For anyone coming to this page from Google:
For EDITING video:
To capture HDMI content in Ubuntu, you can use HDMI capture USB boxes (such as Magewell XI100DUSB-HDMI) or HDMI PCI cards (such as Blackmagic Intensity Pro).
Also, you may need to use a Linux-centric video solution such as ShotCut if you want these cards to work well.
For LIVE STREAMING video:
The above-mentioned cards might work but will require gstreamer in-between to make the Intensity Pro's inputs available in V4L(2).
Also, please note that for any of this to work, your video has to come out in unprotected mode (non-HDCP), otherwise your capturing won't show any video/audio.