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The motion detection stuff on pi is indeed very easy.. There is even a lovely package called "motion" that does all the stuff for you. The only issue really with using a pi for this kind of stuff is ensuring that it is resilient to suddenly having its power cord yanked, all of this home automation stuff is only good if you don't have to faff with it once it is installed.
The pi is, of course, overkill for stuff like this, it is expensive for one and despite not being very thirsty it is still more powerful than it needs to be for the job, but against this it is very convenient :-)
Quite interested in these YUN things, but again you are paying for convenience. I'll take a look at the mbed stuff.
I'm an electronic engineering student currently working in industry, in embedded systems, and honestly it's nice seeing people getting excited about this. Electronics seems full of cynics all-too-ready to scoff at the idea of having an internet-connected toaster than looking into the innovation and interesting/useful stuff that can be done.
I'm really keen to hear about people's projects here! It's really easy to get a pi working with any generic webcam so I've been thinking about setting that up as a timelapse or connected to a motion sensor of some sort so that anyone walking into my room gets a snap taken of them, then using the pi to upload the data to somewhere remote/secure (not always the same thing!)
Also, it's maybe worth pointing out that a rPi is a very different thing to an arduino. The arduino being far better suited to this kind of project, unless you're connecting to the web/crunching serious data. the rPi is a basic computer, the arduino is a microcontroller.
Anyone seriously interested should look up the mBed platform by ARM, it's like an arduino; user friendly and there are loads of libraries but it has some serious hardware. 80+MHz cpu for example! A good few of my friends at uni used this for their 3rd year projects: http://developer.mbed.org/platforms/mbed-LPC1768/
And had a good deal more success than me