I found an implementation of the Hough transform in MATLAB at Rosetta Code, but I'm having trouble understanding it. Also I would like to modify it to show the original image and the reconstructed lines (de-Houghing).
Any help in understanding it and de-Houghing is appreciated. Thanks
Why is the image flipped?
theImage = flipud(theImage);
I can't wrap my head around the norm function. What is its purpose, and can it be avoided?
EDIT: norm is just a synonym for euclidean distance: sqrt(width^2 + height^2)
rhoLimit = norm([width height]);
Can someone provide an explanation of how/why rho, theta, and houghSpace is calculated?
rho = (-rhoLimit:1:rhoLimit); theta = (0:thetaSampleFrequency:pi); numThetas = numel(theta); houghSpace = zeros(numel(rho),numThetas);
How would I de-Hough the Hough space to recreate the lines?
Calling the function using a 10x10 image of a diagonal line created using the identity (eye) function
theImage = eye(10)
thetaSampleFrequency = 0.1
[rho,theta,houghSpace] = houghTransform(theImage,thetaSampleFrequency)
The actual function
function [rho,theta,houghSpace] = houghTransform(theImage,thetaSampleFrequency)
%Define the hough space
theImage = flipud(theImage);
[width,height] = size(theImage);
rhoLimit = norm([width height]);
rho = (-rhoLimit:1:rhoLimit);
theta = (0:thetaSampleFrequency:pi);
numThetas = numel(theta);
houghSpace = zeros(numel(rho),numThetas);
%Find the "edge" pixels
[xIndicies,yIndicies] = find(theImage);
%Preallocate space for the accumulator array
numEdgePixels = numel(xIndicies);
accumulator = zeros(numEdgePixels,numThetas);
%Preallocate cosine and sine calculations to increase speed. In
%addition to precallculating sine and cosine we are also multiplying
%them by the proper pixel weights such that the rows will be indexed by
%the pixel number and the columns will be indexed by the thetas.
%Example: cosine(3,:) is 2*cosine(0 to pi)
% cosine(:,1) is (0 to width of image)*cosine(0)
cosine = (0:width-1)'*cos(theta); %Matrix Outerproduct
sine = (0:height-1)'*sin(theta); %Matrix Outerproduct
accumulator((1:numEdgePixels),:) = cosine(xIndicies,:) + sine(yIndicies,:);
%Scan over the thetas and bin the rhos
for i = (1:numThetas)
houghSpace(:,i) = hist(accumulator(:,i),rho);
end
pcolor(theta,rho,houghSpace);
shading flat;
title('Hough Transform');
xlabel('Theta (radians)');
ylabel('Rho (pixels)');
colormap('gray');
end