8 neighbours of a pixel after converting to 1D array

Hi

Is there a simple way to access the 8 neighbours of a pixel x(i,j) given by x(i-1,j-1), x(i-1,j), x(i-1,j+1), x(i,j-1), ... ,x(i+1,j+1) after converting x into a 1D array? I have been using for loops to achieve this but it's quite slow if the matrix x is large.

Thanks.

[Sean de Wolski]

Not sure what you mean. Do you, for example, have a 100x100 matrix that you turn into 10000x1 vector and you want to find the neighbors of pixel (24,46)?

[zepp]

Yes. So if the neighbours of pixel (24,46) when viewed in 2D matrix are (23,45), (23,46), (23,47), (24,45), (24,47), (25,45), (25,46), (25,47), how did I get these indices from the 1D vector. I am doing a distance calculation of every pixel with each of its neighbours. So, I want to know if I can process this operation as a vector rather than a matrix.

[Image Analyst]

I'm assuming he is scanning the image and for each pixel, he has created an 8 element 1D array, and he wants to know how to access those elements of his 1D array (because he says "after converting"). He did not ask HOW to create the 1D array - and he seems to imply that he needs to know what to do AFTER it's been created, though that seems rather obvious to me.

[zepp]

I have to run the neighbourhood operation for each pixel in the matrix. I simply use 2 for loops to get the neighbours of each pixel and get the distances. But if I convert the whole matrix into a vector, getting the 8 neighbours for each pixel is not straightforward. I would have to use sub2ind 8 times for each pixel to get the corresponding subscripts of its neighbourhood pixels. This will be quite slow.

[Sean de Wolski]

@Sriram, read my answer. It addresses both of your concerns.

Use the two for-loops on the matrix and keep the column vector also for your column vector needs.

[Image Analyst]

Thanks for the clarification. So your question should have read: "access the 8 neighbours of a pixel x(i,j) given by x(i-1,j-1), x(i-1,j), x(i-1,j+1), x(i,j-1), ... ,x(i+1,j+1) and convert them into a 1D array".

Saying "after converting x into a 1D array" was imprecise since you did not have this 1D array yet, and you never converted x - the entire x - into a 1D array.

Answer 1

[Jan]

w  = 200;
h  = 100;
x  = rand(h, w);
xv = x(:);  % A very fast reshape
pattern = [1,2,3, h+1, h+3, 2*h+1, 2*h+2, 2*h+3];
focus   = h + 2;

% Neighborhood of the pixel at position (2,2):
xv(pattern) - xv(focus)
% Next pixel:
pattern = pattern + 1;
focus   = focus + 1;
xv(pattern) - xv(focus)
% etc. This would happen in a loop of course.
% Consider the edges: pattern = pattern + 3

I cannot create the required loops, because I do not know the wanted output style.

[zepp]

This is what I wanted! Brilliant, thanks!

[zepp]

I have a question about the focus variable. I don't consider the edge pixels (no wraparound) so how can I write the loop so that when the focus reaches k*h - 1, it jumps to (k+1)*h + 2.

[Jan]

for iW = 2:w-1
  for ih = 2:h-1
    pattern = pattern + 1;
    focus   = focus + 1;
    ...
  end
  pattern = pattern + 2;
  focus   = focus + 2;
end

[Sajid Rahim]

clear all;

[filename pathname]=uigetfile('*.jpg;*.png;*.tif;*.tiff;*.gif;*.bmp;');

inputimage=imread([pathname filename]);

I=inputimage;

% I = imread('5.png') ;

I = rgb2gray(I) ;

[y,x] = find(I) ;

figure

imshow(I)

hold on

plot(x,y,'.b')

% x

% y

% z=(y+x)/2

% plot(z,'.r')

a=x(1)

b=y(1) plot(x(1),y(1),'*y')

plot(x(end),y(end),'*y')

% neighbors(1) = (a,b-1);

neighbors(1) = I(a,b-1);

plot(a,b-1,'*r')

neighbors(2) = I(a,b+1);

plot(a,b+1,'*r')

neighbors(3) = I(a,b+2);

plot(a,b+2,'*r')

neighbors(4) = I(a+1,b);

plot(a+1,b,'*r')

neighbors(5) = I(a+1,b+1);

plot(a+1,b+1,'*r')

neighbors(6) = I(a+2,b+2);

plot(a+2,b+2,'*r')

neighbors(7) = I(a+2,b);

plot(a+2,b,'*r')

neighbors(8) = I(a+2,b+1);

plot(a+2,b+1,'*r')

neighbors(9) = I(a+2,b+2);

plot(a+2,b+2,'*r')

this is my code... i findede the 8 neighbours of a fixel ... now i wan to find again 8 neighbours of ech finded fixels neighbours.. plz help me......

[Jan]

@Sajid Rahim: Do not post unrelated code in a thread of someone else, please. Open a new thread for you own problem.

[Gilles]

@Jan, Thanks a lot for this usefull code to find neighboor indices of a pixel after converting a matrix into an 1D array.

Do you know the formules to generalize this code for kernel of large size ?

I want to find the neighboors indices for :

• 5x5 kernel --> 24 neighboors
• 7x7 kernel --> 48 neighboors

Thanks in advance

Answer 2

[Image Analyst]

Yes, To access the 3rd element of your 1D array, you do

thirdElement = array1D(3)

Is that what you meant? It seems like what you asked. It does not depend on the size of x obviously, just on the size of the "ring", so a 3x3 window would have 8 elements, a 5x5 would have 18, and so on.

Answer 3

[Sean de Wolski]

As I mentioned in the comment: I would just reshape the image to its original (or leave it alone) and make a second variable that is the column vector:

x = rand(10000);
x2 = reshape(x,numel(x),1);

Does not require a deep copy of x so the data is only stored in memory once. And reshape of full matrices is up there on the list of the fastest MATLAB functions. You're certainly not paying any penalties to do what I did above.

[zepp]

I'm sorry but I don't understand how this helps as it just converts the matrix into a vector.

My main concern is to get the subscripts of the 2D neighbours of a pixel in 1D form. Let me explain it better, assume a matrix 'a' centred at 5.

a = [1 2 3; 4 5 6; 7 8 9]; % the neighbours of 5

I want a matrix b containing distances of 5 from each of its neighbours.

b = [4 3 2; 1 0 1; 2 3 4];

In a large matrix, I would have to do this for each element(like a sliding window)

I was just wondering if there is a way to vectorise this operation.

[Sean de Wolski]

I doubt vectorization will not be faster than nested for-loops here.

See my answer here: http://www.mathworks.com/matlabcentral/answers/40977#answer_50587

What I am saying is that the overhead you will pay for figuring things out in a column vector will cost much more than using a matrix where you kinda get this spatial information for free. The for-loops will cruise over it and in the time we've you've spent looking into this (which is great, by the way +1!) MATLAB could've done this for millions of matrix elements like this, literally. With parfor loop you could probably get even more!

[zepp]

I'll try parfor and see if it speeds up things. Thanks for your help!

[Sean de Wolski]

How many images do you actually have and how big are they?

[zepp]

200 images and each is 640x480. I have to run it for different neighbourhood sizes (3x3, 5x5, 7x7) etc.