Is it possible to capture HDMI input with an Raspberry PI board (or alternative)? My goal is to capture the HDMI data send from my TV and work with it from the Raspberry PI board.
Capturing HDMI is possible but it requires dedicated hardware called a digitiser or a video capture device. It will not work with a HDMI output. It will not work with a Raspberry Pi unless you add this hardware.
Having said that, the Pi does have an USB port and you can easily find an USB based
HDMI to USB video capture dongle. (Google it)
Make sure that whatever device to buy can work with USB2 (power and bandwith issues!) and that there is driver support for it.
Following up on Keltari's note bout capturing in full resolution:
HDMI 1.0 defines up to 3.96 Gbit/s of video bandwidth (1080p/60 Hz or UXGA) and 8 channel LPCM/192 kHz/24-bit audio. (Source: Wikipedia)
Compare this with USB2's theoretical max bandwidth. which is 480mbit/sec.
Even with smart compression on your digitiser you are likely to run into problems unless you really lower resolution. And to make things worse the rPi model B+ (and I think also other Pi models) has only one USB port. On my B+ that single port (and its bandwidth) is fed to a chip which turns it into 4x USB and Ethernet. But the max thoughput is still limited. If you write to an external USB harddrive (likely since recordings are unlikely to fit on the SD card) then you have to share this bandwidth.