… and the conversion of coordinates is a matter of not so very advanced math: Every pixel (or, to be precise, the center of every pixel…) in the result image of polar unwrap corresponds to an angle and a radius (in this case read “distance to polar unwrap center”). If you still know the parameters CX, CY, Alpha0, RMin, RMax (and optionally AlphaTotal) that have been used in the CreatePolarImage(Ex) call that did the unwrap then determining the angle and the radius is fairly straigthforward:
// assumptions:
// imgUnwrapped = result image of polar unwrap operation
// xu, yu = coordinates in imgUnwrapped for which to calculate x, y in the original image
// input parameters to the CreatePolarImageEx call that created imgUnwrapped:
// cx, cy, alpha0, alphaTotal, rMin, rMax
auto uMaxX = static_cast<double>(ImageWidth(imgUnwrapped) - 1);
auto uMaxY = static_cast<double>(ImageHeight(imgUnwrapped) - 1);
auto alpha = static_cast<double>(xu)/uMaxX * alphaTotal + alpha0;
auto r = static_cast<double>(yu)/uMaxY * (rMax - rMin) + rMin;
auto x = cx + r * cos(alpha);
auto y = cy + r * sin(alpha);
If you used CreatePolarImage instead of CreatePolarImageEx then alphaTotal simply amounts to 360°. In the object-oriented APIs for C#, C++ and Python (see here) these two functions correspond to the PolarTransform extension/static member method on the Image object (C# and C++) or the cvb.polar_transform function (Python).