Globally Optimal Affine and Metric Upgrades in Stratified Autocalibration

We present a practical, stratified autocalibration algorithm with theoretical guarantees of global optimality. Given a projective reconstruction, the first stage of the algorithm upgrades 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, the algorithm upgrades this affine reconstruction 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 problem structure to restrict the search space for the DIAC and the plane at infinity to a small, fixed number of branc...

• Type: Conference
• Year: 2007
• Where: ICCV
• Authors: Manmohan Krishna Chandraker, Sameer Agarwal, David J. Kriegman, Serge Belongie
• Keywords: Affine Reconstruction, Computer Vision, ICCV 2007, Infinite Homography Relation, Non-convex Objective Functions, Stratified Autocalibration Algorithm, Tight Convex Relaxations