MWAC wrote:
you don't need photoshop, it can be done in camera.
Get the lens as close to the fence as possible (don't touch the fence, you'll scratch the lens). Shot with a large aperture, wait till your subject is away from the fence. You'll create a DoF that works for you and makes the fence disappear.
All I can add to the advice from MWAC is that the technique works if the animal or other subject is not too close to the fence.