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The paper addresses the problem of recovering 3D non-rigid shape models from image sequences. For example, given a video recording of a talking person, we would like to estimate a 3D model of the lips and the full face and its internal modes of variation. Many solutions that recover 3D shape from 2D image sequences have been proposed; these so-called structure-from-motion techniques usually assume that the 3D object is rigid. For example, C. Tomasi and T. Kanades' (1992) factorization technique is based on a rigid shape matrix, which produces a tracking matrix of rank 3 under orthographic projection. We propose a novel technique based on a non-rigid model, where the 3D shape in each frame is a linear combination of a set of basis shapes. Under this model, the tracking matrix is of higher rank, and can be factored in a three-step process to yield pose, configuration and shape. To the best of our knowledge, this is the first model free approach that can recover from single-view video sequences nonrigid shape models. We demonstrate this new algorithm on several video sequences. We were able to recover 3D non-rigid human face and animal models with high accuracy.
Bregler et al. (Thu,) studied this question.