Obtain the LUT transformation knowing the input (RAW image) and the output (adjusted image)

Hello,

I am usign a software that allows to adjustRAW images using LUT. However, I would like to obtain the LUT that I have used for a particular image, so I can apply the same transformation to any images without using the particular software.

I am attaching two images: i) with the LUT off, so input=output and ii) with the LUT that I have chosen to adjust the image. I am interested in getting a sharp edge between the two interfaces on the right area of the image. In the RAW image, it is difficult to distinguish the edge. However, customizing the LUT I can obtain a sharp edge.

I would like to be able to obtain the LUT (polynomial curve) that transforms the RAW images to the desired (adjusted) image.

I would really appreciate it if you can help me with the script. I am not sure where to start.

Thanks