Derivation of bilinear interpolation algorithm and code realization _ bilinear interpolation

Bilinear interpolation is a more important interpolation method, especially in the field of digital image processing. This blog is divided into three parts: one is the derivation of bilinear interpolation algorithm, the second is the implementation of bilinear interpolation algorithm, the third is the results of the operation of the algorithm.

Derivation of a bilinear interpolation algorithm

Two code implementation (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-del
        Ta_r). * (Delta_c) + ... chan (in4_ind). * (Delta_r). * (Delta_c);
    Out (:,:, idx) = CAST (TMP, Class (IM));
 End

Three-bilinear linear interpolation operation result

>>i = Imread (' lena.jpg ');
>> Figure,imshow (I)
>> S = bilinearinterpolation (i,[1000,1000]);
>> Figure,imshow (S)