VTK_Learning_频域处理_低通滤波（理想+巴特沃兹）

客官°小女子只卖身不卖艺 2023-07-10 12:42 124阅读 0赞

# 1.低通滤波器 #

> 低通滤波是将频域图像中的高频部分滤除而通过低频部分。图像的边缘和噪声对应于频域图像中的高频部分，而低通滤波的作用即是减弱这部分的能量，从而达到图像平滑去噪的目的。

#  2.理想低通滤波器 #

> 最简单的低通滤波器是理想低通滤波器，基本思想是给定一个频率阈值，将高于该阈值的所有部分设置为0，而低于该频率的部分保持不变。
> 
> **理想是指该滤波器不能用电子元器件来实现，但是可以通过计算机来模拟。**
> 
> 在VTK中定义了理想低通滤波器，下面我们来看下怎么使用该滤波器来对图像进行低通滤波:
> 
>     #include <vtkAutoInit.h>
>     VTK_MODULE_INIT(vtkRenderingOpenGL);
>      
>     #include <vtkSmartPointer.h>
>     #include <vtkJPEGReader.h>
>     #include <vtkImageFFT.h>
>     #include <vtkImageIdealLowPass.h>
>     #include <vtkImageData.h>
>     #include <vtkImageRFFT.h>
>     #include <vtkImageCast.h>
>     #include <vtkImageExtractComponents.h>
>     #include <vtkImageActor.h>
>     #include <vtkRenderer.h>
>     #include <vtkRenderWindow.h>
>     #include <vtkRenderWindowInteractor.h>
>      
>     int main()
>     {
>     	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<vtkImageIdealLowPass> lowPassFilter =
>     		vtkSmartPointer<vtkImageIdealLowPass>::New();
>     	lowPassFilter->SetInputConnection(fftFilter->GetOutputPort());
>     	lowPassFilter->SetXCutOff(0.05);
>     	lowPassFilter->SetYCutOff(0.05);
>     	lowPassFilter->Update();
>      
>     	vtkSmartPointer<vtkImageRFFT> rfftFilter =
>     		vtkSmartPointer<vtkImageRFFT>::New();
>     	rfftFilter->SetInputConnection(lowPassFilter->GetOutputPort());
>     	rfftFilter->Update();
>      
>     	vtkSmartPointer<vtkImageExtractComponents> ifftExtractReal =
>     		vtkSmartPointer<vtkImageExtractComponents>::New();
>     	ifftExtractReal->SetInputConnection(rfftFilter->GetOutputPort());
>     	ifftExtractReal->SetComponents(0);
>      
>     	vtkSmartPointer<vtkImageCast> castFilter =
>     		vtkSmartPointer<vtkImageCast>::New();
>     	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, 0, 0);
>      
>     	vtkSmartPointer<vtkRenderer> rightRenderer =
>     		vtkSmartPointer<vtkRenderer>::New();
>     	rightRenderer->AddActor(erodedActor);
>     	rightRenderer->SetViewport(rightViewport);
>     	rightRenderer->ResetCamera();
>     	rightRenderer->SetBackground(1.0, 1.0, 1.0);
>      
>     	vtkSmartPointer<vtkRenderWindow> renderWindow =
>     		vtkSmartPointer<vtkRenderWindow>::New();
>     	renderWindow->AddRenderer(rightRenderer);
>     	renderWindow->AddRenderer(leftRenderer);
>     	renderWindow->SetSize(640, 320);
>     	renderWindow->SetWindowName("Frequency_IdealLowPassFilter");
>      
>     	vtkSmartPointer<vtkRenderWindowInteractor> interactor =
>     		vtkSmartPointer<vtkRenderWindowInteractor>::New();
>     	interactor->SetRenderWindow(renderWindow);
>     	renderWindow->Render();
>     	interactor->Start();
>      
>     	return 0;
>     }
> 
> 首先读入一副图像，通过vtkImageFFT将图像转换到频域空间。vtkImageIdealLowPass对频域图像做理想低通滤波，需要用户设置每个方向的截断频率，相应的设置函数SetXCutOff()和SetYCutOff()。执行完毕后，需要通过vtkImageRFFT将处理后的频域图像转换至空域图像。需要注意的是，转换后的图像每个像素都是一个复数，需要vtkImageExtractComponents将该图像的第一个分量提出出来显示，否则图像不能正确显示。由于傅里叶变换输入输出的数据类型都是double，为了方便显示，还需要将其转换为Unsigned char类型，这里vtkImageCast负责类型转换。  
> 下面是对图像做低通滤波的效果:
> 
> ![20170129120815649][]
> 
> 从结果看，在过滤掉图像的高频部分后，图像变得模糊，丢失了许多细节，**另外还可以看到图像会存在一定的振铃效应，这也是理想低通滤波的特点**。

#  3.巴特沃兹低通滤波器 #

> 在实际中经常使用的是巴特沃斯滤波器。巴特沃斯滤波器对应的转移函数（可以看做是一个系数矩阵）是：
> 
> ![20170129120952119][]
> 
> 其中D(u,v)表示频域点(u,v)到频域图像原点的距离，称为截止频率，当D(u,v) = 时，H(u,v)=0.5，即对应的频域能量将为原来的一半。因为巴特沃斯低通滤波器在高低频间的过渡平滑，因此不会出现明显的振铃效应。VTK中实现巴特沃斯低通滤波器的类是vtkImageButterworthLowPass.
> 
> 其使用过程如下:  
>  
> 
>     #include <vtkAutoInit.h>
>     VTK_MODULE_INIT(vtkRenderingOpenGL);
>      
>     #include <vtkSmartPointer.h>
>     #include <vtkJPEGReader.h>
>     #include <vtkImageFFT.h>
>     #include <vtkImageButterworthLowPass.h>
>     #include <vtkImageRFFT.h>
>     #include <vtkImageExtractComponents.h>
>     #include <vtkImageCast.h>
>     #include <vtkImageActor.h>
>     #include <vtkRenderer.h>
>     #include <vtkRenderWindow.h>
>     #include <vtkRenderWindowInteractor.h>
>     #include <vtkInteractorStyleImage.h>
>      
>     int main()
>     {
>     	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<vtkImageButterworthLowPass> lowPassFilter =
>     		vtkSmartPointer<vtkImageButterworthLowPass>::New();
>     	lowPassFilter->SetInputConnection(fftFilter->GetOutputPort());
>     	lowPassFilter->SetXCutOff(0.05);
>     	lowPassFilter->SetYCutOff(0.05);
>     	lowPassFilter->Update();
>      
>     	vtkSmartPointer<vtkImageRFFT> rfftFilter =
>     		vtkSmartPointer<vtkImageRFFT>::New();
>     	rfftFilter->SetInputConnection(lowPassFilter->GetOutputPort());
>     	rfftFilter->Update();
>      
>     	vtkSmartPointer<vtkImageExtractComponents> ifftExtractReal =
>     		vtkSmartPointer<vtkImageExtractComponents>::New();
>     	ifftExtractReal->SetInputConnection(rfftFilter->GetOutputPort());
>     	ifftExtractReal->SetComponents(0);
>      
>     	vtkSmartPointer<vtkImageCast> castFilter =
>     		vtkSmartPointer<vtkImageCast>::New();
>     	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, 0, 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->AddRenderer(leftRenderer);
>     	rw->AddRenderer(rightRenderer);
>     	rw->SetSize(640, 320);
>     	rw->SetWindowName("ButterworthLowPassExample");
>      
>     	vtkSmartPointer<vtkRenderWindowInteractor> rwi =
>     		vtkSmartPointer<vtkRenderWindowInteractor>::New();
>     	vtkSmartPointer<vtkInteractorStyleImage> style =
>     		vtkSmartPointer<vtkInteractorStyleImage>::New();
>     	rwi->SetInteractorStyle(style);
>     	rwi->SetRenderWindow(rw);
>     	rwi->Start();
>      
>     	return 0;
>     }
> 
> vtkImageButterworthLowPass与理想低通滤波器的使用一样。为了便于比较，这里设置X和Y方向的截止频率时，与理想低通滤波器设置一致，下面是相应的执行结果:
> 
> ![20170129122136824][]
> 
> **从结果来看，巴特沃斯低通滤波器产生的图像更为平滑，不会出现振铃现象。**

[20170129120815649]: https://img-blog.csdn.net/20170129120815649
[20170129120952119]: https://img-blog.csdn.net/20170129120952119
[20170129122136824]: https://img-blog.csdn.net/20170129122136824