The best way to start with sixth sense is to get some background in 'Image Processing'. Matlab is a great tool for this. This video is somewhat mid-range, assuming that you have a decent background in computer programming. If you don't, then you can find similar videos for beginners on youtube.
Since Matlab runs on a computer, you don't need a smartphone. It simply takes inputs from a webcam and processes it.
If you want to implement sixth sense as a standalone device ..you'll have to use a microcontroller like arduino which takes care of the computation.
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It will take a lot more than a smart phone to power that. That dude has spent a lot of time and money to develop his prototype. To to mention how educated he is to be able to put that together.