Applications of Lie groups and Lie algebra to computer vision: A brief survey

Recent years an extensive literature appears using the Lie groups theory to solve the problems of computer vision. Lie groups theory is the natural representation of a space of transformations. Lie algebra is the tangent space of Lie groups at the identity. From Lie groups to Lie algebra, we can establish a mapping from the multiplicative structure to an equivalent vector space representation, which makes correlation calculation become rational and precise. Based on the linear structure of Lie algebra, many statistical learning methods can be readily applied. This survey briefly reviews the different approaches about the use of Lie groups theory that have been developed by research; introducing the mathematical background of Lie groups theory corresponding to computer vision; describing the main approaches in details according two categories.