Rotate components on image around a fixed point

Question

I have an binarized image

and a center

cvx = Import@"https://i.stack.imgur.com/1QoEo.png";
center = {258.19137417775005`, 150.8459811782782`};
HighlightImage[cvx, center]

gives

I want to rotate this white triangle by 180 degree around this center point and keep the original image dimension.

If I run

rotCvx = 
 ImageTransformation[cvx, RotationTransform[\[Pi], center], 
  PlotRange -> All, Background -> White]

which gives

But this is not the correct rotated one. You can see from

ImageAdd[cvx, rotCvx]

gives

The correct one should give

So how to rotate components on image around a fixed point?

Answer 1

Well, this may be easy to overlook, but it's actually mentioned in Details and Options section of document of ImageTransformation:

In 2D, the range of the coordinate system for the input image is assumed to be {{0,1},{0,a}}, where a is the aspect ratio. The bottom-left corner of the image corresponds to coordinates {0,0} by default.

Other coordinate systems can be specified by setting the DataRange option.

Typical settings for DataRange include: Full - same ranges as the input image

So, you just need DataRange -> Full:

rotCvx = ImageTransformation[cvx, RotationTransform[π, center], 
  Background -> White, DataRange -> Full]