Abstract

Many vision problems, such as ob ject recognition and image synthesis, are greatly impacted by deformation of ob jects. In this paper, we develop a deformation model based on Lie algebraic analysis. This work aims to provide a generative model that explicitly decouples defor- mation from appearance, which is fundamentally different from the prior work that focuses on deformation-resilient features or metrics. Specifi- cally, the deformation group for each ob ject can be characterized by a set of Lie algebraic basis. Such basis for different ob jects are related via par- allel transport. Exploiting the parallel transport relations, we formulate an optimization problem, and derive an algorithm that jointly estimates the deformation basis for a class of ob jects, given a set of images re- sulted from the action of the deformations. We test the proposed model empirically on both character recognition and face synthesis.