Using dynamics to recover Euclidian 3-dimensional structure from 2-dimensional perspective projections

Mario Sznaier, Mustafa Ayazoglu, Octavia Camps
2009 Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference  
In this paper we consider the problem of recovering the 3-dimensional Euclidian structure of a rigid object from multi-frame point correspondence data in a sequence of 2-D images obtained under perspective projection. The main idea is to recast the problem as the identification of an LTI system based on partial data. The main result of the paper shows that, under mild conditions, the lowest order system whose projections interpolate the 2-D data, yields (up to a single scaling constant) the
more » ... g constant) the correct 3 dimensional Euclidean coordinates of the points. Finally, we show that the problem of finding this system (and hence the associated 3-D data) can be recast into a rank minimization form that can be efficiently solved using convex relaxations. In contrast, existing approaches to the problem, based on iterative matrix factorizations can recover structure only up to a projective transformation that does not preserve the Euclidian geometry of the object.
doi:10.1109/cdc.2009.5399578 dblp:conf/cdc/SznaierAC09 fatcat:u6ant5xnffejtgajla5odlrhru