How To Access Another Computer "locally"

Here's my problem:

1) I have a website running on a Linux server somewhere

2) I have a big hard drive at home with a bunch of videos.

3) I want to be able to manipulate the videos at home from the server. I want to be able to do this like run ffmpeg commands on it to get the video length, or create a thumbnail from any frame of the video.

Here are the caveats:

- I do NOT want the complete video to be uploaded to the server every time i have to manipulate a video. In the case of thumbnailing, the processing should be done on my home computer, but the output should be copied over to the server.

- Speed is not an issue. This doesnt have to be the fastest solution in the world.

- My home computer is running linux now, but I can change it to whatever I want.

- My server is a shared host; I do not have full root access. However, my host is kind enough to give me reasonable leverage.

I'm thinking the way that this could happen would be by mounting my home computers disk on the server so that I can access the files "locally". I don't know how to do this though, or even if this is the right way to do this.