efficient_subpixel_registration.rar_REGISTRATION_The D.A._subpix

function [output Greg] = dftregistration(buf1ft,buf2ft,usfac) % function [output Greg] = dftregistration(buf1ft,buf2ft,usfac); % Efficient subpixel image registration by crosscorrelation. This code % gives the same precision as the FFT upsampled cross correlation in a % small fraction of the computation time and with reduced memory % requirements. It obtains an initial estimate of the crosscorrelation peak % by an FFT and then refines the shift estimation by upsampling the DFT % only in a small neighborhood of that estimate by means of a % matrix-multiply DFT. With this procedure all the image points are used to % compute the upsampled crosscorrelation. % Manuel Guizar - Dec 13, 2007 % Portions of this code were taken from code written by Ann M. Kowalczyk % and James R. Fienup. % J.R. Fienup and A.M. Kowalczyk, "Phase retrieval for a complex-valued % object by using a low-resolution image," J. Opt. Soc. Am. A 7, 450-458 % (1990). % Citation for this algorithm: % Manuel Guizar-Sicairos, Samuel T. Thurman, and James R. Fienup, % "Efficient subpixel image registration algorithms," Opt. Lett. 33, % 156-158 (2008). % Inputs % buf1ft Fourier transform of reference image, % DC in (1,1) [DO NOT FFTSHIFT] % buf2ft Fourier transform of image to register, % DC in (1,1) [DO NOT FFTSHIFT] % usfac Upsampling factor (integer). Images will be registered to % within 1/usfac of a pixel. For example usfac = 20 means the % images will be registered within 1/20 of a pixel. (default = 1) % Outputs % output = [error,diffphase,net_row_shift,net_col_shift] % error Translation invariant normalized RMS error between f and g % diffphase Global phase difference between the two images (should be % zero if images are non-negative). % net_row_shift net_col_shift Pixel shifts between images % Greg (Optional) Fourier transform of registered version of buf2ft, % the global phase difference is compensated for. % Default usfac to 1 if exist('usfac')~=1, usfac=1; end % Compute error for no pixel shift if usfac == 0, CCmax = sum(sum(buf1ft.*conj(buf2ft))); rfzero = sum(abs(buf1ft(:)).^2); rgzero = sum(abs(buf2ft(:)).^2); error = 1.0 - CCmax.*conj(CCmax)/(rgzero*rfzero); error = sqrt(abs(error)); diffphase=atan2(imag(CCmax),real(CCmax)); output=[error,diffphase]; % Whole-pixel shift - Compute crosscorrelation by an IFFT and locate the % peak elseif usfac == 1, [m,n]=size(buf1ft); CC = ifft2(buf1ft.*conj(buf2ft)); [max1,loc1] = max(CC); [max2,loc2] = max(max1); rloc=loc1(loc2); cloc=loc2; CCmax=CC(rloc,cloc); rfzero = sum(abs(buf1ft(:)).^2)/(m*n); rgzero = sum(abs(buf2ft(:)).^2)/(m*n); error = 1.0 - CCmax.*conj(CCmax)/(rgzero(1,1)*rfzero(1,1)); error = sqrt(abs(error)); diffphase=atan2(imag(CCmax),real(CCmax)); md2 = fix(m/2); nd2 = fix(n/2); if rloc > md2 row_shift = rloc - m - 1; else row_shift = rloc - 1; end if cloc > nd2 col_shift = cloc - n - 1; else col_shift = cloc - 1; end output=[error,diffphase,row_shift,col_shift]; % Partial-pixel shift else % First upsample by a factor of 2 to obtain initial estimate % Embed Fourier data in a 2x larger array [m,n]=size(buf1ft); mlarge=m*2; nlarge=n*2; CC=zeros(mlarge,nlarge); CC(m+1-fix(m/2):m+1+fix((m-1)/2),n+1-fix(n/2):n+1+fix((n-1)/2)) = ... fftshift(buf1ft).*conj(fftshift(buf2ft)); % Compute crosscorrelation and locate the peak CC = ifft2(ifftshift(CC)); % Calculate cross-correlation [max1,loc1] = max(CC); [max2,loc2] = max(max1); rloc=loc1(loc2);cloc=loc2; CCmax=CC(rloc,cloc); % Obtain shift in original pixel grid from the position of the % crosscorrelation peak [m,n] = size(CC); md2 = fix(m/2); nd2 = fix(n/2); if rloc > md2 row_shift = rloc - m - 1; else row_shift = rloc - 1; end if cloc > nd2 col_shift = cloc - n - 1; else col_shift = cloc - 1; end row_shift=row_shift/2; col_shift=col_shift/2; % If upsampling > 2, then refine estimate with matrix multiply DFT if usfac > 2, %%% DFT computation %%% % Initial shift estimate in upsampled grid row_shift = round(row_shift*usfac)/usfac; col_shift = round(col_shift*usfac)/usfac; dftshift = fix(ceil(usfac*1.5)/2); %% Center of output array at dftshift+1 % Matrix multiply DFT around the current shift estimate CC = conj(dftups(buf2ft.*conj(buf1ft),ceil(usfac*1.5),ceil(usfac*1.5),usfac,... dftshift-row_shift*usfac,dftshift-col_shift*usfac))/(md2*nd2*usfac^2); % Locate maximum and map back to original pixel grid [max1,loc1] = max(CC); [max2,loc2] = max(max1); rloc = loc1(loc2); cloc = loc2; CCmax = CC(rloc,cloc); rg00 = dftups(buf1ft.*conj(buf1ft),1,1,usfac)/(md2*nd2*usfac^2); rf00 = dftups(buf2ft.*conj(buf2ft),1,1,usfac)/(md2*nd2*usfac^2); rloc = rloc - dftshift - 1; cloc = cloc - dftshift - 1; row_shift = row_shift + rloc/usfac; col_shift = col_shift + cloc/usfac; % If upsampling = 2, no additional pixel shift refinement else rg00 = sum(sum( buf1ft.*conj(buf1ft) ))/m/n; rf00 = sum(sum( buf2ft.*conj(buf2ft) ))/m/n; end error = 1.0 - CCmax.*conj(CCmax)/(rg00*rf00); error = sqrt(abs(error)); diffphase=atan2(imag(CCmax),real(CCmax)); % If its only one row or column the shift along that dimension has no % effect. We set to zero. if md2 == 1, row_shift = 0; end if nd2 == 1, col_shift = 0; end output=[error,diffphase,row_shift,col_shift]; end % Compute registered version of buf2ft if (nargout > 1)&&(usfac > 0), [nr,nc]=size(buf2ft); Nr = ifftshift([-fix(nr/2):ceil(nr/2)-1]); Nc = ifftshift([-fix(nc/2):ceil(nc/2)-1]); [Nc,Nr] = meshgrid(Nc,Nr); Greg = buf2ft.*exp(i*2*pi*(-row_shift*Nr/nr-col_shift*Nc/nc)); Greg = Greg*exp(i*diffphase); elseif (nargout > 1)&&(usfac == 0) Greg = buf2ft*exp(i*diffphase); end return function out=dftups(in,nor,noc,usfac,roff,coff) % function out=dftups(in,nor,noc,usfac,roff,coff); % Upsampled DFT by matrix multiplies, can compute an upsampled DFT in just % a small region. % usfac Upsampling factor (default usfac = 1) % [nor,noc] Number of pixels in the output upsampled DFT, in % units of upsampled pixels (default = size(in)) % roff, coff Row and column offsets, allow to shift the output array to % a region of interest on the DFT (default = 0) % Recieves DC in upper left corner, image center must be in (1,1) % Manuel Guizar - Dec 13, 2007 % Modified from dftus, by J.R. Fienup 7/31/06 % This code is intended to provide the same result as if the following % operations were performed % - Embed the array "in" in an array that is usfac times larger in each % dimension. ifftshift to bring the center of the image to (1,1). % - Take the FFT of the larger array % - Extract an [nor, noc] region of the result. Starting with the % [roff+1 coff+1] element. % It achieves this result by computing the DFT in the output array without % the need to zeropad. Much faster and memory efficient than the % zero-padded FFT approach if [nor noc] are much smaller than [nr*usfac nc*usfac] [nr,nc]=size(in); % Set defaults if exist('roff')~=1, roff=0; end if exist('coff')~=1, coff=0; end if exist('usfac')~=1, usfac=1; end if exist('noc')~=1, noc=nc; end if exist('nor')~=1, nor=nr; end % Compute kernels and obtain DFT by matr