VTK 频域处理_高通滤波（理想+巴特沃兹）

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：

 1 #include <vtkAutoInit.h>
 2 VTK_MODULE_INIT(vtkRenderingOpenGL);
 3  
 4 #include <vtkSmartPointer.h>
 5 #include <vtkJPEGReader.h>
 6 #include <vtkImageFFT.h>
 7 #include <vtkImageIdealHighPass.h>
 8 #include <vtkImageRFFT.h>
 9 #include <vtkImageCast.h>
10 #include <vtkImageExtractComponents.h>
11 #include <vtkRenderer.h>
12 #include <vtkImageActor.h>
13 #include <vtkRenderWindow.h>
14 #include <vtkRenderWindowInteractor.h>
15 #include <vtkInteractorStyleImage.h>
16  
17 int main(int argc, char* argv[])
18 {
19     vtkSmartPointer<vtkJPEGReader> reader =
20         vtkSmartPointer<vtkJPEGReader>::New();
21     reader->SetFileName("lena.jpg");
22     reader->Update();
23  
24     vtkSmartPointer<vtkImageFFT> fftFilter =
25         vtkSmartPointer<vtkImageFFT>::New();
26     fftFilter->SetInputConnection(reader->GetOutputPort());
27     fftFilter->Update();
28  
29     vtkSmartPointer<vtkImageIdealHighPass> highPassFilter =
30         vtkSmartPointer<vtkImageIdealHighPass>::New();
31     highPassFilter->SetInputConnection(fftFilter->GetOutputPort());
32     highPassFilter->SetXCutOff(0.1);
33     highPassFilter->SetYCutOff(0.1);
34     highPassFilter->Update();
35  
36     vtkSmartPointer<vtkImageRFFT> rfftFilter =
37         vtkSmartPointer<vtkImageRFFT>::New();
38     rfftFilter->SetInputConnection(highPassFilter->GetOutputPort());
39     rfftFilter->Update();
40  
41     vtkSmartPointer<vtkImageExtractComponents> ifftExtractReal =
42         vtkSmartPointer<vtkImageExtractComponents>::New();
43     ifftExtractReal->SetInputConnection(rfftFilter->GetOutputPort());
44     ifftExtractReal->SetComponents(0);
45  
46     vtkSmartPointer<vtkImageCast> castFilter =
47         vtkSmartPointer<vtkImageCast>::New();
48     castFilter->SetInputConnection(ifftExtractReal->GetOutputPort());
49     castFilter->SetOutputScalarTypeToUnsignedChar();
50     castFilter->Update();
51     /
52     vtkSmartPointer<vtkImageActor> originalActor =
53         vtkSmartPointer<vtkImageActor>::New();
54     originalActor->SetInputData(reader->GetOutput());
55  
56     vtkSmartPointer<vtkImageActor> erodedActor =
57         vtkSmartPointer<vtkImageActor>::New();
58     erodedActor->SetInputData(castFilter->GetOutput());
59     /
60     double leftViewport[4] = { 0.0, 0.0, 0.5, 1.0 };
61     double rightViewport[4] = { 0.5, 0.0, 1.0, 1.0 };
62     vtkSmartPointer<vtkRenderer> leftRenderer =
63         vtkSmartPointer<vtkRenderer>::New();
64     leftRenderer->AddActor(originalActor);
65     leftRenderer->SetViewport(leftViewport);
66     leftRenderer->SetBackground(1.0, 1.0, 1.0);
67     leftRenderer->ResetCamera();
68     vtkSmartPointer<vtkRenderer> rightRenderer =
69         vtkSmartPointer<vtkRenderer>::New();
70     rightRenderer->AddActor(erodedActor);
71     rightRenderer->SetViewport(rightViewport);
72     rightRenderer->SetBackground(1.0, 1.0, 1.0);
73     rightRenderer->ResetCamera();
74     /
75     vtkSmartPointer<vtkRenderWindow> rw =
76         vtkSmartPointer<vtkRenderWindow>::New();
77     rw->SetSize(640, 320);
78     rw->AddRenderer(leftRenderer);
79     rw->AddRenderer(rightRenderer);
80     rw->SetWindowName("IdealHighPassExample");
81  
82     vtkSmartPointer<vtkRenderWindowInteractor> rwi =
83         vtkSmartPointer<vtkRenderWindowInteractor>::New();
84     vtkSmartPointer<vtkInteractorStyleImage> style =
85         vtkSmartPointer<vtkInteractorStyleImage>::New();
86     rwi->SetInteractorStyle(style);
87     rwi->SetRenderWindow(rw);
88     rwi->Start();
89  
90     return 0;
91 }

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。

下面是理想高通滤波的执行结果：

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。

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：

 1 #include <vtkAutoInit.h>
 2 VTK_MODULE_INIT(vtkRenderingOpenGL);
 3  
 4 #include <vtkSmartPointer.h>
 5 #include <vtkJPEGReader.h>
 6 #include <vtkImageFFT.h>
 7 #include <vtkImageButterworthHighPass.h>
 8 #include <vtkImageRFFT.h>
 9 #include <vtkImageExtractComponents.h>
10 #include <vtkImageCast.h>
11 #include <vtkRenderer.h>
12 #include <vtkImageActor.h>
13 #include <vtkRenderWindow.h>
14 #include <vtkRenderWindowInteractor.h>
15 #include <vtkInteractorStyleImage.h>
16  
17 int main(int argc, char* argv[])
18 {
19     vtkSmartPointer<vtkJPEGReader> reader =
20         vtkSmartPointer<vtkJPEGReader>::New();
21     reader->SetFileName("lena.jpg");
22     reader->Update();
23  
24     vtkSmartPointer<vtkImageFFT> fftFilter =
25         vtkSmartPointer<vtkImageFFT>::New();
26     fftFilter->SetInputConnection(reader->GetOutputPort());
27     fftFilter->Update();
28  
29     vtkSmartPointer<vtkImageButterworthHighPass> highPassFilter =
30         vtkSmartPointer<vtkImageButterworthHighPass>::New();
31     highPassFilter->SetInputConnection(fftFilter->GetOutputPort());
32     highPassFilter->SetXCutOff(0.1);
33     highPassFilter->SetYCutOff(0.1);
34     highPassFilter->Update();
35  
36     vtkSmartPointer<vtkImageRFFT> rfftFilter =
37         vtkSmartPointer<vtkImageRFFT>::New();
38     rfftFilter->SetInputConnection(highPassFilter->GetOutputPort());
39     rfftFilter->Update();
40  
41     vtkSmartPointer<vtkImageExtractComponents> ifftExtractReal =
42         vtkSmartPointer<vtkImageExtractComponents>::New();
43     ifftExtractReal->SetInputConnection(rfftFilter->GetOutputPort());
44     ifftExtractReal->SetComponents(0);
45  
46     vtkSmartPointer<vtkImageCast> castFilter =
47         vtkSmartPointer<vtkImageCast>::New();
48     castFilter->SetInputConnection(ifftExtractReal->GetOutputPort());
49     castFilter->SetOutputScalarTypeToUnsignedChar();
50     castFilter->Update();
51     
52     vtkSmartPointer<vtkImageActor> originalActor =
53         vtkSmartPointer<vtkImageActor>::New();
54     originalActor->SetInputData(reader->GetOutput());
55  
56     vtkSmartPointer<vtkImageActor> erodedActor =
57         vtkSmartPointer<vtkImageActor>::New();
58     erodedActor->SetInputData(castFilter->GetOutput());
59     //
60     double leftViewport[4] = { 0.0, 0.0, 0.5, 1.0 };
61     double rightViewport[4] = { 0.5, 0.0, 1.0, 1.0 };
62     vtkSmartPointer<vtkRenderer> leftRenderer =
63         vtkSmartPointer<vtkRenderer>::New();
64     leftRenderer->AddActor(originalActor);
65     leftRenderer->ResetCamera();
66     leftRenderer->SetViewport(leftViewport);
67     leftRenderer->SetBackground(1.0, 1.0, 1.0);
68  
69     vtkSmartPointer<vtkRenderer> rightRenderer =
70         vtkSmartPointer<vtkRenderer>::New();
71     rightRenderer->AddActor(erodedActor);
72     rightRenderer->SetViewport(rightViewport);
73     rightRenderer->SetBackground(1.0, 1.0, 1.0);
74     rightRenderer->ResetCamera();
75     
76     vtkSmartPointer<vtkRenderWindow> rw =
77         vtkSmartPointer<vtkRenderWindow>::New();
78     rw->AddRenderer(leftRenderer);
79     rw->AddRenderer(rightRenderer);
80     rw->SetSize(640, 320);
81     rw->Render();
82     rw->SetWindowName("Frequency_ButterworthHighPass");
83     /
84     vtkSmartPointer<vtkRenderWindowInteractor> rwi =
85         vtkSmartPointer<vtkRenderWindowInteractor>::New();
86     vtkSmartPointer<vtkInteractorStyleImage> style =
87         vtkSmartPointer<vtkInteractorStyleImage>::New();
88     rwi->SetInteractorStyle(style);
89     rwi->SetRenderWindow(rw);
90     rwi->Start();
91  
92     return 0;
93 }

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。

下图是执行结果：