Check for pixel values in a neighborhood

Question

I'm trying to write a MATLAB script that does the following:

Given: pixel coordinates(x,y) for a .jpg image Goal: Check, within a 5 pixel radius of given coordinates, if there is a pixel of a certain value.

For example, let's say I'm given the coordinates (100,100), then I want to check the neighborhood of (100,100) within my image for any pixels that are black (0,0,0). So perhaps, pixel (103, 100) and (104,100) might have the value (0,0,0).

Current code:

x_coord = uint32(coord(:,1));  
y_coord = uint32(coord(:,2));
count = 0;

for i = 1:length(x_coord)
    %(img(x,y) returns pixel value at that (x,y)
    %Note 0 = black. Indicating that, at that position, the image is just 
    % black 
    if img(x_coord(i),y_coord(i)) == 0 
        count = count + 1;
    end
end

It currently only checks at an exact location. Not in a local neighborhood. How to could I extend this?

EDIT: Also note, as long as there as at least one pixel in the neighborhood with the value, I increment count. I'm not trying to enumerate how many pixels in the neighborhood have that value, just trying to find evidence of at least one pixel that has that value.

EDIT:

Even though I am unable to identify an error with the code, I am not able to get the exact results I want. Here is the code I am using.

val = 0; %pixel value to check
N = 50; % neighbourhood radius

%2D grid of coordinates surrounding center coordinate
[R, C] = ndgrid(1 : size(img, 1), 1 : size(img, 2));

for kk = 1 : size(coord, 1)
    r = coord(kk, 1); c = coord(kk, 2); % Get pixel locations

    % mask of valid locations within the neighbourhood (avoid boundary problems)
    mask = (R - r).^2 + (C - c).^2 <= N*N;         

    pix = img(mask); % Get the valid pixels
    valid = any(pix(:) ~= val);
    % Add either 0 or 1 depending if we have found any matching pixels
    if(valid == 1)
        img = insertMarker(img, [r c], 'x', 'color', 'red', 'size', 10);
        imwrite(img, images(i).name,'tiff');
    end
    count = count + valid; 
end

Answer 1

An easier way to do this would be to use indexing to grab a neighbourhood, then to check to see if any of the pixels in the neighbourhood have the value that you're looking for, use any on a flattened version of this neighbourhood. The trick with grabbing the right neighbourhood is to first generate a 2D grid of coordinates that span the entire dimensions of your image, then simply use the equation of a circle with the centre of it being each coordinate you are looking at and determine those locations that satisfy the following equation:

(x - a)^2 + (y - b)^2 <= N^2

N is the radius of the observation window, (a, b) is a coordinate of interest while (x, y) is a coordinate in the image. Use meshgrid to generate the coordinates.

You would use the above equation to create a logical mask, index into your image to pull the locations that are valid within the mask and check how many pixels match the one you want. Another added benefit with the above approach is that you are not subject to any out of bounds errors. Because you are pre-generating the list of all valid coordinates in your image, generating the mask will confine you within the boundaries of the image so you never have to check for out of boundaries conditions.... even when you specify coordinates to search that are out of bounds.

Specifically, assuming your image is stored in img, you would do:

count = 0; % Remembers total count of pixels matching a value
val = 0; % Value to match
N = 50; % Radius of neighbourhood

% Generate 2D grid of coordinates
[x, y] = meshgrid(1 : size(img, 2), 1 : size(img, 1));

% For each coordinate to check...
for kk = 1 : size(coord, 1)
    a = coord(kk, 1); b = coord(kk, 2); % Get the pixel locations
    mask = (x - a).^2 + (y - b).^2 <= N*N; % Get a mask of valid locations
                                           % within the neighbourhood        
    pix = img(mask); % Get the valid pixels
    count = count + any(pix(:) == val); % Add either 0 or 1 depending if 
                                        % we have found any matching pixels
end

Answer 2

The proposed solution:

fc = repmat(-5:5,11,1);
I = (fc.^2+fc'.^2)<=25;
fc_x = fc(I);
fc_y = fc'; fc_y = fc_y(I);

for i = 1:length(x_coord)
    x_toCheck = fc_x + x_coord(i);
    y_toCheck = fc_y + y_coord(i);
    I = x_toCheck>0 & x_toCheck<=yourImageWidth;
    I = I.*(y_toCheck>0 & y_toCheck<=yourImageHeight);
    x_toCheck = x_toCheck(logical(I));
    y_toCheck = y_toCheck(logical(I));

    count = sum(img(x_toCheck(:),y_toCheck(:)) == 0);
end

---

If your img function can only check one pixel at a time, just add a for loop:

for i = 1:length(x_coord)
    x_toCheck = fc_x + x_coord(i);
    y_toCheck = fc_y + y_coord(i);
    I = x_toCheck>0 & x_toCheck<=yourImageWidth;
    I = I.*(y_toCheck>0 & y_toCheck<=yourImageHeight);
    x_toCheck = x_toCheck(logical(I));
    y_toCheck = y_toCheck(logical(I));
    for j = 1:length(x_toCheck)
        count = count + (img(x_toCheck(j),y_toCheck(j)) == 0);
    end
end

---

Step-by-step:

You first need to get all the coordinates within 5 pixels range of the given coordinate.

We start by building a square of 11 pixels in length/width.

fc = repmat(-5:5,11,1);
fc_x = fc;
fc_y = fc';
plot(fc_x,fc_y,'.');

We now need to build a filter to get rid of those points outside the 5-pixel radius.

I = (fc.^2+fc'.^2)<=25;

Apply the filter, so we can get a circle of 5-pixel radius.

fc_x = fc_x(I);
fc_y = fc_y(I);

Next translate the centre of the circle to the given coordinate:

x_toCheck = fc_x + x_coord(i);
y_toCheck = fc_y + y_coord(i);

You need to check whether part of the circle is outside the range of your image:

I = x_toCheck>0 & x_toCheck<=yourImageWidth;
I = I.*(y_toCheck>0 & y_toCheck<=yourImageHeight);
x_toCheck = x_toCheck(logical(I));
y_toCheck = y_toCheck(logical(I));

Finally count the pixels:

count = sum(img(x_toCheck,y_toCheck) == 0);