Alright I did some more research on Mobileye and this is what I found out.
Originally, I was under the impression that Mobileye relied on STMicroelectronics to make the chips that process the images to look for moving objects (and annotate moving objects as geometric shapes that can be quickly interpreted by whatever software program). However, after reading more it looks like Mobileye is doing two main things:
1. They've designed a vision-processor System-On-Chip together with STMicroelectronics,
Mobileye and STMicroelectronics Deploy One-Millionth Driver Safety Device . This is the chip inside the camera that processes the images and translates moving objects into geometric shapes. They've released the EyeQ1 and the EyeQ2 chips and they are currently working on the EyeQ3 chip.
2. They've designed software to analyze the output of their EyeQ chips and integrate it into a driver safety system, ie., their
Mobileye 560 product
Now a lot of OEMs have integrated Mobileye's EyeQ1 and EyeQ2 chips into their cars to provide for lane departure warning, adaptive cruise control, forward collision warning, etc. My guess is that Mobileye is providing them with their EyeQ2 chip (probably bundled with a camera) and also is providing some software on top of that as well to integrate into safety features. I also think OEMs can just buy the EyeQ2 chip and then provide their own software to build their own safety systems as well. It's up to the OEMs.
It looks like Mobileye will be releasing their EyeQ3 SoC soon. Here's a very informative article on it:
http://can-newsletter.org/uploads/media/raw/5b1ebaa50b50a1e7fa4b6043de56dd5f.pdf
The same article link also shows an eyetracking system Mobileye has developed, which I think Tesla could use as well.
So, my speculation is that Tesla is going to use Mobileye's EyeQ3 chip and camera system, as well as their Eyetracking module as well. Then, rather than relying on the software safety system the Mobileye is building on top of the EyeQ3 chip, Tesla is choosing to build their own software system. So, Tesla's cars will take the data from the EyeQ3 chip/camera system and interpret it, and basically create their own autopilot system.
To oversimplify it, I think Tesla will use Mobileye's hardware (video-processor chip and camera system) but will develop their own software for their auto pilot system.