Resolution project
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This document provides code for a function called finterp that uses Fourier interpolation to increase the sampling of an image. The function takes an input image, desired new size, and optional apodization filter as inputs. It pads the Fourier transformed image, applies an optional Hanning filter, performs inverse Fourier transform and rescaling to produce the output image.
![RESOLUTION PROJECT (SAMPLE ASSIGNMENT)
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This sample assignment Use Fourier interpolation to increase sampling of an image. Also
includes an optional filter.
finterp(f,newsize,apod)
function f1 = finterp(f,newsize,apod)
% NEWIMAGE = finterp(IMAGE,NEWSIZE,APOD)
% Resizes the image IMAGE using Fourier interpolation.
%
% NEWSIZE is the desired size of the interpolated image. This can be a
% 2-element vector for non-square images. If NEWSIZE is a scalar, the
% output image will be square (i.e. NEWSIZE=256 will create a 256x256 image).
%
% APOD is an optional parameter to apodize the image (by a Hanning filter)
% to reduce ringing in the output image
% APOD = 0 or blank (DEFAULT) -- no apodization
% 0 < APOD < 1 -- Apodize
%
% The Hanning filter is = 1 for x<xL
% = 0 for x>xH
% between xL and xH, the filter transmission is a half-cycle of cos^2
% For this function, xH is assumed to be the highest frequency in f, and
% xL = APOD * xH
%
% Michael Hawks, Department of Engineering Physics, Air Force Institute of
% Technology
% 5 July 2013
if nargin<3, apod=0;
elseif apod>=1, error('ERROR: APOD must be between 0 and 1');
end
if ndims(f)~=2, error('ERROR: FINTERP only defined for 2-D arrays'); beep; end
newsize=[1,1].*newsize; % ensure newsize is 2D -- if input is one number, this makes a
info@assignmentpedia.com](https://image.slidesharecdn.com/resolutionproject-130919065835-phpapp01/85/Resolution-project-1-320.jpg)
![square array
if any(size(f)>newsize), f1=f; return; end;
maxI = max(max(f));
minI = min(min(f));
pad = newsize - size(f); % number of elements to add
pad1 = floor(pad/2); % portion to add to right/top
pad2 = pad - pad1; % remainder add to left/bottom
F = fft2(f);
Fpad = padarray(fftshift(F),pad1,'pre');
Fpad = padarray(Fpad,pad2,'post');
if apod>0
[Nx,Ny]=size(Fpad);
H = 0.5.*size(F); % use this as the high-freq cutoff (from -H to +H)
if isodd(Nx); x = -floor(Nx/2):floor(Nx/2);
else x = -((Nx/2)-1):(Nx/2);
end
if isodd(Ny); y = -floor(Ny/2):floor(Ny/2);
else y = -((Ny/2)-1):(Ny/2);
end
filt = hanning(x,apod*H(1),H(1))' * hanning(y,apod*H(2),H(2));
Fpad = Fpad.*filt;
end
ft = ifft2(ifftshift(Fpad));
f1 = (ft.*conj(ft)).^0.5; % assume we want a real-valued image out, but asymmetric padding
could add an
% imaginary componenet so we approximate by SQRT(F F*)
% rescale/normalize the image. This is kind of a hack, but it should take
% care of everything
f1 = f1 - min(min(f1)); f1 = f1./max(max(f1));
f1 = f1 .* maxI + minI;
% ...............
function i = isodd(x)
i = ( floor(x/2) ~= (x/2) );
% ...............
function f = hanning(x,xL,xH)](https://image.slidesharecdn.com/resolutionproject-130919065835-phpapp01/85/Resolution-project-2-320.jpg)
Resolution project
- 1. RESOLUTION PROJECT (SAMPLE ASSIGNMENT) Our online Tutors are available 24*7 to provide Help with Help with Resolution Project Homework/Assignment or a long term Graduate/Undergraduate Help with Resolution Project. Our Tutors being experienced and proficient in Help with Resolution Project ensure to provide high quality Help with Resolution Project Homework Help. Upload your Help with Resolution Project Assignment at ‘Submit Your Assignment’ button or email it to . You can use our ‘Live Chat’ option to schedule an Online Tutoring session with our Help with Resolution Project Tutors. This sample assignment Use Fourier interpolation to increase sampling of an image. Also includes an optional filter. finterp(f,newsize,apod) function f1 = finterp(f,newsize,apod) % NEWIMAGE = finterp(IMAGE,NEWSIZE,APOD) % Resizes the image IMAGE using Fourier interpolation. % % NEWSIZE is the desired size of the interpolated image. This can be a % 2-element vector for non-square images. If NEWSIZE is a scalar, the % output image will be square (i.e. NEWSIZE=256 will create a 256x256 image). % % APOD is an optional parameter to apodize the image (by a Hanning filter) % to reduce ringing in the output image % APOD = 0 or blank (DEFAULT) -- no apodization % 0 < APOD < 1 -- Apodize % % The Hanning filter is = 1 for x<xL % = 0 for x>xH % between xL and xH, the filter transmission is a half-cycle of cos^2 % For this function, xH is assumed to be the highest frequency in f, and % xL = APOD * xH % % Michael Hawks, Department of Engineering Physics, Air Force Institute of % Technology % 5 July 2013 if nargin<3, apod=0; elseif apod>=1, error('ERROR: APOD must be between 0 and 1'); end if ndims(f)~=2, error('ERROR: FINTERP only defined for 2-D arrays'); beep; end newsize=[1,1].*newsize; % ensure newsize is 2D -- if input is one number, this makes a [email protected]
- 2. square array if any(size(f)>newsize), f1=f; return; end; maxI = max(max(f)); minI = min(min(f)); pad = newsize - size(f); % number of elements to add pad1 = floor(pad/2); % portion to add to right/top pad2 = pad - pad1; % remainder add to left/bottom F = fft2(f); Fpad = padarray(fftshift(F),pad1,'pre'); Fpad = padarray(Fpad,pad2,'post'); if apod>0 [Nx,Ny]=size(Fpad); H = 0.5.*size(F); % use this as the high-freq cutoff (from -H to +H) if isodd(Nx); x = -floor(Nx/2):floor(Nx/2); else x = -((Nx/2)-1):(Nx/2); end if isodd(Ny); y = -floor(Ny/2):floor(Ny/2); else y = -((Ny/2)-1):(Ny/2); end filt = hanning(x,apod*H(1),H(1))' * hanning(y,apod*H(2),H(2)); Fpad = Fpad.*filt; end ft = ifft2(ifftshift(Fpad)); f1 = (ft.*conj(ft)).^0.5; % assume we want a real-valued image out, but asymmetric padding could add an % imaginary componenet so we approximate by SQRT(F F*) % rescale/normalize the image. This is kind of a hack, but it should take % care of everything f1 = f1 - min(min(f1)); f1 = f1./max(max(f1)); f1 = f1 .* maxI + minI; % ............... function i = isodd(x) i = ( floor(x/2) ~= (x/2) ); % ............... function f = hanning(x,xL,xH)
- 3. if ndims(squeeze(x))==1, x=1:x; dx=1; else dx=abs(x(2)-x(1)); end f=zeros(1,length(x)); if x(1) >= 0; % one-sided filter jL = find(abs(x-xL)<dx,1); if isnan(jL); jL=1; end jH = find(abs(x-xH)<dx,1); if isnan(jH); jH=length(x); end f(1:jL)=1; f(jH:end)=0; k = jL:jH; f(k)=0.5 + 0.5*cos(pi*(k-jL)/(jH-jL)); else j1 = find(abs(x+xL)<dx,1); if isnan(j1); j1=1; end j2 = find(abs(x-xL)<dx,1); if isnan(j2); j2=length(x); end j3 = find(abs(x+xH)<dx,1); if isnan(j3); j3=1; end j4 = find(abs(x-xH)<dx,1); if isnan(j4); j4=length(x); end f(1:j3)=0; f(j4:end)=0; f(j1:j2)=1; k = j2:j4; f(k)=0.5 + 0.5*cos(pi*(k-j2)/(j4-j2)); k = j3:j1; f(k)=0.5 - 0.5*cos(pi*(k-j3)/(j3-j1)); end visit us at www.assignmentpedia.com or email us at [email protected] or call us at +1 520 8371215