MATLAB: Can anyone show me the algorithm to perform bi-cubic interpolation of an image

bi-cubic interpolation

I need to determine bi-cubic interpolation of an image. Please show me how it is done.

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I = imread('cameraman.tif') ;
[nx,ny] =size(I) ;
[X,Y] = meshgrid(1:ny,1:nx) ;
x = linspace(1,nx,500) ;
y = linspace(1,ny,500) ;
[Xi,Yi] = meshgrid(x,y) ;
I1 = interp2(X,Y,double(I),Xi,Yi) ;
imshow(uint8(I1)) ;

Also have a look on imresize

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MATLAB: Algorithm of Bicubic Interpolation

The algorithm is described in the following reference.

% "Cubic Convolution Interpolation for Digital Image % Processing", Robert G. Keys, IEEE Trans. on Acoustics, Speech, and % Signal Processing, Vol. 29, No. 6, Dec. 1981, pp. 1153-1160.

Its convolution based interpolation. The specific cubic convolution kernel is described in terms of a piecewise equation in MATLAB code before. This will make more sense if you have access to the paper.

y = zeros(1,length(x));
reshape(y,size(x));
x(x < 0.0) = -x(x < 0.0);
q = (x <= 1);            % Coefficients: 1.5, -2.5, 0.0, 1.0
y(q) = ((1.5 * x(q) - 2.5) .* x(q)) .* x(q) + 1.0;
q = (1 < x & x <= 2);    % Coefficients: -0.5, 2.5, -4.0, 2.0
y(q) = ((-0.5 * x(q) + 2.5) .* x(q) - 4.0) .* x(q) + 2.0;

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MATLAB: Algorithm of Bicubic Interpolation

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