function [Q] = Q_RL(I, phi)
% 
% Written by:
% -- 
% John L. Weatherwax                2005-08-04
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
% Epage 
% 
%-----

[di,dj] = phi_to_xy_increment(phi);

% Make sure that the pixels of I have values that are indexed from 1,2,...N_g this way we can use MATLAB one based indexing
uElts = unique( I(:) );
N_g   = length(uElts);
Icp   = zeros(size(I));
for ii=1:N_g
  inds = find( I(:)==uElts(ii) );
  Icp(inds) = ii;
end
I = Icp;

[M,N] = size(I);
N_r   = max(M,N);
Q     = zeros(N_g,N_r);

for ii=1:M % row index 
  for jj=1:N % column index 

    Iij = I(ii,jj);
    
    % Determine if this pixel already in a run...
    d = -1; % try to step backwards
    ii_new = ii+di*d;
    in_I_Range = (ii_new > 0) && (ii_new < M+1);
    jj_new = jj+dj*d;
    in_J_Range = (jj_new > 0) && (jj_new < N+1);
    if( in_I_Range && in_J_Range && (Iij==I(ii_new,jj_new)) )
      pixel_already_in_a_run = 1;
    else
      pixel_already_in_a_run = 0;      
    end
    
    % find the longest run length starting at (ii,jj) and going in direction phi:
    %
    mrl = max_run_length_phi(I, ii,jj, phi);
    
    if( ~pixel_already_in_a_run )
      Q(Iij,mrl+1) = Q(Iij,mrl+1) + 1;
    end
    
  end
end