A novel fast method for L ∞ problems in multiview geometry

Abstract

Optimization using the L ∞ norm is an increasingly important area in multiview geometry. Previous work has shown that globally optimal solutions can be computed reliably using the formulation of generalized fractional programming, in which algorithms solve a sequence of convex problems independently to approximate the optimal L ∞ norm error. We found the sequence of convex problems are highly related and we propose a method to derive a Newton-like step from any given point. In our method, the feasible region of the current involved convex problem is contracted gradually along with the Newton-like steps, and the updated point locates on the boundary of the new feasible region. We propose an effective strategy to make the boundary point become an interior point through one dimension augmentation and relaxation. Results are presented and compared to the state of the art algorithms on simulated and real data for some multiview geometry problems with improved performance on both runtime and Newton-like iterations. © 2012 Springer-Verlag.