Hi there! This is a good question..
For one thing, many pro photographers wouldn't always want to remove all the shades under the products for their 360 product views as it often gives a better impression of the 3D depth. If you are ok leaving some minor product shade on your 360-degree images, it's usually much easier.
So, there are pretty much two main options:
1) If your product is not white or light grey, the approach is to try to overexpose your product background during the photo-shoot as much as possible. In other words, the background behind and below your product has to be much brighter than your product on the set. The more contrast you can achieve between your background and the product the better.
Sometimes you would want to put a couple of light sources behind your product, shooting at your backdrop like in this example
or this one
- note the two smaller lights behind the fin.
On other occasions you can put your light source directly behind the backdrop shooting at the backdrop towards your product. Here's an example with the light source behind the backdrop link
Another light source in our case usually sits right above the product pointing towards the table to light up the table itself. Sometimes it helps putting a white semi-translucent sheet under the product as the reflection it produces helps with the shades in various ways. And then of course your other lights that actually illuminate the product at the front..
Also, depending on your 360 photography turntable manufacturer, the rotating platform itself can be translucent allowing you to put a light source under the table shooting straight up, eliminating most of the product shade (can also make the product look weird with a lot of shine at the bottom of the product). Here's Ortery's Photobench with the bottom illumination for example - link
So if you have sufficient contrast in your final 360 product images, you can often just use a standard photographic filter effect called Levels (that we also added in the new version of our software link
) to overexpose your image highlights even further to make the background pure white (if it's not there yet straight out of the camera), may be leaving some shade under the product if the product itself goes too bright as you move the Whites slider.
You can see the whole process of making the background pure white on that tennis rocket sample above in this video using our software: http://www.youtube.com/watch?v=W3uFpXy1ne4
2) If you can not get enough contrast with your lighting setup as per above or your product is very lightly colored, it's usually a lot of manual work to remove the background completely which involves creating a clipping path for each image. When this happens, we sometimes sub-contract other companies to help out with the clipping path as they specialize in this specific area (just google Clipping path and there'll be plenty of reasonably priced offers).
I hope this helps!