5.6.3 高通滤波（理想高通滤波+巴特沃斯高通滤波）

1.理想高通滤波器
高通滤波与低通滤波正好相反，是频域图像的高频部分通过而抑制低频部分。在图像中图像的边缘对应高频分量，因此高通滤波的效果是图像锐化。同样最简单的高通滤波器是理想高通滤波器。通过设置一个频率阈值，将高于该阈值的频率部分通过，而低于阈值的低频部分设置为0。

VTK中理想高通滤波的实例如下：

/*         ******理想高通滤波**********             */
#include <vtkSmartPointer.h>
#include <vtkJPEGReader.h>
#include <vtkImageFFT.h>
#include <vtkImageIdealHighPass.h>
#include <vtkImageRFFT.h>
#include <vtkImageCast.h>
#include <vtkImageExtractComponents.h>
#include <vtkRenderer.h>
#include <vtkImageActor.h>
#include <vtkRenderWindow.h>
#include <vtkRenderWindowInteractor.h>
#include <vtkInteractorStyleImage.h>

int main()
{
	vtkSmartPointer<vtkJPEGReader> reader =vtkSmartPointer<vtkJPEGReader>::New();
	reader->SetFileName("data\lena-gray.jpg");
	reader->Update();

	vtkSmartPointer<vtkImageFFT> fftFilter = vtkSmartPointer<vtkImageFFT>::New();//将图像域转换到频域空间
	fftFilter->SetInputConnection(reader->GetOutputPort());
	fftFilter->Update();

	vtkSmartPointer<vtkImageIdealHighPass> highPassFilter = vtkSmartPointer<vtkImageIdealHighPass>::New();
	highPassFilter->SetInputConnection(fftFilter->GetOutputPort());//定义图像高通滤波对象
	highPassFilter->SetXCutOff(0.1);//设置X和Y方向的截止频率
	highPassFilter->SetYCutOff(0.1);
	highPassFilter->Update();

	vtkSmartPointer<vtkImageRFFT> rfftFilter = vtkSmartPointer<vtkImageRFFT>::New();//将处理后的图像转换到空域中
	rfftFilter->SetInputConnection(highPassFilter->GetOutputPort());
	rfftFilter->Update();

	vtkSmartPointer<vtkImageExtractComponents> ifftExtractReal = vtkSmartPointer<vtkImageExtractComponents>::New();
	ifftExtractReal->SetInputConnection(rfftFilter->GetOutputPort());
	ifftExtractReal->SetComponents(0);//提取实部分量

	vtkSmartPointer<vtkImageCast> castFilter = vtkSmartPointer<vtkImageCast>::New();//数据类型转换
	castFilter->SetInputConnection(ifftExtractReal->GetOutputPort());
	castFilter->SetOutputScalarTypeToUnsignedChar();
	castFilter->Update();
	/
	vtkSmartPointer<vtkImageActor> originalActor = vtkSmartPointer<vtkImageActor>::New();
	originalActor->SetInputData(reader->GetOutput());

	vtkSmartPointer<vtkImageActor> erodedActor = vtkSmartPointer<vtkImageActor>::New();
	erodedActor->SetInputData(castFilter->GetOutput());
	/
	double leftViewport[4] = { 0.0, 0.0, 0.5, 1.0 };
	double rightViewport[4] = { 0.5, 0.0, 1.0, 1.0 };
	vtkSmartPointer<vtkRenderer> leftRenderer = vtkSmartPointer<vtkRenderer>::New();
	leftRenderer->AddActor(originalActor);
	leftRenderer->SetViewport(leftViewport);
	leftRenderer->SetBackground(1.0, 1.0, 1.0);
	leftRenderer->ResetCamera();
	vtkSmartPointer<vtkRenderer> rightRenderer = vtkSmartPointer<vtkRenderer>::New();
	rightRenderer->AddActor(erodedActor);
	rightRenderer->SetViewport(rightViewport);
	rightRenderer->SetBackground(1.0, 1.0, 1.0);
	rightRenderer->ResetCamera();
	/
	vtkSmartPointer<vtkRenderWindow> rw = vtkSmartPointer<vtkRenderWindow>::New();
	rw->SetSize(640, 320);
	rw->AddRenderer(leftRenderer);
	rw->AddRenderer(rightRenderer);
	rw->SetWindowName("IdealHighPassExample");

	vtkSmartPointer<vtkRenderWindowInteractor> rwi = vtkSmartPointer<vtkRenderWindowInteractor>::New();
	vtkSmartPointer<vtkInteractorStyleImage> style = vtkSmartPointer<vtkInteractorStyleImage>::New();
	rwi->SetInteractorStyle(style);
	rwi->SetRenderWindow(rw);
	rwi->Start();

	return 0;
}

运行结果如下：

低通-滤波；高通-锐化（从结果看出高通滤波后图像得到锐化处理，图像中仅剩下边缘。）同低通滤波一样，首先将读入图像通过vtkImageFFT转换到频域空间，定义vtkImageIdealHighPass对象，并通过SetXCutOff ()和SetYCutOff() 设置X和Y方向的截止频率。然后通过vtkImageRFFT将处理后的图像转换到空域中，得到高通滤波图像。为了显示的需要，还需要提取图像分量和数据类型的转换。

2.巴特沃兹高通滤波
理想高通滤波器不能通过电子元器件来实现，而且存在振铃现象。在实际中最常使用的高通滤波器是巴特沃斯高通滤波器。该滤波器的转移函数是：

D(u,v)表示频域中点到频域平面的距离，是截止频率。当D(u,v)大于时，对应的H(u,v)逐渐接近1，从而使得高频部分得以通过；而当D(u,v)小于时，H(u,v)逐渐接近0，实现低频部分过滤。巴特沃斯高通滤波器在VTK中对应vtkImageButterworthHighPass类。

下面代码说明了vtkImageButterworthHighPass对图像进行高通滤波：

/*******************巴特沃特高斯高通滤波***********************************/
#include <vtkSmartPointer.h>
#include <vtkJPEGReader.h>
#include <vtkImageFFT.h>
#include <vtkImageButterworthHighPass.h>
#include <vtkImageRFFT.h>
#include <vtkImageExtractComponents.h>
#include <vtkImageCast.h>
#include <vtkRenderer.h>
#include <vtkImageActor.h>
#include <vtkRenderWindow.h>
#include <vtkRenderWindowInteractor.h>
#include <vtkInteractorStyleImage.h>

int main(int argc, char* argv[])
{
	vtkSmartPointer<vtkJPEGReader> reader = vtkSmartPointer<vtkJPEGReader>::New();
	reader->SetFileName("lena.jpg");
	reader->Update();

	vtkSmartPointer<vtkImageFFT> fftFilter = vtkSmartPointer<vtkImageFFT>::New();
	fftFilter->SetInputConnection(reader->GetOutputPort());
	fftFilter->Update();

	vtkSmartPointer<vtkImageButterworthHighPass> highPassFilter = vtkSmartPointer<vtkImageButterworthHighPass>::New();
	highPassFilter->SetInputConnection(fftFilter->GetOutputPort());
	highPassFilter->SetXCutOff(0.1);
	highPassFilter->SetYCutOff(0.1);//xy轴的截止频率
	highPassFilter->Update();

	vtkSmartPointer<vtkImageRFFT> rfftFilter = vtkSmartPointer<vtkImageRFFT>::New();// 转换回空域中
	rfftFilter->SetInputConnection(highPassFilter->GetOutputPort());
	rfftFilter->Update();

	vtkSmartPointer<vtkImageExtractComponents> ifftExtractReal = vtkSmartPointer<vtkImageExtractComponents>::New();
	ifftExtractReal->SetInputConnection(rfftFilter->GetOutputPort());
	ifftExtractReal->SetComponents(0);//提取复数中的实部

	vtkSmartPointer<vtkImageCast> castFilter = vtkSmartPointer<vtkImageCast>::New();//数据转换为unsigned char类型
	castFilter->SetInputConnection(ifftExtractReal->GetOutputPort());
	castFilter->SetOutputScalarTypeToUnsignedChar();
	castFilter->Update();
	
	vtkSmartPointer<vtkImageActor> originalActor = vtkSmartPointer<vtkImageActor>::New();
	originalActor->SetInputData(reader->GetOutput());

	vtkSmartPointer<vtkImageActor> erodedActor = vtkSmartPointer<vtkImageActor>::New();
	erodedActor->SetInputData(castFilter->GetOutput());
	//
	double leftViewport[4] = { 0.0, 0.0, 0.5, 1.0 };
	double rightViewport[4] = { 0.5, 0.0, 1.0, 1.0 };
	vtkSmartPointer<vtkRenderer> leftRenderer =	vtkSmartPointer<vtkRenderer>::New();
	leftRenderer->AddActor(originalActor);
	leftRenderer->ResetCamera();
	leftRenderer->SetViewport(leftViewport);
	leftRenderer->SetBackground(1.0, 1.0, 1.0);

	vtkSmartPointer<vtkRenderer> rightRenderer = vtkSmartPointer<vtkRenderer>::New();
	rightRenderer->AddActor(erodedActor);
	rightRenderer->SetViewport(rightViewport);
	rightRenderer->SetBackground(1.0, 1.0, 1.0);
	rightRenderer->ResetCamera();
	
	vtkSmartPointer<vtkRenderWindow> rw = vtkSmartPointer<vtkRenderWindow>::New();
	rw->AddRenderer(leftRenderer);
	rw->AddRenderer(rightRenderer);
	rw->SetSize(640, 320);
	rw->Render();
	rw->SetWindowName("Frequency_ButterworthHighPass");
	/
	vtkSmartPointer<vtkRenderWindowInteractor> rwi = vtkSmartPointer<vtkRenderWindowInteractor>::New();
	vtkSmartPointer<vtkInteractorStyleImage> style = vtkSmartPointer<vtkInteractorStyleImage>::New();
	rwi->SetInteractorStyle(style);
	rwi->SetRenderWindow(rw);
	rwi->Start();

	return 0;
}

 运行结果如下：

解释说明：vtkImageButterworthHighPass与理想高通滤波使用方法一致。需要设置X和Y轴的截止频率，为了便于比较，其截止频域与理想高通滤波设置一致。

参考资料：

1.《The Visualization Toolkit – AnObject-Oriented Approach To 3D Graphics (4th Edition)》
2. 张晓东, 罗火灵. VTK图形图像开发进阶[M]. 机械工业出版社, 2015.

所用软件：vtk7.0+visual studio 2013

注：此文知识学习笔记，仅记录完整程序和实现结果，具体原理参见：

https://blog.csdn.net/www_doling_net/article/details/8541534

https://blog.csdn.net/shenziheng1/article/category/6114053/4
 

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