Form Index Image Processing

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Nikolau
Nikolau on 22 Nov 2022
Commented: Image Analyst on 22 Nov 2022
Hello Guys,
I am struggling to get the Form Index from a bw image. The form index (FI) isdescribed as the sum of the changes in radius: and it is represented by the attached model. where R is the radius of the particle in different directions, and θ is the directional angle. In Equation 1, the form index of a circle is zero, because there are no changes in radii. I would apreciate if there is someone that can help me with it

Accepted Answer

Image Analyst
Image Analyst on 22 Nov 2022
Try this:
% Demo by Image Analyst
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;
markerSize = 40;
%--------------------------------------------------------------------------------------------------------
% READ IN IMAGE
folder = [];
baseFileName = 'eight.tif';
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)
rows = 242
columns = 308
numberOfColorChannels = 1
%--------------------------------------------------------------------------------------------------------
% Display the image.
subplot(2, 2, 1);
imshow(grayImage);
impixelinfo;
axis('on', 'image');
title('Original Gray Scale Image', 'FontSize', fontSize, 'Interpreter', 'None');
if numberOfColorChannels > 1
% It's not really gray scale like we expected - it's color.
fprintf('It is not really gray scale like we expected - it is color\n');
% Extract the blue channel.
grayImage = grayImage(:, :, 3);
end
% Update 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)
rows = 242
columns = 308
numberOfColorChannels = 1
% Maximize window.
g = gcf;
g.WindowState = 'maximized';
drawnow;
%--------------------------------------------------------------------------------------------------------
% Show the histogram
subplot(2, 2, 2);
imhist(grayImage);
title('Histogram of Original Image', 'FontSize', fontSize, 'Interpreter', 'None');
grid on;
%--------------------------------------------------------------------------------------------------------
% Interactively and visually set a threshold on a gray scale image.
% https://www.mathworks.com/matlabcentral/fileexchange/29372-thresholding-an-image?s_tid=srchtitle
lowThreshold = 0;
highThreshold = 200;
% [lowThreshold, highThreshold] = threshold(lowThreshold, highThreshold, grayImage)
%--------------------------------------------------------------------------------------------------------
% Create a mask
mask = grayImage >= lowThreshold & grayImage <= highThreshold;
% Fill blobs
mask = imfill(mask,"holes");
% Take blobs only 1000 pixels or larger in area
mask = bwareaopen(mask, 1000);
subplot(2, 2, 3);
imshow(mask, []);
impixelinfo;
axis('on', 'image');
title('Mask', 'FontSize', fontSize, 'Interpreter', 'None');
%--------------------------------------------------------------------------------------------------------
% Measure blob sizes
props = regionprops(mask, 'Area', 'Centroid');
allAreas = [sort([props.Area], 'descend')]
allAreas = 1×4
4786 4773 4770 4769
subplot(2, 2, 4);
histogram(allAreas);
title('Histogram of blob areas', 'FontSize', fontSize, 'Interpreter', 'None');
grid on;
% Plot the borders of all the blobs in the overlay above the original grayscale image
% using the coordinates returned by bwboundaries().
% bwboundaries() returns a cell array, where each cell contains the row/column coordinates for an object in the image.
imshow(grayImage); % Optional : show the original image again. Or you can leave the binary image showing if you want.
% Here is where we actually get the boundaries for each blob.
boundaries = bwboundaries(mask);
% boundaries is a cell array - one cell for each blob.
% In each cell is an N-by-2 list of coordinates in a (row, column) format. Note: NOT (x,y).
% Column 1 is rows, or y. Column 2 is columns, or x.
numberOfBoundaries = size(boundaries, 1); % Count the boundaries so we can use it in our for loop
% Here is where we actually plot the boundaries of each blob in the overlay.
hold on; % Don't let boundaries blow away the displayed image.
for k = 1 : numberOfBoundaries
thisBoundary = boundaries{k}; % Get boundary for this specific blob.
x = thisBoundary(:,2); % Column 2 is the columns, which is x.
y = thisBoundary(:,1); % Column 1 is the rows, which is y.
plot(x, y, 'r-', 'LineWidth', 2); % Plot boundary in red.
% Compute the Form Index
xCenter = props(k).Centroid(1);
yCenter = props(k).Centroid(2);
% Get all the radii as we move around the boundary.
radii = sqrt((x - xCenter).^2 + (y - yCenter).^2);
% Get the sum of differences to get the Form Index
FI(k) = sum(abs(diff(radii)));
end
FI % Show in command window.
FI = 1×4
72.8062472085245 71.5919083047267 69.0889051455168 65.4482079330172
hold off;
caption = sprintf('%d Outlines, from bwboundaries()', numberOfBoundaries);
fontSize = 15;
title(caption, 'FontSize', fontSize);
axis('on', 'image'); % Make sure image is not artificially stretched because of screen's aspect ratio.
  4 Comments
Image Analyst
Image Analyst on 22 Nov 2022
Look, here is one with irregularly shaped blobs, some smooth and convex and some not. I compute the FI both taking abs and without taking abs.
% Demo by Image Analyst
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;
markerSize = 40;
%--------------------------------------------------------------------------------------------------------
% READ IN IMAGE
folder = [];
baseFileName = 'toyobjects.png';
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)
%--------------------------------------------------------------------------------------------------------
% Display the image.
subplot(2, 2, 1);
imshow(grayImage);
impixelinfo;
axis('on', 'image');
title('Original Gray Scale Image', 'FontSize', fontSize, 'Interpreter', 'None');
if numberOfColorChannels > 1
% It's not really gray scale like we expected - it's color.
fprintf('It is not really gray scale like we expected - it is color\n');
% Extract the blue channel.
grayImage = grayImage(:, :, 3);
end
% Update 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)
% Maximize window.
g = gcf;
g.WindowState = 'maximized';
drawnow;
%--------------------------------------------------------------------------------------------------------
% Show the histogram
subplot(2, 2, 2);
imhist(grayImage);
title('Histogram of Original Image', 'FontSize', fontSize, 'Interpreter', 'None');
grid on;
%--------------------------------------------------------------------------------------------------------
% Interactively and visually set a threshold on a gray scale image.
% https://www.mathworks.com/matlabcentral/fileexchange/29372-thresholding-an-image?s_tid=srchtitle
lowThreshold = 0;
highThreshold = 200;
% [lowThreshold, highThreshold] = threshold(lowThreshold, highThreshold, grayImage)
%--------------------------------------------------------------------------------------------------------
% Create a mask
% mask = grayImage >= lowThreshold & grayImage <= highThreshold;
mask = grayImage ~= 127;
% Fill blobs
mask = imfill(mask,"holes");
% Take blobs only 1000 pixels or larger in area
mask = bwareaopen(mask, 1000);
subplot(2, 2, 3);
imshow(mask, []);
impixelinfo;
axis('on', 'image');
title('Mask', 'FontSize', fontSize, 'Interpreter', 'None');
%--------------------------------------------------------------------------------------------------------
% Measure blob sizes
props = regionprops(mask, 'Area', 'Centroid');
allAreas = [sort([props.Area], 'descend')]
subplot(2, 2, 4);
histogram(allAreas);
title('Histogram of blob areas', 'FontSize', fontSize, 'Interpreter', 'None');
grid on;
% Plot the borders of all the blobs in the overlay above the original grayscale image
% using the coordinates returned by bwboundaries().
% bwboundaries() returns a cell array, where each cell contains the row/column coordinates for an object in the image.
imshow(grayImage); % Optional : show the original image again. Or you can leave the binary image showing if you want.
% Here is where we actually get the boundaries for each blob.
boundaries = bwboundaries(mask);
% boundaries is a cell array - one cell for each blob.
% In each cell is an N-by-2 list of coordinates in a (row, column) format. Note: NOT (x,y).
% Column 1 is rows, or y. Column 2 is columns, or x.
numberOfBoundaries = size(boundaries, 1); % Count the boundaries so we can use it in our for loop
% Here is where we actually plot the boundaries of each blob in the overlay.
hold on; % Don't let boundaries blow away the displayed image.
for k = 1 : numberOfBoundaries
thisBoundary = boundaries{k}; % Get boundary for this specific blob.
x = thisBoundary(:,2); % Column 2 is the columns, which is x.
y = thisBoundary(:,1); % Column 1 is the rows, which is y.
plot(x, y, 'r-', 'LineWidth', 2); % Plot boundary in red.
% Compute the Form Index
xCenter = props(k).Centroid(1);
yCenter = props(k).Centroid(2);
% Get all the radii as we move around the boundary.
radii = sqrt((x - xCenter).^2 + (y - yCenter).^2);
% Get the sum of differences to get the Form Index
FI(k) = sum(diff(radii));
FIabs(k) = sum(abs(diff(radii)));
end
FI % Show in command window.
FIabs
hold off;
caption = sprintf('%d Outlines, from bwboundaries()', numberOfBoundaries);
fontSize = 15;
title(caption, 'FontSize', fontSize);
axis('on', 'image'); % Make sure image is not artificially stretched because of screen's aspect ratio.
You see the FI without taking the abs are all zero as expected:
FI =
0 0 0 0
FIabs =
149.325027041666 218.54116484628 245.790271754549 84.1212568797374

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