How do I calculate eccentricity or RMSE value from black and white image?

Hello,

I have a question regrading to image analysis.

Here, I have a image like this black and white image.

i=imread(['BW_20220804_0301.jpg'])

i = 2150×2150

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

imshow(i)

I want to calculate how much this quarter-circular shaped image (white area) eccentric when we impose ideal quarter circle.

Also, I want to know a radius of the ideal quarter circle.

How can I make this?

Thanks, HyoJae.

Answer 1

[Udit06]

Hi HyoJae,

I understand that you want to make a quarter circle which is just large enough to cover the entire white region in your binary image. Assuming the white region is always at the lower-right corner of the image, you can follow the steps mentioned below:

1. Find the coordinates of points in the white region.
2. Find the point belonging to the white region, which is at the maximum distance from the lower-right corner of the image.
3. Use the maximum distance obtained as the radius to draw the quarter circle.

Here is the implementation of above steps in MATLAB:

binaryImage=imread("BW_20220804_0301.jpg"); 
% Step 1: Find the coordinates of the white object 
[rows, cols] = find(binaryImage == 1); 

minX = min(cols); 
maxY = max(rows); 

% Step 2: Calculate the radius of the quarter circle 
fig_size=2150; 
radius= max(sqrt((cols-fig_size).^2 + (rows-fig_size).^2)) 

% Step 3: Draw the quarter circle on the image 
figure; 
imshow(binaryImage); % Replace 'yourImage' with your actual image 
hold on; 

% Calculate the center point of the quarter circle 
center = [size(binaryImage, 2), size(binaryImage, 1)]; 

% Draw the quarter circle using the 'rectangle' function 
rectangle('Position', [center(1) - radius, center(2) - radius, radius*2, radius*2], ... 
    'Curvature', [1, 1], 'EdgeColor', 'r', 'LineWidth', 2); 

hold off; 

To determine the extent to which the white region deviates from an ideal quarter circle, you can calculate the area difference between the white region and the corresponding ideal quarter circle.

I hope this helps.