How to find the center of 4 points on an image?

I have an image of the foot that was devided into different cells. I need to find the center of each cell. I was wondering if the best way to do so is to pick the 4 points on the vertices of the cell and let Matlab find the center?

Attache is the image. Let me know if you have any ideas. Thanks.

[Tommy]

You could create a polyshape based on the four vertices and then use centroid.

[Milad Zarei]

Yes, I think that would work. I'll give it a shot. Thanks!

Answer 1

[Ameer Hamza]

try this code. It requires functions from image preocessing toolbox.

im = im2double(imread('image.jpeg'));

%% remove red text
im_gray = rgb2gray(im);
im_gray(~(im_gray < 0.2)) = 1;
im_gray = double(imbinarize(im_gray));

%% find the polygons
regions = bwconncomp(im_gray);
pxlList = regions.PixelIdxList;
outlier = isoutlier(cellfun(@(x) numel(x), pxlList));
pxlList(outlier) = [];

%% find centers
centers = zeros(numel(pxlList), 2);
for i=1:numel(pxlList)
    im_zeros = zeros(size(im_gray));
    im_zeros(pxlList{i}) = 1;
    rp = regionprops(im_zeros);
    centers(i, :) = rp.Centroid;
end

%%
imshow(im);
hold on
plot(centers(:,1), centers(:,2), 'r+', 'LineWidth', 2, 'MarkerSize', 10);

[Tommy]

Very nice

[Milad Zarei]

Wow! that's very neat. Thank you so much. Where is the coordinate system that you measured the center in? Is it on the bottom left of the image?

The goal was to find the centers and measure the distance to these black lines (as the coordinate system). Do you have any ideas how I can get the distance between the center and the axes?

[Image Analyst]

Coordinate system is in pixels, or matrix indexes. So like any matrix, (1,1) is in the upper left, and row indexes increase going down, and column indexes increase going across from left to right.

To get the point to line distance, see the function below, and the attached script for a full demo.

% Get the distance from a point (x3, y3) to
% a line defined by two points (x1, y1) and (x2, y2);
% Reference: http://mathworld.wolfram.com/Point-LineDistance2-Dimensional.html
function distance = GetPointLineDistance(x3,y3,x1,y1,x2,y2)
try
	
	% Find the numerator for our point-to-line distance formula.
	numerator = abs((x2 - x1) * (y1 - y3) - (x1 - x3) * (y2 - y1));
	
	% Find the denominator for our point-to-line distance formula.
	denominator = sqrt((x2 - x1) ^ 2 + (y2 - y1) ^ 2);
	
	% Compute the distance.
	distance = numerator ./ denominator;
catch ME
	callStackString = GetCallStack(ME);
	errorMessage = sprintf('Error in program %s.\nTraceback (most recent at top):\n%s\nError Message:\n%s',...
		mfilename, callStackString, ME.message);
	WarnUser(errorMessage)
end
return; % from GetPointLineDistance()
end

[Milad Zarei]

Yes, the indexes increase from left to right and from down to up. (like a standard CS)

[Image Analyst]

I don't know what CS is but indexes increase from up to down, not "down to up". In other words, the top line is 1 and increases as you go downwards. This is the opposite of like what you see when you call plot(), scatter(), and those kinds of graphical functions.

[Ameer Hamza]

It is possible to do the coordinate transformation, but the actual problem is to define the required coordinate frame. It is most probably possible to automatically determine the coordinate axis, but It will require quite a lot of effort to figure everything out. Here I show a way where you need to specify the coordinate axis and origin manually. Run the attached file. Thanks to Image Analyst, it includes the function GetPointLineDistance to calculate coordinates in the required axis. The following animation shows how you need to define the axis for your required coordinates.

[Milad Zarei]

Ameer, I am honestly impressed. This is so neat. Good job.

Just a quick question. The first code, it finds the centers in pixles (not mm), right?

[Ameer Hamza]

I am glad to be of help.

Yes, It finds centers in pixel coordinates. You can convert it to mm according to your scale.