To plot the inertia axis using the centroid you can calculate the principal axis of inertia. These axes can be determined from the image's covariance matrix, and they provide a way to understand the orientation and elongation of the shape.
You can then use eigenvalue decomposition on the covariance matrix to find the principal axes. Have a look at the code below:
% Load your binary image
image = imread('Cattura.jpg'); % Replace with your image file
if size(image, 3) == 3
image = rgb2gray(image); % Convert to grayscale if necessary
end
binaryImage = imbinarize(image);
% Find coordinates of white pixels
[y_indices, x_indices] = find(binaryImage);
% Calculate the centroid
centroid_x = mean(x_indices);
centroid_y = mean(y_indices);
% Center the coordinates
x_centered = x_indices - centroid_x;
y_centered = y_indices - centroid_y;
% Create the covariance matrix
cov_matrix = cov(x_centered, y_centered);
% Calculate eigenvalues and eigenvectors
[eigenvectors, eigenvalues] = eig(cov_matrix);
% Sort eigenvectors by eigenvalues in descending order
[~, order] = sort(diag(eigenvalues), 'descend');
eigenvectors = eigenvectors(:, order);
eigenvalues = diag(eigenvalues);
eigenvalues = eigenvalues(order);
% Plot the image and the principal axes
figure;
imshow(binaryImage);
hold on;
plot(centroid_x, centroid_y, 'ro', 'MarkerSize', 10, 'LineWidth', 2);
% Draw the principal axes with lengths proportional to the square root of eigenvalues
colors = ['r', 'g']; % Define colors as a character array
for i = 1:2
vector = eigenvectors(:, i);
quiver(centroid_x, centroid_y, sqrt(eigenvalues(i)) * vector(1), sqrt(eigenvalues(i)) * vector(2), ...
'Color', colors(i), 'LineWidth', 2, 'MaxHeadSize', 2);
end
title('Inertia Axes of Nevus');
hold off;
% Optional: Rotate the image to align the principal axis with the x-axis
angle = atan2(eigenvectors(2, 1), eigenvectors(1, 1));
angle_degrees = rad2deg(angle);
rotated_image = imrotate(binaryImage, -angle_degrees, 'bilinear', 'crop');
% Show rotated image
figure;
imshow(rotated_image);
title('Rotated Image');
Here is the output of the above code in MATLAB R2023b:
For further information refer to the following documentation:
Eigenvalues: www.mathworks.com/help/matlab/math/eigenvalues.html?searchHighlight=eigenvalues&s_tid=srchtitle_support_results_1_eigenvalues
Hope this answers your query.
