Probably in all 2D mappers (at least in mitkSurfaceMapper2D and mitkUnstructuredGridMapper2D) the method Geometry2D::Map(...) is called as often as there are points to render (thousands to millions of times).

The method Geometry2D::Map() in turn calls Geometry3D::BackTransform() which fetches the inverse transform each time. Although the inverse is cached in the base class itk::MatrixOffsetTransformBase of the member m_IndexToWorldTransform (as far as I see it by just looking at the code), caching the inverse ourselves in the Geometry3D class speeds up rendering four-fold (both in release and binary).

Attached the changes as a patch.