If you do not need to perform any image processing on your data, it is probably easier to use the vtk::DICOMImageReader class to read your DICOM series.
Otherwise, if you “need” to use ITK to read the DICOM series, you could convert your itk::Image instance to a vtk::ImageData instance using the itk::ImageToVTKImageFilter, as shown in this example.
In either case, using this example for your visualization purposes should be straightforward:
https://lorensen.github.io/VTKExamples/site/Cxx/Medical/MedicalDemo4/
You should just plug the output of the vtk::DICOMImageReader or vtk::ImageData object to the vtk::FixedPointVolumeRayCastMapper instead of the vtk::MetaImageReader output used in the example.
HTH,
JON HAITZ