The Raspberry Pi is like a cross between a microcontroller like the Arduino and a full Linux desktop computer. It is much more computationally capable than an Arduino, and has the advantage of being able to use PC grade hardware like monitors, speakers, and nearly any USB device. However, it does not have as many GPIO pins available and operates at 3.3V instead of 5V like many Arduinos. The reason is that the Raspberry Pi is actually designed to be an inexpensive computer, not a microcontroller. It is inexpensive at just $25 or $35, and is extremely popular. As a result, there is a lot of support and documentation around for it, unlike other micocromputers.
One of the great advantages of a microcomputer, aside from the improved hardware and peripheral support, is that you get to use high level programming languages like python and even OpenGL for 3D displays. Image processing is easily done using simple webcams and using OpenCV, which the Arduino is far too underpowered to do. Since the Raspberry Pi is so popular, there are some great libraries that make it very easy to interface with the GPIO - even ones that imitate the familiar Arduino interface.