I need to do a least squares fit on an image

I need to run a code that does the least squares fit on an image. I was asked to find the equation of any line in the image using this method. Once I load the image how do I proceed?

[Riccardo Scorretti]

Could you formulate more precisely your problem? What do you want to do exactly? An example would help.

[Jessica Solorzano]

I was given an image and I was asked to find the equation for any line in the image using the hough transform and the least squares fit

[Image Analyst]

OK, can you post your image? It sounds like they want you to do it, not us, so if you need help, post your hough code and we can fix it.

[Jessica Solorzano]

this is the image.

And this was my hough code.

Answer 1

[Pratyush Swain]

Hey Jessica,

I understand you want to find the equation for hough line in an image through least squares method.

Please refer to the following code example where I have demonstrated how to leverage least square fit method to find hough lines equation using the provided image:

image = imread('image.jpeg'); % Loading testing image
grayImage = rgb2gray(image);
% Perform Edge Detection
edgeImage = edge(grayImage, 'Canny');
% Apply Hough Transform
[H, theta, rho] = hough(edgeImage);
% Extract Line Parameters
numPeaks = 10; % Number of peaks to detect
peaks = houghpeaks(H, numPeaks);
lines = houghlines(edgeImage, theta, rho, peaks);
% Fit Lines using Least Squares
lineEquations = cell(numPeaks, 1);
for k = 1:numPeaks
    xy = [lines(k).point1; lines(k).point2];
    disp(xy)
    x = xy(:, 1);
    y = xy(:, 2);
    p = polyfit(x, y, 1); % Perform least squares fitting
    slope = p(1);
    intercept = p(2);
    lineEquations{k} = sprintf('y = %.2fx + %.2f', slope, intercept);
end
% Display the Image with Detected Lines
figure;
imshow(image);
hold on;
for k = 1:numPeaks
    xy = [lines(k).point1; lines(k).point2];
    plot(xy(:, 1), xy(:, 2), 'LineWidth', 2, 'Color', 'r');
    text(xy(1, 1), xy(1, 2), lineEquations{k}, 'Color', 'g', 'FontSize', 8);
end
hold off;
% Show Line Equations
disp('Line Equations:');
for k = 1:numPeaks
    disp(lineEquations{k})
end

For more information, please refer to these links.

1-https://in.mathworks.com/help/matlab/ref/polyfit.html

2-https://www.mathworks.com/help/images/ref/houghlines.html

3-https://www.mathworks.com/help/images/ref/houghpeaks.html

Hope this helps.