post processing - Is there an inverse function which will return an HDR picture to its original?

I want to return my original picture from an HDR-picture which I made with Adobe Photoshop CS6. Does an inverse function exist to do this?

The HDR technique takes two pictures where there is more light in one picture and then makes one picture from these two, I think.

Is there any way to return the exact original picture from the HDR picture?

If so, I am interested in the mathematical characteristics of this technique.

Answer

It is very important to understand the difference between a high dynamic range image, and a high dynamic range image that has been tonemapped back down to low dynamic range for display on a standard monitor.

This is a high dynamic range image that has been produced from multiple exposures:

http://www.mattgrum.com/photo_se/hdr.jpg

Looks dull and lifeless because you're viewing it on a low dynamic range monitor. What you can do is locally adjust the contrast, so as to maximise the dynamic range of your monitor in every part of the image. This process is called tonemapping:

http://www.mattgrum.com/photo_se/tonemapped.jpg

If you've done this tonemapping step (which is easy to detect as it makes your images look like the above), then you're out of luck, you'll never get back to the original(s), as it's a highly nonlinear filter that takes whole neighbouring image areas into account.

However if you've merely done a merge-to-HDR-image, then that process is entirely reversible, you can get back any of the original images by just truncating the dynamic range at the appropriate points:

http://www.mattgrum.com/photo_se/bottom.jpg