频率域滤波【5】：自定义滤波

//快速傅里叶变换
void fft2Image(InputArray _src, OutputArray _dst)
{
	//得到Mat类型
	Mat src = _src.getMat();
	//判断位深
	CV_Assert(src.type() == CV_32FC1 || src.type() == CV_64FC1);
	CV_Assert(src.channels() == 1 || src.channels() == 2);
	int rows = src.rows;
	int cols = src.cols;
	//为了进行快速的傅里叶变换，我们经行和列的扩充,找到最合适扩充值
	Mat padded;
	int rPadded = getOptimalDFTSize(rows);
	int cPadded = getOptimalDFTSize(cols);
	//进行边缘扩充,扩充值为零
	copyMakeBorder(src, padded, 0, rPadded - rows, 0, cPadded - cols, BORDER_CONSTANT, Scalar::all(0));
	//快速的傅里叶变换（双通道：用于存储实部 和 虚部）
	dft(padded, _dst, DFT_COMPLEX_OUTPUT);
}
//求傅里叶变换的幅度谱 amplitude spectrum
void amplitudeSpectrum(InputArray _srcFFT, OutputArray _dstSpectrum)
{
	//判断傅里叶变换是两个通道
	CV_Assert(_srcFFT.channels() == 2);
	//分离通道
	vector<Mat> FFT2Channel;
	split(_srcFFT, FFT2Channel);
	//计算傅里叶变换的幅度谱 sqrt(pow(R,2)+pow(I,2))
	magnitude(FFT2Channel[0], FFT2Channel[1], _dstSpectrum);
}
//傅里叶谱的灰度级显示
Mat graySpectrum(Mat spectrum)
{
	Mat dst;
	log(spectrum + 1, dst);
	//归一化
	normalize(dst, dst, 0, 1, NORM_MINMAX);
	//为了进行灰度级显示，做类型转换
	dst.convertTo(dst, CV_8UC1, 255, 0);
	return dst;
}
//求相位谱 phase spectrum
Mat phaseSpectrum(Mat _srcFFT)
{
	//相位谱
	Mat phase;
	phase.create(_srcFFT.size(), CV_64FC1);
	//分离通道
	vector<Mat> FFT2Channel;
	split(_srcFFT, FFT2Channel);
	//计算相位谱
	for (int r = 0; r<phase.rows; r++)
	{
		for (int c = 0; c < phase.cols; c++)
		{
			//实部 虚部
			double real = FFT2Channel[0].at<double>(r, c);
			double imaginary = FFT2Channel[1].at<double>(r, c);
			// atan2 的返回值范围 [0,180] [-180,0]
			phase.at<double>(r, c) = atan2(imaginary, real);
		}
	}
	return phase;
}

//自定义滤波器
bool drawing_box = false;
Point downPoint;
Rect rectFilter;
bool gotRectFilter = false;
void mouseRectHandler(int event, int x, int y, int, void*)
{
	switch (event)
	{
		//按下鼠标左键
	case CV_EVENT_LBUTTONDOWN:
		drawing_box = true;
		//记录起点
		downPoint = Point(x, y);
		break;
		//移动鼠标
	case CV_EVENT_MOUSEMOVE:
		if (drawing_box)
		{
			//鼠标移动到 downPoint 的右下角
			if (x >= downPoint.x && y >= downPoint.y)
			{
				rectFilter.x = downPoint.x;
				rectFilter.y = downPoint.y;
				rectFilter.width = x - downPoint.x;
				rectFilter.height = y - downPoint.y;
			}
			//鼠标移到到 downPoint 的右上角
			if (x >= downPoint.x && y <= downPoint.y)
			{
				rectFilter.x = downPoint.x;
				rectFilter.y = y;
				rectFilter.width = x - downPoint.x;
				rectFilter.height = downPoint.y - y;
			}
			//鼠标移动到 downPoint 的左上角
			if (x <= downPoint.x && y <= downPoint.y)
			{
				rectFilter.x = x;
				rectFilter.y = y;
				rectFilter.width = downPoint.x - x;
				rectFilter.height = downPoint.y - y;
			}
			//鼠标移动到 downPoint 的左下角
			if (x <= downPoint.x && y >= downPoint.y)
			{
				rectFilter.x = x;
				rectFilter.y = downPoint.y;
				rectFilter.width = downPoint.x - x;
				rectFilter.height = y - downPoint.y;
			}
		}
		break;
		//松开鼠标左键
	case CV_EVENT_LBUTTONUP:
		drawing_box = false;
		gotRectFilter = true;
		break;
	default:
		break;
	}
}

//自定义滤波器
Mat self_Filter(Mat &src, Mat &F, Mat &spectrum,  Point maxLoc)
{
	Mat selfFilter;////自定义滤波器
	Mat F_selfFilter;//自定义傅里叶变换
	Mat FselfSpectrum;//自定义傅里叶变换的傅里叶谱灰度级
	Mat result;
	string windowName = "幅度谱的灰度级";

	F_selfFilter = F.clone();
	namedWindow(windowName, CV_WINDOW_AUTOSIZE);
	setMouseCallback(windowName, mouseRectHandler, NULL);
	for (;;)
	{
		spectrum(rectFilter).setTo(0);
		/* -- 第六步：自定义滤波器与傅里叶变换点乘 -- */
		F_selfFilter(rectFilter).setTo(Scalar::all(0));
		imshow(windowName, spectrum);
		//按下 "Esc" 键退出编辑
		if (waitKey(10) == 27)
			break;
	}

	//自定义傅里叶变换的傅里叶谱
	amplitudeSpectrum(F_selfFilter, FselfSpectrum);
	//自定义傅里叶谱的灰度级的显示
	FselfSpectrum = graySpectrum(FselfSpectrum);
	/* -- 第七、八步：对自定义傅里叶变换执行傅里叶逆变换，并只取实部 -- */
	dft(F_selfFilter, result, DFT_SCALE + DFT_INVERSE + DFT_REAL_OUTPUT);
	/* -- 第九步：同乘以(-1)^(x+y) -- */
	for (int r = 0; r < result.rows; r++)
	{
		for (int c = 0; c < result.cols; c++)
		{
			if ((r + c) % 2)
				result.at<float>(r, c) *= -1;
		}
	}
	//注意将结果转换 CV_8U 类型
	result.convertTo(result, CV_8UC1, 1.0, 0);
	/* -- 第十步：截取左上部分,大小等于输入图像的大小 --*/
	result = result(Rect(0, 0, src.cols, src.rows)).clone();
	return result;
}

void main()
{	/* -- 第一步：读入图像矩阵 -- */
	Mat image = imread("lena.jpg", 0);
	Mat fI;
	image.convertTo(fI, CV_32FC1);
	/* -- 第二步：每一个数乘以(-1)^(r+c) -- */
	for (int r = 0; r < fI.rows; r++)
	{
		for (int c = 0; c < fI.cols; c++)
		{
			if ((r + c) % 2)
				fI.at<float>(r, c) *= -1;
		}
	}
	/* -- 第三、四步：补零和快速傅里叶变换 -- */
	Mat F;//图像的快速傅里叶变换
	fft2Image(fI, F);
	//傅里叶谱
	Mat amplSpec;
	amplitudeSpectrum(F, amplSpec);
	//傅里叶谱的灰度级显示
	Mat spectrum = graySpectrum(amplSpec);
	//找到傅里叶谱的最大值的坐标
	Point maxLoc;
	minMaxLoc(spectrum, NULL, NULL, NULL, &maxLoc);

	Mat result;
	//低通
	//result  = LPFilter(image, F, maxLoc, 0, 25);

	//高通
	//result = ihpFilter(image, F, maxLoc, 0, 25);

	//带阻
	//result = brFilter(image, F, maxLoc, 0, 50, 40);

	//带通
	//result = bpFilter(image, F, maxLoc, 0, 50, 40);

	//自定义滤波器
	result = self_Filter(image, F, spectrum, maxLoc);

	cout << "";
}

原图：

傅里叶：

自定义：

反变换：