双线性插值算法推导及代码实现

双线性插值，是一种比较重要的插值方法，尤其在数字图像处理领域。本篇博文分为三个部分：一是双线性插值的算法推导，二是双线性插值的算法实现，三是算法的运行结果。

一 双线性插值的算法推导



二 代码实现（matlab）

function [out] = bilinearInterpolation(im, out_dims)

in_rows = size(im,1);
in_cols = size(im,2);
out_rows = out_dims(1);
out_cols = out_dims(2);

S_R = in_rows / out_rows;
S_C = in_cols / out_cols;

[cf, rf] = meshgrid(1 : out_cols, 1 : out_rows);

rf = rf * S_R;
cf = cf * S_C;
r = floor(rf);
c = floor(cf);

r(r < 1) = 1;
c(c < 1) = 1;
r(r > in_rows - 1) = in_rows - 1;
c(c > in_cols - 1) = in_cols - 1;

delta_R = rf - r;
delta_C = cf - c;

in1_ind = sub2ind([in_rows, in_cols], r, c);
in2_ind = sub2ind([in_rows, in_cols], r+1,c);
in3_ind = sub2ind([in_rows, in_cols], r, c+1);
in4_ind = sub2ind([in_rows, in_cols], r+1, c+1);

out = zeros(out_rows, out_cols, size(im, 3));
out = cast(out, class(im));

for idx = 1 : size(im, 3)
chan = double(im(:,:,idx)); %// Get i'th channel
%// Interpolate the channel
tmp = chan(in1_ind).*(1 - delta_R).*(1 - delta_C) + ...
chan(in2_ind).*(delta_R).*(1 - delta_C) + ...
chan(in3_ind).*(1 - delta_R).*(delta_C) + ...
chan(in4_ind).*(delta_R).*(delta_C);
out(:,:,idx) = cast(tmp, class(im));
end

三 双线性插值运行结果

>>I = imread('lena.jpg');

>> figure,imshow(I)

>> S = bilinearInterpolation(I,[1000,1000]);

>> figure,imshow(S)