Which software for Windows/Mac/Linux allow me to connect a DSLR (any DSLR brand is fine) and see in realtime (and record) the result of passing the live video feed through a filter?
A great tool that I personally work with is vvvv. A very mighty visual programming toolkit somewhat comparable to Quartz Composer on Mac but available for Windows (only for Windows for now but future versions might be multi plattform according to the devs).
For getting started I highly recommend this cheat sheet http://vvvv.org/sites/default/files/uploads/dontpanic_45beta25_1_0.pdf
Nice thing is that you can capture video over USB with a few canon DSRLs and don't necessarily need an HDMI capture card.
While you can capture frame with the "Writer" node, usually you would utilize Fraps for capturing the renderer (which can be lossless or in h264)
If software is all you're interested in, here are a few options:
Personally I've only tried Quartz. It's hugely powerful and free, but the learning curve can be quite steep. It's more of a node programming language for video graphics, that's what makes it so powerful.
Some downsides are that it's not actively developed anymore and that it only runs on OSX.
I'm excited to try Pixel Conduit soon. It seems to be an attempt at a modern version of quartz, and the free version seems pretty powerful.
If you want to record the video as well you might have to look at a separate program called Syphon.
I used a Blackmagic Intensity Extreme box to get the live video from our Sony XDCAMs into my Macbook Pro. I had to use Black Syphon to get the feed from the Blackmagic box and send it into Quartz for live processing.
I've been using Resolume to do exactly that. It works really well and is way more user friendly than Quartz. Though you can also use Quartz in it. Resolume also can record the video to an output file out of the box.
Pixel Conduit didn't seem to have gained much traction unfortunately. So I never used it in a production environment, I only played with it.
There isn't any single package to do this for most cameras. On Canon DSLRs for example, you need EOS Utility to interface with the camera's LivePreview, then need another piece of software to adapt the EOS Utility's feed in to a live video stream that can be operated on by the operating system (such as a Windows Media Capture stream). Then you need a piece of software to actually apply effects in real time to such a stream.
Alternately, the higher quality/higher budget option is to use something like an HDMI capture device or better yet, an ATEM video mixer to provide hardware assisted capture and alteration of the stream. This is much more reliable and higher quality since video is pretty intense to work on in real time and specialized hardware does the best job of dealing with it.