Shape from motion revisited

Abstract

This brief tutorial paper on Shape from Motion (SfM), the profound 3D object modeling method, focuses on mathematical background for the batch scenario. Error bounds for pixels with respect to depth change are derived to analyze the applicability of orthographic projection versus perspective projection. Key geometric properties, used for SfM algorithms design and analysis, are stated and proved. Moreover, the case of measurement matrix with rank two, for non planar shapes is fully characterized and its role in shape ambiguity explored. Other sources of SfM ambiguity are presented what justifies the definition of ambiguous error function used for nonlinear optimization of rotation coefficients. Experiments refer to head pose identification and 3D face animation and show the good visual accuracy of SfM approach for digital 3D face projects. © 2014 Springer International Publishing.