VTK_Learning_频域处理_低通滤波(理想+巴特沃兹)
作者:互联网
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: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:
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:
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。
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标签:1.0,VTK,vtkSmartPointer,沃兹,图像,New,include,leftRenderer,通滤波 来源: https://blog.csdn.net/weixin_38293453/article/details/104612570