Theory of Bicubic interpolation

39 views (last 30 days)
Shubha B.
Shubha B. on 23 Feb 2021
Commented: Shubha B. on 25 Feb 2021
For the bicubic code which is given in the this link https://www.mathworks.com/matlabcentral/answers/405846-bicubic-interpolation-direct-interpolation-formula-matlab-source-code, where can I get the expalnation of this code. The explanation which is given in the link https://en.wikipedia.org/wiki/Bicubic_interpolation
is not matching.

Answers (1)

Bruno Luong
Bruno Luong on 24 Feb 2021
Edited: Bruno Luong on 24 Feb 2021
It has been answered here
In 2D you do in one direction followedred by another.
%%
x = [-1:2];
y = [-1:2];
[X,Y] = meshgrid(x,y);
xq = rand;
yq = rand;
Z = rand(size(X));
Zq = interp2(x,y,Z,xq,yq,'bicubic')
% Check bicubic formula
Pl = [1.5,-2.5,0,1];
Pr = [-0.5,2.5,-4,2];
cubicp = @(x) (x<=1).*polyval(Pl,x) + (x>1 & x<2).*polyval(Pr,x);
cubic = @(x) cubicp(abs(x));
Zq = 0;
[~,i0] = histc(xq,x);
[~,j0] = histc(yq,y);
for i = i0-1:i0+2
for j = j0-1:j0+2
k = sub2ind(size(Z),j,i);
Zq = Zq + cubic(X(k)-xq)*cubic(Y(k)-yq)*Z(k);
end
end
Zq
  3 Comments
Bruno Luong
Bruno Luong on 25 Feb 2021
Edited: Bruno Luong on 25 Feb 2021
The theory is in the Key's paper on the reference of the document of interp1 and interp2 and in the link II provide (coeffcient in eqt 4 do you read it?).
Apparently it's free access here
Mostly coefficients are computed to provide a smooth convolution kernel and compact support.
The example I give is formula for interpolation at a singe point (xq,yq).
For more points just loop on it. No relevant if you want to understand the formula.

Sign in to comment.

Categories

Find more on Interpolation in Help Center and File Exchange

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!