CGMatter looks into tracking, and projections to remove objects in Blender.
There are plenty of tools out there that will allow you to track for visual effects and remove objects from a shot. Mocha Pro is excellent at this kind of work. If your visual effects shot is in 3D; however, things get a little more complicated. Blender can be a one-stop-shop for this type of VFX, having 2D video compositor, tracking capabilities and like most 3D programs, can create camera projections.
Check out this three-part tutorial from CGMatters that shows all the steps to remove objects from your shot, using Blender. The tutorial covers a technique that uses tracking and projection paintings to generate a clean plate that will track over the original footage.