Question

I am trying to implement the generalized Hough transform as presented in this paper in MATLAB. I’ve also tried using this document to understand the algorithm. I am stuck on figuring out how to calculate the gradient angle to find Φ to use in the R-Table.

I have tried to run this matlab implementation, but the contour function tries to access negative indices. The missing functions are below.

distance.m

function [ d ] = distance( x1, y1, x2, y2 )
  d = sqrt( (x2-x1)^2 + (y2-y1)^2 );   
end

barycenter.m

function [ xo, yo ] = barycenter( img )
%   gravitational center coordinates of a shape 

  [rows, cols] = size(img);
  x = ones(rows, 1)*(1:cols);
  y = (1:rows)'*ones(1,cols);
  area = sum(sum(img));
  xo = sum(sum(double(img) .* x)) / area;
  yo = sum(sum(double(img) .* y)) / area;

end

modelHough.m

function [H]=ModelHough(imgRGB)
% Generalized Hough Transform Modeling

% Image Binarization
imgBW = rgb2gray(imgRGB);
imgBI = imgBW < 255;

% Retrieving information about the contour: points and number (N)
N = contour(imgBI);

% Model initialization:
    % row = beta value * 100
    % column = number of the couple (alpha, distance)
    % 3rd dimension: 1 = alpha, 2 = distance
H=zeros(round(100*2*pi),N,2);

% Compute of the barycenter coordinates
[ xo, yo ] = barycenter(imgBI);

% for each contour point
for i=1:N

    % beta compute for ith contour point
    b = beta(N, imgBI, i);

    % research of the first column
    k=1;
    while H(b+1,k,2)~=0
       k=k+1;
    end

    % compute of the alpha value
    H(b+1, k, 1) = alpha(N, i, imgBI);

    % compute of the distance value
    H(b+1, k, 2) = distance( xo, yo, i, b );

end

Answer 1

Use a suitable edge detector. You could start off with the Sobel operator. The gradient angle is atan(Gy/Gx) as described in the wiki article.