calculate homography from hough line intersection in matlab

% Homography from Hough Line Intersection

% Tags: matlab, image-processing, computer-vision, homography, hough-transform

% Given a set of line intersections in two images, this code calculates % the homography matrix that maps one image to the other.

% First, we need to obtain the line intersections using the Hough Transform. % Once we have the line intersections, we can use least-squares estimation % to obtain the homography matrix.

%% Load images img1 = imread('image1.jpg'); img2 = imread('image2.jpg');

%% Compute Hough transform for line intersections [H1,theta1,rho1] = hough(img1,'RhoResolution',1,'ThetaResolution',1); [H2,theta2,rho2] = hough(img2,'RhoResolution',1,'ThetaResolution',1);

% Find peak values and corresponding rho and theta values for H1 and H2 numpeaks = 100; % Customize for your application peaks1 = houghpeaks(H1,numpeaks,'Threshold',0); peaks2 = houghpeaks(H2,numpeaks,'Threshold',0); rho1_peaks = rho1(peaks1(:,1)); theta1_peaks = theta1(peaks1(:,2)); rho2_peaks = rho2(peaks2(:,1)); theta2_peaks = theta2(peaks2(:,2));

% Compute line intersection points points1 = houghlines(img1,theta1_peaks,rho1_peaks); points2 = houghlines(img2,theta2_peaks,rho2_peaks);

% Combine point sets points = [points1; points2];

%% Compute homography matrix using least-squares estimation N = size(points,1); A = zeros(2N,9); for i=1:N x1 = points(i,1); y1 = points(i,2); x2 = points(i,3); y2 = points(i,4); A(2i-1,:) = [-x1,-y1,-1,0,0,0,x1x2,y1x2,x2]; A(2i,:) = [0,0,0,-x1,-y1,-1,x1y2,y1*y2,y2]; end [U,S,V] = svd(A); h = V(:,end); H = reshape(h,3,3)';

% Normalize homography matrix H = H/H(3,3);

main.m

Note: This code assumes that the line intersections have already been extracted using the Hough Transform in Matlab. The number of peak values to extract from the Hough Transform can be customized according to the specific application.
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