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

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?? ^_^

[Walter Roberson]

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]

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 ^_^

Answer 1

[Walter Roberson]

[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?

[Elsya Nurul Aini]

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]

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)

Answer 2

[Jan]

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, :);

[Elsya Nurul Aini]

Thanks alot for the answer Mr. Simon =)

I will try it!! ;)

Answer 3

[Elsya Nurul Aini]

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??

[Walter Roberson]

What are the size() of each of the array? If one of them is not the same size as the others, which one is it? Now go back to the code and figure out why that one is smaller.

[Elsya Nurul Aini]

sorry, i'm late for reply =)

i'd been doing experiments on images with size 512x512

this is the list of size of each array:

G_n = [512 512] ==> north

G_s = [512 512] ==> south

G_e = [512 511] ==> east

G_w = [511 512] ==> west

G_ne = [512 511] ==> northeast

G_nw = [512 512] ==> northwest

G_se = [511 511] ==> southeast

G_sw = [511 512] ==> southwest

So, what should i do to make it have same size?

thanks before =)

[Jan]

Did you use my code, but forget to include the "G_[] = pre;" lines? Then add these lines.

[Walter Roberson]

If you are in the south-most row, what is south of it that you could calculate a "south" value for that row?

[Jan]

Did you use my code, but forget to include the "G_[] = pre;" lines? Then add these lines.

Using the mean of these values is unusual: The gradient in n-s and e-w direction have a shorter base line, while the gradients in ne-sw and nw-se direction use a base line, which is sqrt(2) times longer.

[Elsya Nurul Aini]

Dear All,,

please pardon me because my research about image gradient is fairly new.

i'd checked the error and correct me if my analysis is wrong. obviously, after i add "G_[] = pre" lines where the "pre = NaN(size())" line is modified into "pre = zeros(size())" line, it can be calculated. So, i think the value of it is the mean of Gd(x,y).

And so, what do you think?? =)

[Walter Roberson]

Is it meaningful to be using those zeros that are not being replaced by calculated values?

[Elsya Nurul Aini]

heheheee :D

Actually, i'm really not sure about it :D. It just can be calculated when i used those zeros. So, can you correct me?? =)

[Walter Roberson]

You could apply your functions to your G_* arrays indexed at (2:end-1, 2:end-1) . You at least have calculated data for all those locations. But Jan or I cannot offer corrected code as it does not make sense to us to be taking the mean or whatever of those values; see Jan's comments about the differing scales.

[Jan]

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.

[Walter Roberson]

Jan, I think you missed the absolute value bars in the original problem statement.