A closed-form solution to non-rigid shape and motion recovery

Abstract: "Recovery of 3D shape and motion of non-static scenes from a monocular video sequence is important for applications like human computer interaction. If every point in the scene randomly deforms at each frame, it is impossible to recover the deforming shapes. In practice, many non-rigid objects, e.g. face under various expressions, deform regularly and their shapes are, or approximately are, weighted combination of certain shape bases. Shape and motion recovery under such situations thus has attracted many interests. Previous work on this problem [6, 4, 12] utilized only the orthonormality constraints on camera rotations (rotation constraints), but failed to apply another constraints [sic] on the shape bases (basis constraints). This paper proves that the solutions obtained using only the rotation constraints are inherently ambiguous. The ambiguity arises from the fact that, the shape bases are not unique since their linear transformation is a new set of eligible bases. To eliminate the ambiguity, we introduce the basis constraints that implicitly determine the shape bases uniquely. This paper proves that, under the weak-perspective projection model, once both the basis and the rotation constraints are imposed, we achieve a closed-form solution to the problem of non-rigid shape and motion recovery. The accuracy and robustness of our closed-form solution is evaluated quantitatively on synthetic data and qualitatively on real video sequences."