标签：end 变换 crop zernike zern indices Zernike 泽泥克
function zern = zernike(r,t,n,m)
% Returns a matrix corresponding to the Zernike polynomial of radial
% degree n and azimuthal degree m.
% Matrices r and t correspond to the radii and angles of points on an
% x-y grid satisfying 1>x>-1 and 1>y>-1; they are obtained via
% cart2pol. See example for clarification.
% Must satisfy n - m >= 0, n - m even, and n >= 0. n and m are
% both integers.
% Function elliptical_crop should be used in this context to ignore all
% data outside of the unit circle.
%
% Example 1:
%
% % Display the 'power' Zernike polynomial (n = 2, m = 0) over a
% % 100x100 grid.
%
% x=linspace(-1,1,100);
% y=linspace(1,-1,100);
% [x,y] = meshgrid(x,y);
% [t,r] = cart2pol(x,y);
% z_power = zernike(r,t,2,0);
% figure, imagesc(elliptical_crop(z_power,1));
% colormap jet;
%
% Example 2:
%
% % Display all Zernike polynomials up to radial degree 4 over a
% % 100x100 grid.
%
% for n = 0:4
% for m = -n:2:n
% x=linspace(-1,1,100);
% y=linspace(1,-1,100);
% [x,y] = meshgrid(x,y);
% [t,r] = cart2pol(x,y);
% zern_mat = zernike(r,t,n,m);
% figure, imagesc(elliptical_crop(zern_mat,1));
% title(strcat('n = ',{' '},string(n),', m = ',{' '},string(m)));
% colormap jet;
% end
% end
%
%
% Functions required for use: elliptical_crop, zernike_radial
% See also: zernike_moments, zernike_recreation
%
% Evan Czako, 8.14.2019
% -------------------------------------------
if mod(n-m,2) == 1
error('n-m must be even');
end
if n < 0
error('n must both be positive')
end
if floor(n) ~= n || floor(m) ~= m
error('n and m must both be integers')
end
if m < 0
zern = -zernike_radial(r,n,-m).*sin(m*t);
else
zern = zernike_radial(r,n,m).*cos(m*t);
end
end
function zernikeMatrices = zernike_mats(im,zernike_indices)
% Returns an array of matrices corresponding to the Zernike polynomials
% of degrees n and m as defined by the two columns of zernike_indices,
% where the first column contains values of n and the second column
% contains values of m. The dimensions of these matrices will be the
% same as that of im.
% This code is intended to be used as a helper function for
% zernike_moments and zernike_recreation.
%
% Example:
%
% % Create some function z(x,y) over a 125x75 grid.
%
% x=linspace(-1,1,75);
% y=linspace(1,-1,125);
% [x,y] = meshgrid(x,y);
% z = x.^2+y;
% figure,imagesc(elliptical_crop(z,1));
% colormap jet;
% title('z(x,y)');
%
% % Specify the indices of Zernike polynomials of interest. In this
% % case, the indices correspond to the "piston", "x-tilt", "y-tilt",
% % and "power" Zernike polynomials.
%
% indices = [0 0; 1 -1; 1 1; 2 0];
% zern_mats = zernike_mats(z,indices);
% for i = 1:size(zern_mats,3)
% figure, imagesc(elliptical_crop(zern_mats(:,:,i),1));
% colormap jet;
% title(indices(i,:));
% end
%
% % The images displayed show these four Zernike polynomials over
% % 125x75 grids.
%
% Functions required for use: zernike, zernike_radial, elliptical_crop
% See also: zernike_moments, zernike_recreation
%
% Evan Czako, 8.14.2019
% -------------------------------------------
dim=size(im);
x=linspace(-1,1,dim(2));
y=linspace(1,-1,dim(1));
[x,y] = meshgrid(x,y);
[t,r] = cart2pol(x,y);
zernikeMatrices = [];
for i = 1:size(zernike_indices,1)
zernikeMatrices(:,:,i) = zernike(r,t,zernike_indices(i,1),zernike_indices(i,2));
zernikeMatrices(:,:,i) = elliptical_crop(zernikeMatrices(:,:,i),1);
end
end
标签：end,变换,crop,zernike,zern,indices,Zernike,泽泥克 来源： https://blog.csdn.net/casioplmf/article/details/122030361
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