How to do Interpolation for paired images.?

I have a pair of projected images of a 3d object and I want to find the intermediate image between the projected images by interpolation in Fourier domain. Eg the projected images are at 0 degree and 50°. How to find the intermediate image say @ 25° by interpolation 2/1 in fourier domain..??

Answer 1

[Matt J]

This might help,

https://www.mathworks.com/matlabcentral/fileexchange/22665-n-dimensional-fourier-interpolation

[Sebastian Joseph]

Thanks.

I wish to have out put image as interpolated one in between the source image projection angles. It can be done through either interp1 or interp2. I would like to have pixel to pixel comparison and the midplane or image interpolant point be half of the pixel difference between the source ones. How can I proceed for simplified versions?.?

[Sebastian Joseph]

Hi,

I tried for one of the ways as shown in below for interpolation, but every time i am getting the result (attached) and is far away from which i want. I want a result similar to the input images but in a projection angle of 25 degree.

The code:.

%%
clc; clear all; 
close all;

% Initialization of Input Images

A1 = im2double(rgb2gray(imread('cuphex 0degree.png')));
A5 = im2double(rgb2gray(imread('cuphex 50degree.png')));

% Fourier Transorm of Input Image

A1 = fftshift(fft2(ifftshift(1.*A1)));
A5 = fftshift(fft2(ifftshift(1.*A5)));


[M,N] = size(A1);
Nx = N;
Mx = 2*N;

height = size(A1,1);
width = size(A1,2);


%Taking Vectors from input images

for ii = 1:height

    input_fftA1 = A1(ii,:,:);
    input_fftA1(:,1:2:2*N) = A1(ii,:,:);
    
    [x y] = size(input_fftA1);
    [x0 y0] = meshgrid(1:y, 1:x);
    
    input_fftA5 = A5(ii,:,:);
    input_fftA5(:,2:2:2*N) = A5(ii,:,:);
    
    [x1 y1] = size(input_fftA5);
    [x01 y01] = meshgrid(1:y1, 1:x1);

%     figure(1), imagesc(abs(input_fftA1));
%     figure(3), imagesc(abs(input_fftA5));
        
end 

% Interpolation Plane
      mj1 = 1.5:2:2*Mx+1;
      mj2 = 1.5:2:2*M+1;
      mj3 = mj2'+mj1;
      
%       figure(), plot(mj1);
%       figure(), imagesc(mj1);
%       hold all
%       figure(), plot(mj2);
%       figure(), imagesc(mj2);
%       figure(), plot(mj3);
%       figure(), imagesc(mj3);

% Interpolation

 Out_img = interp2(x0,y0,mj3,x01,y01, 'linear'); %spline , 'extrap'

 
 imagesc(Out_img);
 
 out = Out_img;
 out(isnan(out))=0;%replace Nan
 plot(out);
out1=reshape(out,length(N),[]);

plot(out1);
imagesc(out1);

% IFFT of the result
% Fourier Transorm of Input Image

A3 = fftshift(ifft2(ifftshift(out1)));
imagesc(A3);

I am really got stucked with this. Could you let me know where i am making mistake..??

[Sebastian Joseph]

I would like to have intermediate image between paired image. between 0 and 50 degree image. some what 25 degree image like this.(attached)