How to Segment 3D Volume?

How to Segment the 3D picture like the flowing:

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The video starts from an already segmented image and just demonstrates separation of segments. This separation is a relatively easy task, as the joint space is large and image quality of feet can be high (since there is practically no radiation concerns when imaging extremities).

You can do not just this separation but the full image segmentation and separation in one combined step in 3D Slicer. Slicer also offers useful post-processing operations, such as smoothing and solidification. You can find step-by-step tutorial here:

3D Slicer, Segment Editor, and most of the effects are based on VTK. You are free to take and use anything in your application, without any restrictions. However, it is usually easier to trim down/customize/extend 3D Slicer to implement your workflow instead of start developing a new application from scratch.