Digital image stabilization is a fascinating subject. On one hand, the core idea is simple (average out motion over time in some way then pan and zoom the image to compensate for deviations from the average); on the other, it's not easy to get right since outside of random jitter some camera motion, even rapid, can be what the camera operator wants.

Here's an example of an actual algorithm used for digital IS: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.148....