,y) and its neighboring point in one of eight compass direction that can determined by this equation :

Gd(x,y) = |I(x,y)-I(xd,yd)|

where :

(xd,yd) neighbors to (x,y) in direction d, and I(x,y) and I(xd,yd) denote the gray-level values at locations (x,y) and I(xd,yd). Here d is a value denoting one of eight compass direction.

The value of eight compass direction is

north = [2,10,-6];

north_east = [1,9,-7];

east = [0,8,-8];

south_east = [7,15,-1];

south = [6,14,-2];

south_west = [5,13,-3];

west = [4,12,-4];

nort_west = [3,11,-5];

My problem is how to determined d to take a value of eight compass direction, so i can determined the neighbors point?? i'm really new in gradient based eight direction. Can anyone help me, please?? ^_^

Answer 1

[nrow, ncol] = size(I);
for x = 1 : ncol
  for y = 1 : nrow
    if y < nrow; G0(x,y) = abs(I(x,y) - I(x,y+1)); end  %E
    if x ~= 1 && y < nrow; G1(x,y) = abs(I(x,y) - I(x-1,y+1)); end %NE
    if x ~= 1; G2(x,y) = abs(I(x,y) - I(x-1,y)); end  %N
    [...]
    if x < ncol & y < nrow; G8(x,y) = abs(I(x,y) - I(x+1,y+1)); end %SE
  end
end

So now what?