Curvature detection from outlines of the binary image

This is my binary image. I used canny method to detect edge.

I want to identify these curvature(or spline), and plot them on the image.

(Left side and right side have different radius of curvatures.)

I searched several image processing techniques about this kind of problems, but I'm not sure where to start.

Any coment would be very helpful to me.

Thank you.

Answer 1

[Image Analyst]

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 = 16;
markerSize = 20;
%--------------------------------------------------------------------------------------------------------
%    READ IN TEST IMAGE
folder = pwd;
baseFileName = 'DW image.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 size
[rows, columns, numberOfColorChannels] = size(grayImage)

rows =    761

columns =    922

numberOfColorChannels =      3

if numberOfColorChannels == 3
    grayImage = rgb2gray(grayImage);
end
% Convert to binary
binaryImage = grayImage > 128;
%--------------------------------------------------------------------------------------------------------
% Display the image.
subplot(1, 2, 1);
imshow(binaryImage, []);
impixelinfo;
axis('on', 'image');
title('Original Binary Image', 'FontSize', fontSize, 'Interpreter', 'None');
% Maximize window.
g = gcf;
g.WindowState = 'maximized';
g.Name = 'Demo by Image Analyst';
g.NumberTitle = 'off';
drawnow;
%--------------------------------------------------------------------------------------------------------
% Scan the image column by column
topRows = nan(1, columns);
for col = 1 : columns
    t = find(binaryImage(:, col), 1, 'first');
    if ~isempty(t)
        % Only look at rows below row 103 and above 300.
        if t >= 103 && t <= 300
            topRows(col) = t;
        end
    end
end
subplot(1, 2, 2);
plot(topRows, 'b-', 'LineWidth', 2);
grid on
axis ij
% Fit a quadratic to the left half
goodColumns = ~isnan(topRows);
x = find(goodColumns);
y = topRows(goodColumns);
hold on;
polynomialOrder = 4;
coefficients = polyfit(x, y, polynomialOrder)

coefficients = 1×5

3.48880567786257e-09 -6.96896072580378e-06 0.00582763348942092 -2.28797501728093 443.86351083415

xFit = min(x) : max(x);
yFit = polyval(coefficients, xFit);
plot(xFit, yFit, 'r-', 'LineWidth',2);
xlabel('Column', 'FontSize',fontSize);
ylabel('Row (Line)', 'FontSize',fontSize);
caption = sprintf('Polynomial of order %d fitted through top rows', polynomialOrder);
title(caption, 'FontSize',fontSize);

[DW]

Thank you very much.

The codes were very clear and I think I can modify this for further applications I want.

It was really helpful.

Thank you again!