Three-dimensional head pose estimation from a single 2D image is a challenging task with extensive applications. Existing approaches lack the capability to deal with multiple pose-related and -unrelated factors in a uniform way. Most of them can provide only one-dimensional yaw estimation and suffer from limited representation ability for out-of-sample testing inputs. These drawbacks lead to limited performance when extensive variations exist on faces in-the-wild. To address these problems, we propose a coarse-to-fine pose estimation framework, where the unit circle and 3-sphere are employed to model the manifold topology on the coarse and fine layer respectively. It can uniformly factorize multiple factors in an instance parametric subspace, where novel inputs can be synthesized under a generative framework. Moreover, our approach can effectively avoid the manifold degradation problem when 3D pose estimation is performed. The results on both experimental and in-the-wild databases demonstrate the validity and superior performance of our approach compared with the state-of-the-arts. 
From circle to 3-sphere: Head pose estimation by instance parameterization