Is there a way to extract a person from a video without having a blue- (or green-)screen?
Any software which can do this?
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If you have a frame where the person does not exist, you can use a tool called a difference matte. (You'll need to scroll down to the section titled "Difference Matte Effect" for a description.) It will find a difference between the frame without the person, and the frames with a person and remove areas that are the same, leaving only the difference (in this case the person). As linked, After Effects has such a tool. Many other video editors have it as well.
Final Cut Pro X has a plugin called Pro Removal that can remove moving things from the scene on fixed camera shots.
Also there is a tutorial for After Effects that shows how remove objects from scene using the tracker.
Also you can clean frame by frame using Photoshop or similar if you have a good amount of time to spend or a crew to help you in the task.