Shape and motion reconstruction of non rigid objects from their 2D projections under uniform expansion conditions

This paper deals with the 3D-motion and structure reconstruction of a particular class of nonrigid objects based on a sequence of their 2D orthographic projections (images). The investigation focuses on the case where it is known a-priori that the object deforms continuously in a uniform manner performing either expansion or contraction at a constant but, at the same time, unknown rate. Epipolar equations are properly extended to meet the requirements of this particular problem. It is shown that four point correspondences over four views yield a unique solution to motion and structure reconstruction. The theory is supported by a numerical result.