Yes! There is definitely a way to extract/remove a persona from a video without the need to use a blue, white, green, black, gray or any color background. You can try Adobe Premiere if the person is not moving side to side, or my favorite editing tool: Adobe After Effects. You can use the Clone Tool in Adobe After Effects. In the case you can't use those apps from the Adobe Creative Suite, try the Boris FX Motion Key. It may do the trick for you.
Another tool you could use is Mocha Pro, which is the industry's standard for object/person removal. Once you have use any of the tools or software, you can try figuring out a method of completing the removal without the help of the software doing it for you.
I look forward to hearing from you. I hope this information helps.