Paper Info
Title
Globally Optimal Algorithms for Stratified Autocalibration
Abstract
We present practical algorithms for stratified autocalibration with theoretical guarantees of global optimality. Given a projective reconstruction, we first upgrade it to affine by estimating the position of the plane at infinity. The plane at infinity is computed by globally minimizing a least squares formulation of the modulus constraints. In the second stage, this affine reconstruction is upgraded to a metric one by globally minimizing the infinite homography relation to compute the dual image of the absolute conic (DIAC). The positive semidefiniteness of the DIAC is explicitly enforced as part of the optimization process, rather than as a post-processing step.For each stage, we construct and minimize tight convex relaxations of the highly non-convex objective functions in a branch and bound optimization framework. We exploit the inherent problem structure to restrict the search space for the DIAC and the plane at infinity to a small, fixed number of branching dimensions, independent of the number of views. Chirality constraints are incorporated into our convex relaxations to automatically select an initial region which is guaranteed to contain the global minimum.Experimental evidence of the accuracy, speed and scalability of our algorithm is presented on synthetic and real data.
Year
DOI
Venue
2010
10.1007/s11263-009-0305-2
International Journal of Computer Vision
Keywords
Field
DocType
Autocalibration,Multiple view geometry,Global optimization,Convex relaxations
Affine transformation,Plane at infinity,Mathematical optimization,Branch and bound,Global optimization,DIAC,Computer science,Algorithm,Convex function,Homography,Conic section
Journal
Volume
Issue
ISSN
90
2
0920-5691
Citations 
PageRank 
References 
13
0.60
38
Authors
4
Name
Order
Citations
PageRank
Manmohan Chandraker145125.58
Sameer Agarwal210328478.10
David Kriegman37693451.96
Serge J. Belongie4125121010.13