Transfinite interpolation

I want to use transfinite interpolation to fill the region inside the image. I want to know if there is any function or code in ITK that could do this? I already had the positions of the white points.

If these points are in order (clockwise or counter-clockwise), then you could make a poly-line out of them. This discussion could be of interest to you. Current PolylineMask2DImageFilter’s doxygen page.