图像放大并进行BiCubic插值 Matlab/C++代码
BiCubic插值原理：
双三次插值又称立方卷积插值。三次卷积插值是一种更加复杂的插值方式。该算法利用待采样点周围16个点的灰度值作三次插值，不仅考虑到4 个直接相邻点的灰度影响，而且考虑到各邻点间灰度值变化率的影响。三次运算可以得到更接近高分辨率图像的放大效果，但也导致了运算量的急剧增加。这种算法需要选取插值基函数来拟合数据，其最常用的插值基函数如图1所示，本次实验采用如图所示函数作为基函数。
构造BiCubic函数：
其中，a取-0.5.
BiCubic函数具有如下形状：
[source: R. Keys, (1981). "Cubic convolution interpolation for digital image processing". IEEE Transactions on Signal Processing, Acoustics, Speech, and Signal Processing 29 (6): 1153–1160.]
对待插值的像素点(x,y)（x和y可以为浮点数），取其附近的4x4邻域点(xi,yj), i,j = 0,1,2,3。按如下公式进行插值计算：
Matlab实现代码：
%双三次插值具体实现
clc,clear;
fff=imread('E:\Documents\BUPT\DIP\图片\lena.bmp');
ff =rgb2gray(fff);%转化为灰度图像
[mm,nn]=size(ff); %将图像隔行隔列抽取元素，得到缩小的图像f
m=mm/2;
n=nn/2;
f =zeros(m,n);
for i=1:m
for j=1:n
f(i,j)=ff(2*i,2*j);
end
end
k=5; %设置放大倍数 bijiao1 =imresize(f,k,'bilinear');%双线性插值结果比较 bijiao =uint8(bijiao1);
a=f(1,:);
c=f(m,:); %将待插值图像矩阵前后各扩展两行两列,共扩展四行四列
b=[f(1,1),f(1,1),f(:,1)',f(m,1),f(m,1)];
d=[f(1,n),f(1,n),f(:,n)',f(m,n),f(m,n)];
a1=[a;a;f;c;c];
b1=[b;b;a1';d;d];
ffff=b1';
f1=double(ffff);
g1 =zeros(k*m,k*n);
fori=1:k*m %利用双三次插值公式对新图象所有像素赋值
u=rem(i,k)/k;
i1=floor(i/k)+2;
A=[sw(1+u) sw(u) sw(1-u) sw(2-u)];
for j=1:k*n
v=rem(j,k)/k;
j1=floor(j/k)+2;
C=[sw(1+v);sw(v);sw(1-v);sw(2-v)];
B=[f1(i1-1,j1-1) f1(i1-1,j1) f1(i1-1,j1+1)f1(i1-1,j1+2)
f1(i1,j1-1) f1(i1,j1) f1(i1,j1+1) f1(i1,j1+2)
f1(i1+1,j1-1) f1(i1+1,j1) f1(i1+1,j1+1) f1(i1+1,j1+2)
f1(i1+2,j1-1) f1(i1+2,j1) f1(i1+2,j1+1)f1(i1+2,j1+2)];
g1(i,j)=(A*B*C);
end
end
g=uint8(g1);
imshow(uint8(f));title('缩小的图像'); %显示缩小的图像
figure,imshow(ff);title('原图'); %显示原图像
figure,imshow(g);title('双三次插值放大的图像'); %显示插值后的图像
figure,imshow(bijiao);title('双线性插值放大结果'); %显示插值后的图像
mse=0;
ff=double(ff);
g=double(g);
ff2=fftshift(fft2(ff)); %计算原图像和插值图像的傅立叶幅度谱
g2=fftshift(fft2(g));
figure,subplot(1,2,1),imshow(log(abs(ff2)),[8,10]);title('原图像的傅立叶幅度谱');
subplot(1,2,2),imshow(log(abs(g2)),[8,10]);title('双三次插值图像的傅立叶幅度谱');
基函数代码： functionA=sw(w1) w=abs(w1); ifw<1&&w>=0 A=1-2*w^2+w^3; elseifw>=1&&w<2 A=4-8*w+5*w^2-w^3; else A=0; end
C++实现代码：
#include "opencv2/imgproc/imgproc.hpp" #include "opencv2/highgui/highgui.hpp" #include <iostream> #include <cmath> #include <fstream> using namespace cv; using namespace std; #define PI 3.14159265 float BiCubicPoly(float x); void MyScaleBiCubicInter(Mat& src, Mat& dst, float TransMat[3][3]); /** * @function main */ int main( int argc, char** argv ) { // load image char* imageName = "images/Lenna_256.png"; Mat image; image = imread(imageName,1);if(!image.data) { cout << "No image data" << endl; return -1; } // show image namedWindow("image", CV_WINDOW_AUTOSIZE); imshow("image", image); Mat dst; float transMat[3][3] = { {2.0, 0, 0}, {0, 2.0, 0}, {0, 0, 1} };MyScaleBiCubicInter(image, dst, transMat); namedWindow("out_image", CV_WINDOW_AUTOSIZE); imshow("out_image", dst); imwrite("Lenna_scale_biCubic2.jpg", dst); waitKey(0); return 0; } float BiCubicPoly(float x) { float abs_x = abs(x); float a = -0.5; if( abs_x <= 1.0 ) { return (a+2)*pow(abs_x,3) - (a+3)*pow(abs_x,2) + 1; } else if( abs_x < 2.0 ) { return a*pow(abs_x,3) - 5*a*pow(abs_x,2) + 8*a*abs_x - 4*a; } else return 0.0; } void MyScaleBiCubicInter(Mat& src, Mat& dst, float TransMat[3][3]) { CV_Assert(src.data); CV_Assert(src.depth() != sizeof(uchar)); // calculate margin point of dst image float left = 0; float right = 0; float top = 0; float down = 0; float x = src.cols * 1.0f; float y = 0.0f; float u1 = x * TransMat[0][0] + y * TransMat[0][1]; float v1 = x * TransMat[1][0] + y * TransMat[1][1]; x = src.cols * 1.0f; y = src.rows * 1.0f; float u2 = x * TransMat[0][0] + y * TransMat[0][1]; float v2 = x * TransMat[1][0] + y * TransMat[1][1]; x = 0.0f; y = src.rows * 1.0f; float u3 = x * TransMat[0][0] + y * TransMat[0][1]; float v3 = x * TransMat[1][0] + y * TransMat[1][1]; left = min( min( min(0.0f,u1), u2 ), u3); right = max( max( max(0.0f,u1), u2 ), u3); top = min( min( min(0.0f,v1), v2 ), v3); down = max( max( max(0.0f,v1), v2 ), v3); // create dst image dst.create(int(abs(right-left)), int(abs(down-top)), src.type()); CV_Assert( dst.channels() == src.channels() ); int channels = dst.channels(); int i,j; uchar* p; uchar* q0; uchar* q1; uchar* q2; uchar* q3; for( i = 0; i < dst.rows; ++i) { p = dst.ptr<uchar>(i); for ( j = 0; j < dst.cols; ++j) { // x = (j+left)/TransMat[0][0] ; y = (i+top)/TransMat[1][1] ; int x0 = int(x) - 1; int y0 = int(y) - 1; int x1 = int(x); int y1 = int(y); int x2 = int(x) + 1; int y2 = int(y) + 1; int x3 = int(x) + 2; int y3 = int(y) + 2; if( (x0 >= 0) && (x3 < src.cols) && (y0 >= 0) && (y3 < src.rows) ) { q0 = src.ptr<uchar>(y0); q1 = src.ptr<uchar>(y1); q2 = src.ptr<uchar>(y2); q3 = src.ptr<uchar>(y3); float dist_x0 = BiCubicPoly(x-x0); float dist_x1 = BiCubicPoly(x-x1); float dist_x2 = BiCubicPoly(x-x2); float dist_x3 = BiCubicPoly(x-x3); float dist_y0 = BiCubicPoly(y-y0); float dist_y1 = BiCubicPoly(y-y1); float dist_y2 = BiCubicPoly(y-y2); float dist_y3 = BiCubicPoly(y-y3); float dist_x0y0 = dist_x0 * dist_y0; float dist_x0y1 = dist_x0 * dist_y1; float dist_x0y2 = dist_x0 * dist_y2; float dist_x0y3 = dist_x0 * dist_y3; float dist_x1y0 = dist_x1 * dist_y0; float dist_x1y1 = dist_x1 * dist_y1; float dist_x1y2 = dist_x1 * dist_y2; float dist_x1y3 = dist_x1 * dist_y3; float dist_x2y0 = dist_x2 * dist_y0; float dist_x2y1 = dist_x2 * dist_y1; float dist_x2y2 = dist_x2 * dist_y2; float dist_x2y3 = dist_x2 * dist_y3; float dist_x3y0 = dist_x3 * dist_y0; float dist_x3y1 = dist_x3 * dist_y1; float dist_x3y2 = dist_x3 * dist_y2; float dist_x3y3 = dist_x3 * dist_y3; switch(channels) { case 1: { break; } case 3: { p[3*j] = (uchar)(q0[3*x0] * dist_x0y0 + q1[3*x0] * dist_x0y1 + q2[3*x0] * dist_x0y2 + q3[3*x0] * dist_x0y3 + q0[3*x1] * dist_x1y0 + q1[3*x1] * dist_x1y1 + q2[3*x1] * dist_x1y2 + q3[3*x1] * dist_x1y3 + q0[3*x2] * dist_x2y0 + q1[3*x2] * dist_x2y1 + q2[3*x2] * dist_x2y2 + q3[3*x2] * dist_x2y3 + q0[3*x3] * dist_x3y0 + q1[3*x3] * dist_x3y1 + q2[3*x3] * dist_x3y2 + q3[3*x3] * dist_x3y3 ) ; p[3*j+1] = (uchar)(q0[3*x0+1] * dist_x0y0 + q1[3*x0+1] * dist_x0y1 + q2[3*x0+1] * dist_x0y2 + q3[3*x0+1] * dist_x0y3 + q0[3*x1+1] * dist_x1y0 + q1[3*x1+1] * dist_x1y1 + q2[3*x1+1] * dist_x1y2 + q3[3*x1+1] * dist_x1y3 + q0[3*x2+1] * dist_x2y0 + q1[3*x2+1] * dist_x2y1 + q2[3*x2+1] * dist_x2y2 + q3[3*x2+1] * dist_x2y3 + q0[3*x3+1] * dist_x3y0 + q1[3*x3+1] * dist_x3y1 + q2[3*x3+1] * dist_x3y2 + q3[3*x3+1] * dist_x3y3 ) ; p[3*j+2] = (uchar)(q0[3*x0+2] * dist_x0y0 + q1[3*x0+2] * dist_x0y1 + q2[3*x0+2] * dist_x0y2 + q3[3*x0+2] * dist_x0y3 + q0[3*x1+2] * dist_x1y0 + q1[3*x1+2] * dist_x1y1 + q2[3*x1+2] * dist_x1y2 + q3[3*x1+2] * dist_x1y3 + q0[3*x2+2] * dist_x2y0 + q1[3*x2+2] * dist_x2y1 + q2[3*x2+2] * dist_x2y2 + q3[3*x2+2] * dist_x2y3 + q0[3*x3+2] * dist_x3y0 + q1[3*x3+2] * dist_x3y1 + q2[3*x3+2] * dist_x3y2 + q3[3*x3+2] * dist_x3y3 ) ; float thre = 198.0f; if( (abs(p[3*j]-q1[3*x1]) > thre) || (abs(p[3*j+1]-q1[3*x1+1]) > thre) || (abs(p[3*j+2]-q1[3*x1+2]) > thre) ) { p[3*j] = q1[3*x1]; p[3*j+1] = q1[3*x1+1]; p[3*j+2] = q1[3*x1+2]; } break; } } } } } }参考：lichengyu的专栏