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