I'm wanting to buy this IR camera but it says it has RCA output. Is it possible to read this into an mbed without external components(aside from a 12v power source)? If so, how?
By "RCA output" I assume they mean a composite video output. In order to convert that into some sort of digital image that a microcontroller can use, you would need an extremely fast ADC, or simply a video decoder (i.e. one from Maxim IC, Analog Devices, TI) to tease out the image data. Better yet, just get a camera with a digital output, as the digital-to-analog-to-digital path is a waste, as it's costly and performs worse.
NTSC scanlines are transmitted at 15.734 kHz with frequency content up to 4.2 MHz, impossible to handle with a standard microcontroller ADC which have sample rates of 1 Msps at the high end (NXP LPC1768 only has 200 ksps). Furthermore, as Leon points out, your memory is extremely limited. If you read just one QVGA (320 x 240) frame into memory at 8 bits/pixel, that's 76.8 kB, which exceeds the mbed's (NXP LPC1768's) on-board 64 kB RAM.
It's got a video output so you won't be able to use it with the mbed. It isn't fast enough and doesn't have enough memory.