本实验为计算机科学与技术学院计算机专业大四上限选课，2023-2024-1年度课程实验，较以往实验内容发生较大变化

本实验使用vs2019，c++语言，需要提前安装opencv，具体方法请自行搜索。

9.1 傅里叶变换

•利用cv::dft对输入图像（可以只考虑单通道图像）进行傅里叶变换，显示其功率谱，并测试非移中和移中的情况。

#include <iostream>
#include <cmath>
#include <opencv2/opencv.hpp>
#include <cfloat>

using namespace std;
using namespace cv;

Mat imgGray, output_image;

void DFT(Mat inputMat)
{
	Mat transform_image;
	int m = getOptimalDFTSize(inputMat.rows);
	int n = getOptimalDFTSize(inputMat.cols);
	copyMakeBorder(inputMat, inputMat, 0, m - inputMat.rows, 0, n - inputMat.cols, BORDER_CONSTANT, Scalar::all(0));
	Mat planes[] = { Mat_<float>(inputMat), Mat::zeros(inputMat.size(), CV_32F) };
	merge(planes, 2, transform_image);	
	dft(transform_image, transform_image);
	split(transform_image, planes);
	magnitude(planes[0], planes[1], output_image);

	output_image += Scalar(1);
	log(output_image, output_image);
	normalize(output_image, output_image, 0, 1, NORM_MINMAX);
	output_image = output_image(Rect(0, 0, output_image.cols & -2, output_image.rows & -2));
	imshow("未移中", output_image);
	int cx = output_image.cols / 2;
	int cy = output_image.rows / 2;
	Mat q0(output_image, Rect(0, 0, cx, cy));   // 左上区域
	Mat q1(output_image, Rect(cx, 0, cx, cy));  // 右上区域
	Mat q2(output_image, Rect(0, cy, cx, cy));  // 左下区域
	Mat q3(output_image, Rect(cx, cy, cx, cy)); // 右下区域
	Mat tmp;
	q0.copyTo(tmp); q3.copyTo(q0); tmp.copyTo(q3);//左上与右下进行交换
	q1.copyTo(tmp); q2.copyTo(q1); tmp.copyTo(q2);//右上与左下进行交换
}

int main()
{
	Mat img = imread("C:/Users/13441/Desktop/数字图像/back8.png", IMREAD_GRAYSCALE);
	img.convertTo(imgGray, CV_32F);
	imshow("原始图像", img);
	//imshow("新的图像", imgGray);
	Mat dst;
	DFT(img);
	imshow("移中", output_image);
	waitKey(0);
	return 0;
}

 

9.2 频率域滤波

对下图所示输入，进行频率域滤波，去除余弦噪声

#include <opencv2/opencv.hpp>
#include <iostream>
using namespace std;
using namespace cv;

Mat img, output;

void DST_2()
{
    Mat padded;
    int m = getOptimalDFTSize(img.rows);
    int n = getOptimalDFTSize(img.cols);
    copyMakeBorder(img, padded, 0, m - img.rows, 0, n - img.cols, BORDER_CONSTANT, Scalar::all(0));
    padded.convertTo(padded, CV_32FC1);
    Mat planes[] = { padded, Mat::zeros(padded.size() , CV_32FC1) };
    Mat compleximg;
    Mat dst(padded.size(), CV_32FC2);
    merge(planes, 2, compleximg);
    dft(compleximg, compleximg, 0);
    split(compleximg, planes);
    magnitude(planes[0], planes[1], planes[0]);
    planes[0] += Scalar::all(1);
    log(planes[0], planes[0]);
    double MaxV, MinV;
    Point minloc, maxloc;
    Mat rem = planes[0](Rect(1, 0, compleximg.cols / 2, 1));
    minMaxLoc(rem, &MinV, &MaxV, &minloc, &maxloc);
    float* a1 = compleximg.ptr<float>(0, maxloc.x + 1);
    float* a2 = compleximg.ptr<float>(0, compleximg.rows - maxloc.x - 1);
    float* a3 = compleximg.ptr<float>(compleximg.cols - 1, maxloc.x + 1);
    float* a4 = compleximg.ptr<float>(compleximg.cols - 1, compleximg.rows - maxloc.x - 1);
    a1[0] = a2[0] = a3[0] = a4[0] = a1[1] = a2[1] = a3[1] = a4[1] = 0;
    multiply(compleximg, dst, dst);
    normalize(planes[0], planes[0], 1, 0, NORM_MINMAX);
    split(dst, planes);
    magnitude(planes[0], planes[1], planes[0]);
    planes[0] += Scalar::all(1);
    log(planes[0], planes[0]);
    normalize(planes[0], planes[0], 1, 0, NORM_MINMAX);
    idft(dst, dst);
    split(dst, planes);
    magnitude(planes[0], planes[1], planes[0]);
    normalize(planes[0], planes[0], 1, 0, NORM_MINMAX);
    output = planes[0];
}


int main()
{
    img = imread("C:/Users/13441/Desktop/数字图像/back13.png", 0);
    imshow("原始图像", img);
    DST_2();
    imshow("去噪后", output);
    waitKey(0);
    return 0;
}