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 (1≤m≤n). 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.

Date Published: 1 July 2003
PDF: 11 pages
Proc. SPIE 5016, Computational Imaging, (1 July 2003); doi: 10.1117/12.487987

Published in SPIE Proceedings Vol. 5016:
Computational Imaging
Charles A. Bouman; Robert L. Stevenson, Editor(s)