Sobel算子也是一种常用的梯度算子。Sobel算子计算稍微复杂，它采用3x3的模板。计算时模板在图像上移动，并在每个位置上计算对应中心像素的梯度值。

VTK中vtkSobel2D计算图像的sobel算子，使用代码如下：

#include <vtkAutoInit.h>
VTK_MODULE_INIT(vtkRenderingOpenGL);#include <vtkSmartPointer.h>
#include <vtkJPEGReader.h>
#include <vtkImageSobel2D.h>
#include <vtkImageExtractComponents.h>
#include <vtkImageMathematics.h>
#include <vtkImageData.h>
#include <vtkImageShiftScale.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<vtkImageSobel2D> sobelFilter =vtkSmartPointer<vtkImageSobel2D>::New();sobelFilter->SetInputConnection(reader->GetOutputPort());//包含横向和竖向边缘//提取X向边缘成分vtkSmartPointer<vtkImageExtractComponents> xSobel =vtkSmartPointer<vtkImageExtractComponents>::New();xSobel->SetComponents(0);//提取第一成分即X向梯度xSobel->SetInputConnection(sobelFilter->GetOutputPort());xSobel->Update();vtkSmartPointer<vtkImageMathematics> absFilter =vtkSmartPointer<vtkImageMathematics>::New();absFilter->SetOperationToAbsoluteValue();//将属性设置为绝对值模式absFilter->SetInputConnection(xSobel->GetOutputPort());absFilter->Update();double xRange[2];absFilter->GetOutput()->GetScalarRange(xRange);vtkSmartPointer<vtkImageShiftScale> xShiftScale =vtkSmartPointer<vtkImageShiftScale>::New();xShiftScale->SetOutputScalarTypeToUnsignedChar();//强制类型转换 方便显示xShiftScale->SetScale(255 / xRange[1]);//设置属性xShiftScale->SetInputConnection(absFilter->GetOutputPort());xShiftScale->Update();//提取Y向边缘成分vtkSmartPointer<vtkImageExtractComponents> ySobel =vtkSmartPointer<vtkImageExtractComponents>::New();ySobel->SetComponents(1);ySobel->SetInputConnection(sobelFilter->GetOutputPort());ySobel->Update();vtkSmartPointer<vtkImageMathematics> absYsobel =vtkSmartPointer<vtkImageMathematics>::New();absYsobel->SetOperationToAbsoluteValue();absYsobel->SetInputConnection(ySobel->GetOutputPort());absYsobel->Update();double yRange[2];absYsobel->GetOutput()->GetScalarRange(yRange);vtkSmartPointer<vtkImageShiftScale> yShiftScale =vtkSmartPointer<vtkImageShiftScale>::New();yShiftScale->SetOutputScalarTypeToUnsignedChar();yShiftScale->SetScale(255 / yRange[1]);yShiftScale->SetInputConnection(absYsobel->GetOutputPort());yShiftScale->Update();vtkSmartPointer<vtkImageActor> origActor =vtkSmartPointer<vtkImageActor>::New();origActor->SetInputData(reader->GetOutput());vtkSmartPointer<vtkImageActor> xSobelActor =vtkSmartPointer<vtkImageActor>::New();xSobelActor->SetInputData(xShiftScale->GetOutput());vtkSmartPointer<vtkImageActor> ySobelActor =vtkSmartPointer<vtkImageActor>::New();ySobelActor->SetInputData(yShiftScale->GetOutput());/double origView[4] = { 0, 0, 0.33, 1 };double xSobelView[4] = { 0.33, 0, 0.66, 1 };double ySobelView[4] = { 0.66, 0, 1, 1 };vtkSmartPointer<vtkRenderer> origRender =vtkSmartPointer<vtkRenderer>::New();origRender->SetViewport(origView);origRender->AddActor(origActor);origRender->ResetCamera();origRender->SetBackground(1, 0, 0);vtkSmartPointer<vtkRenderer> xSobelRender =vtkSmartPointer<vtkRenderer>::New();xSobelRender->SetViewport(xSobelView);xSobelRender->AddActor(xSobelActor);xSobelRender->ResetCamera();xSobelRender->SetBackground(0, 1, 0);vtkSmartPointer<vtkRenderer> ySobelRender =vtkSmartPointer<vtkRenderer>::New();ySobelRender->SetViewport(ySobelView);ySobelRender->AddActor(ySobelActor);ySobelRender->ResetCamera();ySobelRender->SetBackground(0, 0, 1);//vtkSmartPointer<vtkRenderWindow> rw =vtkSmartPointer<vtkRenderWindow>::New();rw->AddRenderer(origRender);rw->AddRenderer(xSobelRender);rw->AddRenderer(ySobelRender);rw->SetSize(960, 320);rw->SetWindowName("Edge by Soebl");vtkSmartPointer<vtkRenderWindowInteractor> rwi =vtkSmartPointer<vtkRenderWindowInteractor>::New();vtkSmartPointer<vtkInteractorStyleImage> style =vtkSmartPointer<vtkInteractorStyleImage>::New();rwi->SetInteractorStyle(style);rwi->SetRenderWindow(rw);rwi->Initialize();rwi->Start();return 0;
}

该例中计算利用Sobel算子计算图像的梯度图像，然后提取X方向的梯度分量和Y方向的梯度分量。

由于计算Sobel算子的值可能存在负值，因此利用vtkImageMathematics对各个分量图像计算绝对值，再由vtkImageShiftScale将图像的数值范围调节到0-255之间再显示。

执行结果如下：

2.参看资料

1.《C++ primer》
2.《The VTK User’s Guide – 11thEdition》
3.《The Visualization Toolkit – AnObject-Oriented Approach To 3D Graphics (4th Edition)》
4.  张晓东, 罗火灵. VTK图形图像开发进阶[M]. 机械工业出版社, 2015.