Abstract

Recovery of three dimensional (3D) shape and motion of non-static scenes from a monocular video sequence is important for ap- plications like robot navigation and human computer interaction. If every point in the scene randomly moves, it is impossible to recover the non- rigid shapes. In practice, many non-rigid ob jects, e.g. the human face under various expressions, deform with certain structures. Their shapes can be regarded as a weighted combination of certain shape bases. Shape and motion recovery under such situations has attracted much interest. Previous work on this problem [6,4,13] utilized only orthonormality con- straints on the camera rotations (rotation constraints). This paper proves that using only the rotation constraints results in ambiguous and invalid solutions. The ambiguity arises from the fact that the shape bases are not unique because their linear transformation is a new set of eligible bases. To eliminate the ambiguity, we propose a set of novel constraints, basis constraints, which uniquely determine the shape bases. We prove that, under the weak-perspective pro jection model, enforcing both the basis and the rotation constraints leads to a closed-form solution to the problem of non-rigid shape and motion recovery. The accuracy and ro- bustness of our closed-form solution is evaluated quantitatively on syn- thetic data and qualitatively on real video sequences.