It so happens that SO(3), being a Lie group, has a well-defined space of derivatives: its associated Lie algebra so(3) [notice lower case]. In fact, the generators of the group fundamentally arise from the derivatives of rotations around the identity.
The same can be said of English. And in both cases, there are sundry tasks of limited scope where the language is probably not the most natural choice (e.g. operas). However, when one is simultaneously dealing with multiple, disparate domains/constraints simultaneously (e.g. real-time computer vision), such a language might be the least unattractive option thanks to its inclusiveness.
While there have been countless important geometric and mathematical insights applied to/developed in computer vision in the last decade, it's really the rapidly increasing computational power available on commodity hardware that has made many advances in real time vision possible.
During the four years I was doing my PhD [in real time vision, a couple years ahead of Qi Pan in the same group], the amount of useful image processing and linear algebra/geometry that could be computed in 33 ms jumped dramatically.
The computer vision community is collectively realizing that techniques that were always mathematically and statistically sound, but considered too expensive for online processing, can now feasibly be incorporated into real time and interactive systems.
There are fewer rather than more 'tricks' now, and more straightforward representations of the underlying mathematical and probabilistic structures. This is a good thing.
Likewise, real-time reconstruction techniques appropriate for desktops in 2004 can now run very well on embedded platforms.
It's an exciting time for computer vision, as the set of feasible applications is exploding.
http://en.wikipedia.org/wiki/Lie_group#The_Lie_algebra_assoc...