Learning a generic 3D face model from 2D image databases using incremental Structure-from-Motion
Image and Vision Computing
2D-3D registration of deformable shapes with manifold projection
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
Adaptive metric registration of 3D models to non-rigid image trajectories
ECCV'10 Proceedings of the 11th European conference on computer vision conference on Computer vision: Part III
Stratified Generalized Procrustes Analysis
International Journal of Computer Vision
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Many natural objects vary the shapes as linear combinations of certain bases. The measurement of such deformable shapes is coupling of rigid similarity transformations between the objects and the measuring systems and non-rigid deformations controlled by the linear bases. Thus registration and modeling of deformable shapes are coupled problems, where registration is to compute the rigid transformations and modeling is to construct the linear bases. The previous methods [3, 2] separate the solution into two steps. The first step registers the measurements regarding the shapes as rigid and the deformations as random noise. The second step constructs the linear model using the registered shapes. Since the deformable shapes do not vary randomly but are constrained by the underlying model, such separate steps result in registration biased by nonrigid deformations and shape models involving improper rigid transformations. We for the first time present this bias problem and formulate that, the coupled registration and modeling problems are essentially a single factorization problem and thus require a simultaneous solution. We then propose the Direct Factorization method that extends a structure from motion method [16]. It yields a linear closedform solution that simultaneously registers the deformable shapes at arbitrary dimensions (2D \to 2D, 3D \to 3D, . . .) and constructs the linear bases. The accuracy and robustness of the proposed approach are demonstrated quantitatively on synthetic data and qualitatively on real shapes.