function [A,CM,ift] = Appell_rotation_invariants(img,r,p,t,thres,center,radius,coef)
% Appellovy rotační invarianty A
% CM jsou Appellovy komplexní momenty před normalizací na rotaci
%
% img obrázek
% r maximální řád momentů
% p='U' momenty U, p='V' momenty V, 
% t typ normalizace k rotaci
% t=1; odečte se příslušný násobek fáze c_12
% t=2; vynásobí se příslušnou mocninou c_12
% thres práh absolutní hodnoty normalizačního momentu
% If center=1 center of the image is mapped onto the center of the unit disk.
% If center=2 centroid of the image is mapped onto the center of the unit disk.
% If radius=1, the most distant corner is mapped onto the unit circle.
% If radius=2, the most distant nonzero pixel is mapped onto the unit circle.
% If radius=3, the sqrt(m00), is mapped onto the unit circle.
% coef - the radius mapped onto the unit circle is multiplied by coef (implicitly 1).
% It should be set so all objects from a database were mapped into
% the unit disk.

% AM = am(img, r);
% AM = am_normalized(img,r,1,1,1);
% [M,N] = meshgrid(0:r);
% AM = AM./sqrt(factorial(M+N)).*gamma((M+N)/2+1)./factorial(M)./factorial(N);
% AH = amdef(img,r,r);
% AM = am_f(img,r);
% [su,sv]=deal(zeros(1,r+1));
% for ri=0:r
%     for p=0:ri
%         q=ri-p;
%         su(ri+1)=su(ri+1)+abs(AH(p+1,q+1));
%         sv(ri+1)=sv(ri+1)+abs(AM(p+1,q+1));
%     end
%     su(ri+1)=su(ri+1)/(ri+1);
%     sv(ri+1)=sv(ri+1)/(ri+1);
% end
% [M,N] = meshgrid(0:r);
% AM = AM.*(M+N+1)./sqrt(pi.*factorial(M+N).^1.5.*gamma((M+N)/2+1));

% AM = am_pseudonormalized(img,r,p,1,3,0.56);
% AM = am_pseudonormalized(img,r,p,2,3,1);
AM = am_pseudonormalized(img,r,p,center,radius,coef);
CM = cmfromgm(r,AM);
% A = RotInvs(CM,r,t);
[A,ift] = RotInvsSym(CM,r,t,thres);
end