1.理想高通濾波器

高通濾波與低通濾波正好相反，是頻域圖像的高頻部分通過而抑制低頻部分。在圖像中圖像的邊緣對應高頻分量，因此高通濾波的效果是圖像銳化。同樣最簡單的高通濾波器是理想高通濾波器。通過設置一個頻率閾值，將高于該閾值的頻率部分通過，而低于閾值的低頻部分設置為0。

VTK中理想高通濾波的實例如下：

#include <vtkAutoInit.h> VTK_MODULE_INIT(vtkRenderingOpenGL);#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(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<vtkImageIdealHighPass> highPassFilter =vtkSmartPointer<vtkImageIdealHighPass>::New();highPassFilter->SetInputConnection(fftFilter->GetOutputPort());highPassFilter->SetXCutOff(0.1);highPassFilter->SetYCutOff(0.1);highPassFilter->Update();vtkSmartPointer<vtkImageRFFT> rfftFilter =vtkSmartPointer<vtkImageRFFT>::New();rfftFilter->SetInputConnection(highPassFilter->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, 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; }

同低通濾波一樣，首先將讀入圖像通過vtkImageFFT轉換到頻域空間，定義vtkImageIdealHighPass對象，并通過SetXCutOff ()和SetYCutOff() 設置X和Y方向的截止頻率。然后通過vtkImageRFFT將處理后的圖像轉換到空域中，得到高通濾波圖像。為了顯示的需要，還需要提取圖像分量和數據類型的轉換。

下面是理想高通濾波的執行結果：

從結果看出高通濾波后圖像得到銳化處理，圖像中僅剩下邊緣。

2.巴特沃茲高通濾波

理想高通濾波器不能通過電子元器件來實現，而且存在振鈴現象。在實際中最常使用的高通濾波器是巴特沃斯高通濾波器。該濾波器的轉移函數是：

D(u,v)表示頻域中點到頻域平面的距離，是截止頻率。當D(u,v)大于時，對應的H(u,v)逐漸接近1，從而使得高頻部分得以通過；而當D(u,v)小于時，H(u,v)逐漸接近0，實現低頻部分過濾。巴特沃斯高通濾波器在VTK中對應vtkImageButterworthHighPass類。

下面代碼說明了vtkImageButterworthHighPass對圖像進行高通濾波：

#include <vtkAutoInit.h> VTK_MODULE_INIT(vtkRenderingOpenGL);#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);highPassFilter->Update();vtkSmartPointer<vtkImageRFFT> rfftFilter =vtkSmartPointer<vtkImageRFFT>::New();rfftFilter->SetInputConnection(highPassFilter->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, 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; }

vtkImageButterworthHighPass與理想高通濾波使用方法一致。需要設置X和Y軸的截止頻率，為了便于比較，其截止頻域與理想高通濾波設置一致。

下圖是執行結果：

3.參看資料

1.《C++ primer》
2.《The VTK User’s Guide – 11thEdition》
3. ?張曉東, 羅火靈. VTK圖形圖像開發進階[M]. 機械工業出版社, 2015.

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