MATLAB: Identifying the circle that fits the outer white pixels in a binary image (or make external mask)

image analysis

Hi all,

I want to process a series of images similar to the attached one in order to measure their porosities: V_pores / V_total. For my case, in a 2D context, V_total is the surface of circle containing all pores. It is important to know that the radius and center of the circle changes, and also many circular shapes can be identified in between, however, I am only interested, at this moment, in measuring the general surface of the circle (Vt).

Alernatively, I would be interested in applying a mask to the image. But it seems to be more difficult.

Any help would be appreciated. Many thanks.

Best Answer

I = imread("SampleXRmorph.PNG");
[y,x] = find(I) ; 
% Get center of cricle 
C = [mean(x) mean(y)] ; 
% GEt raidus 
d = sqrt((C(1)-x).^2+(C(2)-y).^2) ; 
R = max(d) ;  
% plot circle 
th = linspace(0,2*pi) ; 
xc = C(1)+R*cos(th) ; 
yc = C(2)+R*sin(th) ; 
% 
imshow(I)
hold on
plot(xc,yc,'r')

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Here is a more complete answer:

clc;    % Clear the command window.
close all;  % Close all figures (except those of imtool.)
clear;  % Erase all existing variables. Or clearvars if you want.
workspace;  % Make sure the workspace panel is showing.
format long g;
format compact;
fontSize = 22;
%--------------------------------------------------------------------------------------------------------

%    READ IN IMAGE
folder = pwd;
baseFileName = 'oring03.jpg';
% Get the full filename, with path prepended.
fullFileName = fullfile(folder, baseFileName);
% Check if file exists.
if ~exist(fullFileName, 'file')
	% The file doesn't exist -- didn't find it there in that folder.
	% Check the entire search path (other folders) for the file by stripping off the folder.
	fullFileNameOnSearchPath = baseFileName; % No path this time.
	if ~exist(fullFileNameOnSearchPath, 'file')
		% Still didn't find it.  Alert user.
		errorMessage = sprintf('Error: %s does not exist in the search path folders.', fullFileName);
		uiwait(warndlg(errorMessage));
		return;
	end
end
grayImage = imread(fullFileName);
% Get the dimensions of the image.
% numberOfColorChannels should be = 1 for a gray scale image, and 3 for an RGB color image.
[rows, columns, numberOfColorChannels] = size(grayImage);
if numberOfColorChannels > 1
	% It's not really gray scale like we expected - it's color.
	% Use weighted sum of ALL channels to create a gray scale image.
	grayImage = rgb2gray(grayImage);
	% ALTERNATE METHOD: Convert it to gray scale by taking only the green channel,
	% which in a typical snapshot will be the least noisy channel.
	% grayImage = grayImage(:, :, 2); % Take green channel.
end
% Display the image.




subplot(2, 3, 1);
imshow(grayImage, []);
title('Original Grayscale Image', 'FontSize', fontSize, 'Interpreter', 'None');
impixelinfo;
hFig = gcf;
hFig.WindowState = 'maximized'; % May not work in earlier versions of MATLAB.
drawnow;
% Display histogram
subplot(2, 3, 2);
imhist(grayImage);
grid on;
title('Histogram of original gray image', 'FontSize', fontSize);
%--------------------------------------------------------------------------------------------------------
%    SEGMENTATION OF IMAGE
threshold = 100;
outerMask = grayImage < threshold;
outerMask = imfill(outerMask, 'holes');
outerMask = bwareafilt(outerMask, 1);
% Display the image.
subplot(2, 3, 3);
imshow(outerMask, []);
title('Outer Mask', 'FontSize', fontSize, 'Interpreter', 'None');
impixelinfo;
% Measure area and solidity.

props = regionprops(outerMask, 'Area', 'Solidity', 'ConvexHull', 'EquivDiameter');
fprintf('Outer Area = %d pixels.  Outer Solidity = %.5f\n', props.Area, props.Solidity);
% Fit the convex hull perimeter to a circle.

[xCenter, yCenter, R, a] = FitCircle(props.ConvexHull(:, 1), props.ConvexHull(:, 2));
% Plot that circle in the overlay

hold on;
theta = linspace(0, 2*pi, 2 * (rows + columns));
x = R * cos(theta) + xCenter;
y = R * sin(theta) + yCenter;
plot(x, y, 'r-', 'LineWidth', 2);
% Make a mask of the circle.

circleMask = poly2mask(x, y, rows, columns);
% Do an xor with the mask to see where it's different.

differing = xor(circleMask, outerMask);
% Display the image.
subplot(2, 3, 4);
imshow(differing, []);
title('Non-Circular Parts', 'FontSize', fontSize, 'Interpreter', 'None');
impixelinfo;
% Now get the inner circle.
innerMask = (grayImage >= threshold) & outerMask;
innerMask = imfill(innerMask, 'holes');
innerMask = bwareafilt(innerMask, 1);
% Display the image.
subplot(2, 3, 5);
imshow(innerMask, []);
title('Inner Mask', 'FontSize', fontSize, 'Interpreter', 'None');
impixelinfo;
% Measure area and solidity.
props = regionprops(innerMask, 'Area', 'Solidity', 'ConvexHull', 'EquivDiameter');
fprintf('Inner Area = %d pixels.  Inner Solidity = %.5f\n', props.Area, props.Solidity);
% Fit the convex hull perimeter to a circle.
[xCenter, yCenter, R, a] = FitCircle(props.ConvexHull(:, 1), props.ConvexHull(:, 2));
% Plot that circle in the overlay
hold on;
theta = linspace(0, 2*pi, 2 * (rows + columns));
x = R * cos(theta) + xCenter;
y = R * sin(theta) + yCenter;
plot(x, y, 'r-', 'LineWidth', 2);
% Make a mask of the circle.
circleMask = poly2mask(x, y, rows, columns);
% Do an xor with the mask to see where it's different.
differing = xor(circleMask, innerMask);
% Display the image.
subplot(2, 3, 6);
imshow(differing, []);
title('Non-Circular Parts', 'FontSize', fontSize, 'Interpreter', 'None');
impixelinfo;
function [xCenter, yCenter, R, a] = FitCircle(x,y)
% FitCircle() : Fits a circle in x-y plane.
% Result is center point (xCenter, yCenter) and radius R.  
% "a" is an optional output describing the circle's equation:%
%     x^2+y^2+a(1)*x+a(2)*y+a(3)=0       
% by Bucher izhak 25/oct/1991
n = length(x);  
xx = x.*x; 
yy = y.*y; 
xy = x.*y;
A = [sum(x) sum(y) n;sum(xy) sum(yy) sum(y);sum(xx) sum(xy) sum(x)];
B = [-sum(xx+yy) ; -sum(xx.*y+yy.*y) ; -sum(xx.*x+xy.*y)];
a = A\B;
xCenter = -.5*a(1);
yCenter = -.5*a(2);
R = sqrt((a(1)^2+a(2)^2)/4-a(3));
end

MATLAB: How to crop circular area and measure the ratio of black and white from the binarized image

Measure the ratio of black and white from the binarized image?

Here bw_image is a input binary image.

[rows colm]=size(bw_image);
white_pixels=sum(bw_image(:));
black_pixels=~bw_image;
black_pixels=sum(black_pixels(:));
result=bwareafilt(~bw_image,1,'Largest');
outer_black=sum(result(:));
% Area with respect to circle only
black_pixels_area=(black_pixels-outer_black)/((rows*colm)-outer_black);
fprintf('The Percentage of black pixels covered area is %.2f ',black_pixels_area);
fprintf('\n The ratio black/white is %.2f',black_pixels/white_pixels);

Best Answer

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