I've never played the Wii or Kinect, but to my understanding, the Wii captures user movement with 4 cameras and translates them to controls.
How does this work? Has Nintendo published anything on this? I'd appreciate a mathematical explanation.
Your description sounds more like the Kinect, though it doesn't have 4 cameras either. Maybe you're referring to a camera in each of the 4 Wii controllers. Wikipedia has a nice explanation of how the Wii controller works.
A summary of the article: An optical sensor in the controller captures the infrared LEDs in the sensor bar. It then calculates its distance, orientation and relative position based on the known fixed distance between the LEDs in the bar.
Wii uses 3 mechanisms to track its controller:
Basic implementation was a simple optical calculation of remote's orientation using infrared-sensitive "camera" on top of a controller.
With MotionPlus gyroscope and accelerometer work together (similarly to a smartphone) to detect remote's movement and rotations. It's a much more precise measurement and you don't have to point the controller towards the sensor bar.
The only problem is, it's a relative, not absolute changes we detect, so after some time measurement errors start to add up.
So once in a while infrared camera kicks in and recalibrates the system to fit the LEDs on sensor bar.