# Generalized Hough Transform in Matlab

The generalized Hough transform (GHT), introduced by Dana H. Ballard in 1981, is the modification of the Hough transform using the principle of template matching. The Hough transform was initially developed to detect analytically defined shapes (e.g., line, circle, ellipse etc.). In these cases, we have knowledge of the shape and aim to find out its location and orientation in the image. This modification enables the Hough transform to be used to detect an arbitrary object described with its model.

I have implemented generalized Hough transform in Matlab. This implementation does not support rotation. The code below should be self-explanatory. If you have any question leave a comment!

For the sample input and output images, check the bottom of the post!target = imread('target.png');

reference = imread('reference.png');

% Convert Images to Grayscale:

% First save the original because at the end we will put marks on found

% templates from original image

original_target = target;

target = rgb2gray(target);

reference = rgb2gray(reference);

% Get edges with default threshold:

% I have tried different combinations of Sobel, Prewitt, Canny and Roberts.

% Almost all combinations are working(With different maximum values). The

% Canny seems the most slowest one but it seems like Canny is better in

% means of False Alarm situations. Probably thats why everybody is using

% Canny with Hough transfrom. I have also tried without applying any edge

% method and the code works fine. As far as I read, Hough transform doesn't

% have to work on binary images so, we can actually omit this step. But

% just for the sake of this assignment I will use the edge method which

% will help me get the best hough space in means of being observable by

% human eyes. With the "Sobel/Canny or Prewitt/Canny" 3 template image

% clearly visible but there are also very close maximas everywhere around

% the accumulator, but when I try Canny Canny there is a huge gap between

% true local maximas and others, therefore it has better visibility

%tic

target = edge(target,'Canny');

reference = edge(reference,'Canny');

%toc

% Reference Point: (Middle point)

refX = round(size(reference,1)/2);

refY = round(size(reference,2)/2);

% Get Reference edge point:

[x,y] = find(reference > 0);

maxAngels = 180;

maxPoints = size(x,1);

% Gradient of reference image:

dy = imfilter(double(reference),[1; -1],'same');

dx = imfilter(double(reference),[1 -1],'same');

reference_grad = atan2(dy,dx)*180/pi();

% Rtable:

rtable = zeros(maxAngels, maxPoints, 2);

binCount = zeros(maxAngels);

for i=1:1:maxPoints

bin = reference_grad(x(i), y(i)) + maxAngels;

binCount(bin) = binCount(bin) + 1;

Dx = x(i) - refX;

Dy = y(i) - refY;

rtable(bin, binCount(bin), 1) = Dx;

rtable(bin, binCount(bin), 2) = Dy;

end;

%--------------------------------------------------------------------------

%Accumulator:

% Get the target edge points

[x,y] = find(target > 0);

maxPoints_target = size(x,1);

% Gradient of target:

dy = imfilter(double(target),[1; -1],'same');

dx = imfilter(double(target),[1 -1],'same');

target_grad = atan2(dy,dx)*180/pi();

% Accumulator(Hough space):

size_target = size(target);

accumulator = zeros(size_target);

% Total match:

for i=1:1:maxPoints_target

% The gradient angle:

bin = target_grad(x(i), y(i)) + maxAngels;

for j = 1:1:binCount(bin)

tx = x(i) - rtable(bin, j, 1);

ty = y(i) - rtable(bin, j, 2);

if (tx>0) && (tx<size_target(1)) && (ty>0) && (ty<size_target(2))

accumulator(tx, ty) = accumulator(tx, ty)+1;

end;

end;

end;

%--------------------------------------------------------------------------

% Find local maxima:

max_value1 = max(max(accumulator));

[raw1,col1] = find(accumulator == max_value1);

% Second local maxima

max_value2 = max(max(accumulator(accumulator < (max_value1))));

[raw2,col2] = find(accumulator == max_value2);

% Display:

% P.S: When displaying all the graphs together on subplot, sometimes

% maximum points in accumulator image doesn't look as shiny as they

% actually are. If we display them seperately, we can clearly see them.

imshow(accumulator, []);

pause

imshow(target);

pause

imshow(original_target);

hold on;

plot(col1,raw1,'r.');

plot(col2,raw2,'r.');

pause

subplot(2,2,1),imshow(target),title('Target Image with Edges');

% ----------------------------------

% This part is just for Graph Title:

str = "Accumulator(x,y): ";

for i=1:size(raw1)

str1 = sprintf('(%d, %d) ',raw1(i),col1(i));

str = strcat(str,str1);

end;

for i=1:size(raw2)

str2 = sprintf('(%d, %d) ',raw2(i),col2(i));

str = strcat(str,str2);

end;

% ----------------------------------

subplot(2,2,2),imshow(accumulator, []),title(str);

subplot(2,2,[3,4]),imshow(original_target),title('Target Image with Found Templates ( Red Dots )');

hold on;

plot(col1,raw1,'r.'); % Put red dot

plot(col2,raw2,'r.');

Reference Image:

Target Image where we will be looking for the Reference Image:

Hough Space:

Final Result with little red dots on found templates:

hi thanks for your code and effort, but your code is broken espicaily in this line

“`if (tx>0) && (tx<size_target(1)) && (ty>0) && (ty<size_target(2))“`

Hello thanks for reporting in. First of all I just realised my <> signs are converted to html entities, sorry for that.

And when it comes to why it is not working I have no idea. Because I am sure that code was working. Probably it is converted badly when I posted here and I was still newbie in blogging back then 🙂

If I find my original work, I will replace it with the correct one but no promises.

Thank you again for pointing out.