4D structure from motion: a computational algorithm

A problem of long standing in vision research is the recovery of three-dimensional (3D) structure from two-dimensional (2D) images. Work on structure from motion has focused on the recovery of 3D structure from multiple views of feature points like the vertices of a cube. Recent work on the perception of four-dimensional (4D) structures has prompted us to determine the circumstances under which 4D structure can be recovered from multiple views of feature points projected onto 2D images. We present a computational algorithm to solve this problem under three assumptions: 1 . the correspondence of each feature point over different views is pre-determined; 2. the 4D object undergoes a rigid motion, and 3. the projection from 4D space to 2D images is a orthographic (parallel) one. Four views of five points are required. The algorithm can be generalized to treat the recovery of nD structure from mD views (lmn). We give some results concerning the minimum number of points and views that are required to recover nD structure from mD views by this algorithm.