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

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Elsya Nurul Aini 2012-1-21

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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?? ^_^

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Walter Roberson 2012-1-21

The first number in each of your triples starts at 0 for east and increases by 1 for each multiple of 45 degrees counter-clockwise from east. But I have no idea what the second and third value in each of your triples are intended to represent or how they are to be used.

Elsya Nurul Aini 2012-1-22

thanks for the comment Walter.

actually, i have no idea too about it, and that's why did i ask. =D

So, is there any reference code about eight compass direction that can solve my problem??

thanks before ^_^

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Walter Roberson 2012-1-22

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[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?

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Elsya Nurul Aini 2012-1-22

thank you very much for the reference code ^_^

can you tell me please, why you give a decision on that looping, just like "if y < nrow", " if ~= 1", and so on.

thanks alot before =)

Walter Roberson 2012-1-22

If you do not use those tests then you will get matrix references that are out of range, such as trying to access I(y,0)

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更多回答（2 个）

Jan 2012-1-22

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在 MATLAB Online 中打开

The question is not really clear to me, but I like to guess:

I = rand(100, 100, 3);
m    = size(I, 1);
n    = size(I, 2);
pre  = NaN(size(I));
G_n  = pre;
G_s  = pre;
G_w  = pre;
G_e  = pre;
G_nw = pre;
G_sw = pre;
G_ne = pre;
G_se = pre;
G_n(1:m-1, :, :)    = diff(I, 1, 1);
G_s(2:m, :, :)      = G_n(1:m-1, :, :);
G_e(:, 1:n-1, :)    = diff(I, 1, 2);
G_w(:, 2:n, :)      = G_e(:, 1:n-1, :);
G_ne(2:m, 1:n-1, :) = I(1:m-1, 2:n, :)   - I(2:m, 1:n-1, :);
G_nw(2:m, 2:n, :)   = I(1:m-1, 1:n-1, :) - I(2:m, 2:n, :);
G_se(2:m, 1:n-1, :) = I(1:m-1, 2:n, :)   - I(2:m, 1:n-1, :);
G_sw(2:m, 2:n, :)   = I(1:m-1, 1:n-1, :) - I(2:m, 2:n, :);

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Elsya Nurul Aini 2012-1-22

Thanks alot for the answer Mr. Simon =)

I will try it!! ;)

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Elsya Nurul Aini 2012-1-22

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https://ww2.mathworks.cn/matlabcentral/answers/26697-how-to-calculate-gradient-between-the-currently-processed-point-x-y-and-its-neighboring-point-in-o#answer_34856

在 MATLAB Online 中打开

Thanks All,,

the reference code is very helpfull =)

but i have another problem.

I want to take the mean of Gd(x,y), so i use this coding

n = mean(G_n + G_s + G_e + G_w + G_ne + G_nw + G_se + G_sw);

but there is an error :

??? Error using ==> plus
Matrix dimensions must agree.
Error in ==> tetangga at 13
n = mean(G_n + G_s + G_e + G_w + G_ne + G_nw + G_se + G_sw);

how i can solve this error??

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Jan 2012-1-24

What is the current problem exactly?

If you use "G_e = zeros(size(I))" or "G_e = NaN(size(I))" does not matter the ability to be computed. The problem was, that Ge had the size [512 511], and this meand, that you have called "G_e(:, 1:n-1, :) = diff(I, 1, 2);" without the pre-allocation.

The gradient is a vector for 2D data. Building the mean of the components is not meaningful. If the value is +1 in n-s direction and -1 in w-e direction, the mean 0 is free of use.