1.1 Why use Lie groups for robotics or computer vision?

Many problems in robotics and computer vision involve manipulation and estimation in 2D and 3D geometry. Without a coherent and robust framework for representing and working with such transformations, these tasks are onerous and treacherous. Transformations must be composed, inverted, differentiated, interpolated, optimized, and represented with uncertainty. Lie groups and their associated machinery address all of these operations, and do so in a principled way, so that the treatment of the various transformation groups is uniform.