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224 lines
9.3 KiB
Matlab
224 lines
9.3 KiB
Matlab
function [output, Greg] = dftregistration(buf1ft,buf2ft,usfac)
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% function [output Greg] = dftregistration(buf1ft,buf2ft,usfac);
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% Efficient subpixel image registration by crosscorrelation. This code
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% gives the same precision as the FFT upsampled cross correlation in a
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% small fraction of the computation time and with reduced memory
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% requirements. It obtains an initial estimate of the crosscorrelation peak
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% by an FFT and then refines the shift estimation by upsampling the DFT
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% only in a small neighborhood of that estimate by means of a
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% matrix-multiply DFT. With this procedure all the image points are used to
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% compute the upsampled crosscorrelation.
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% Manuel Guizar - Dec 13, 2007
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%
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% Rewrote all code not authored by either Manuel Guizar or Jim Fienup
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% Manuel Guizar - May 13, 2016
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%
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% Citation for this algorithm:
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% Manuel Guizar-Sicairos, Samuel T. Thurman, and James R. Fienup,
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% "Efficient subpixel image registration algorithms," Opt. Lett. 33,
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% 156-158 (2008).
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%
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% Inputs
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% buf1ft Fourier transform of reference image,
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% DC in (1,1) [DO NOT FFTSHIFT]
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% buf2ft Fourier transform of image to register,
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% DC in (1,1) [DO NOT FFTSHIFT]
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% usfac Upsampling factor (integer). Images will be registered to
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% within 1/usfac of a pixel. For example usfac = 20 means the
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% images will be registered within 1/20 of a pixel. (default = 1)
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%
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% Outputs
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% output = [error,diffphase,net_row_shift,net_col_shift]
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% error Translation invariant normalized RMS error between f and g
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% diffphase Global phase difference between the two images (should be
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% zero if images are non-negative).
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% net_row_shift net_col_shift Pixel shifts between images
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% Greg (Optional) Fourier transform of registered version of buf2ft,
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% the global phase difference is compensated for.
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% Copyright (c) 2016, Manuel Guizar Sicairos, James R. Fienup, University of Rochester
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% All rights reserved.
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%
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% Redistribution and use in source and binary forms, with or without
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% modification, are permitted provided that the following conditions are
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% met:
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%
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% * Redistributions of source code must retain the above copyright
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% notice, this list of conditions and the following disclaimer.
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% * Redistributions in binary form must reproduce the above copyright
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% notice, this list of conditions and the following disclaimer in
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% the documentation and/or other materials provided with the distribution
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% * Neither the name of the University of Rochester nor the names
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% of its contributors may be used to endorse or promote products derived
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% from this software without specific prior written permission.
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%
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% THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
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% AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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% IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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% ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
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% LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
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% CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
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% SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
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% INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
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% CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
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% ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
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% POSSIBILITY OF SUCH DAMAGE.
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if ~exist('usfac','var')
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usfac = 1;
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end
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[nr,nc]=size(buf2ft);
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Nr = ifftshift(-fix(nr/2):ceil(nr/2)-1);
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Nc = ifftshift(-fix(nc/2):ceil(nc/2)-1);
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if usfac == 0
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% Simple computation of error and phase difference without registration
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CCmax = sum(buf1ft(:).*conj(buf2ft(:)));
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row_shift = 0;
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col_shift = 0;
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elseif usfac == 1
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% Single pixel registration
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CC = ifft2(buf1ft.*conj(buf2ft));
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CCabs = abs(CC);
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[row_shift, col_shift] = find(CCabs == max(CCabs(:)));
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CCmax = CC(row_shift,col_shift)*nr*nc;
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% Now change shifts so that they represent relative shifts and not indices
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row_shift = Nr(row_shift);
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col_shift = Nc(col_shift);
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elseif usfac > 1
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% Start with usfac == 2
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CC = ifft2(FTpad(buf1ft.*conj(buf2ft),[2*nr,2*nc]));
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CCabs = abs(CC);
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[row_shift, col_shift] = find(CCabs == max(CCabs(:)),1,'first');
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CCmax = CC(row_shift,col_shift)*nr*nc;
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% Now change shifts so that they represent relative shifts and not indices
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Nr2 = ifftshift(-fix(nr):ceil(nr)-1);
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Nc2 = ifftshift(-fix(nc):ceil(nc)-1);
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row_shift = Nr2(row_shift)/2;
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col_shift = Nc2(col_shift)/2;
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% If upsampling > 2, then refine estimate with matrix multiply DFT
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if usfac > 2,
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%%% DFT computation %%%
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% Initial shift estimate in upsampled grid
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row_shift = round(row_shift*usfac)/usfac;
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col_shift = round(col_shift*usfac)/usfac;
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dftshift = fix(ceil(usfac*1.5)/2); %% Center of output array at dftshift+1
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% Matrix multiply DFT around the current shift estimate
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CC = conj(dftups(buf2ft.*conj(buf1ft),ceil(usfac*1.5),ceil(usfac*1.5),usfac,...
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dftshift-row_shift*usfac,dftshift-col_shift*usfac));
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% Locate maximum and map back to original pixel grid
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CCabs = abs(CC);
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[rloc, cloc] = find(CCabs == max(CCabs(:)),1,'first');
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CCmax = CC(rloc,cloc);
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rloc = rloc - dftshift - 1;
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cloc = cloc - dftshift - 1;
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row_shift = row_shift + rloc/usfac;
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col_shift = col_shift + cloc/usfac;
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end
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% If its only one row or column the shift along that dimension has no
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% effect. Set to zero.
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if nr == 1,
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row_shift = 0;
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end
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if nc == 1,
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col_shift = 0;
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end
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end
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rg00 = sum(abs(buf1ft(:)).^2);
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rf00 = sum(abs(buf2ft(:)).^2);
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error = 1.0 - abs(CCmax).^2/(rg00*rf00);
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error = sqrt(abs(error));
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diffphase = angle(CCmax);
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output=[error,diffphase,row_shift,col_shift];
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% Compute registered version of buf2ft
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if (nargout > 1)&&(usfac > 0),
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[Nc,Nr] = meshgrid(Nc,Nr);
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Greg = buf2ft.*exp(1i*2*pi*(-row_shift*Nr/nr-col_shift*Nc/nc));
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Greg = Greg*exp(1i*diffphase);
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elseif (nargout > 1)&&(usfac == 0)
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Greg = buf2ft*exp(1i*diffphase);
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end
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return
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function out=dftups(in,nor,noc,usfac,roff,coff)
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% function out=dftups(in,nor,noc,usfac,roff,coff);
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% Upsampled DFT by matrix multiplies, can compute an upsampled DFT in just
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% a small region.
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% usfac Upsampling factor (default usfac = 1)
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% [nor,noc] Number of pixels in the output upsampled DFT, in
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% units of upsampled pixels (default = size(in))
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% roff, coff Row and column offsets, allow to shift the output array to
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% a region of interest on the DFT (default = 0)
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% Recieves DC in upper left corner, image center must be in (1,1)
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% Manuel Guizar - Dec 13, 2007
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% Modified from dftus, by J.R. Fienup 7/31/06
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% This code is intended to provide the same result as if the following
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% operations were performed
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% - Embed the array "in" in an array that is usfac times larger in each
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% dimension. ifftshift to bring the center of the image to (1,1).
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% - Take the FFT of the larger array
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% - Extract an [nor, noc] region of the result. Starting with the
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% [roff+1 coff+1] element.
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% It achieves this result by computing the DFT in the output array without
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% the need to zeropad. Much faster and memory efficient than the
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% zero-padded FFT approach if [nor noc] are much smaller than [nr*usfac nc*usfac]
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[nr,nc]=size(in);
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% Set defaults
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if exist('roff', 'var')~=1, roff=0; end
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if exist('coff', 'var')~=1, coff=0; end
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if exist('usfac','var')~=1, usfac=1; end
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if exist('noc', 'var')~=1, noc=nc; end
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if exist('nor', 'var')~=1, nor=nr; end
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% Compute kernels and obtain DFT by matrix products
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kernc=exp((-1i*2*pi/(nc*usfac))*( ifftshift(0:nc-1).' - floor(nc/2) )*( (0:noc-1) - coff ));
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kernr=exp((-1i*2*pi/(nr*usfac))*( (0:nor-1).' - roff )*( ifftshift([0:nr-1]) - floor(nr/2) ));
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out=kernr*in*kernc;
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return
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function [ imFTout ] = FTpad(imFT,outsize)
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% imFTout = FTpad(imFT,outsize)
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% Pads or crops the Fourier transform to the desired ouput size. Taking
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% care that the zero frequency is put in the correct place for the output
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% for subsequent FT or IFT. Can be used for Fourier transform based
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% interpolation, i.e. dirichlet kernel interpolation.
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%
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% Inputs
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% imFT - Input complex array with DC in [1,1]
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% outsize - Output size of array [ny nx]
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%
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% Outputs
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% imout - Output complex image with DC in [1,1]
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% Manuel Guizar - 2014.06.02
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if ~ismatrix(imFT)
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error('Maximum number of array dimensions is 2')
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end
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Nout = outsize;
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Nin = size(imFT);
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imFT = fftshift(imFT);
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center = floor(size(imFT)/2)+1;
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imFTout = zeros(outsize,'like', imFT);
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centerout = floor(size(imFTout)/2)+1;
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% imout(centerout(1)+[1:Nin(1)]-center(1),centerout(2)+[1:Nin(2)]-center(2)) ...
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% = imFT;
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cenout_cen = centerout - center;
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imFTout(max(cenout_cen(1)+1,1):min(cenout_cen(1)+Nin(1),Nout(1)),max(cenout_cen(2)+1,1):min(cenout_cen(2)+Nin(2),Nout(2))) ...
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= imFT(max(-cenout_cen(1)+1,1):min(-cenout_cen(1)+Nout(1),Nin(1)),max(-cenout_cen(2)+1,1):min(-cenout_cen(2)+Nout(2),Nin(2)));
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imFTout = ifftshift(imFTout)*Nout(1)*Nout(2)/(Nin(1)*Nin(2));
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return
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