TY - CONF

T1 - Globally optimal affine and metric upgrades in stratified autocalibration

AU - Chandraker, Manmohan

AU - Agarwal, Sameer

AU - Kriegman, David

AU - Belongie, Serge

PY - 2007

Y1 - 2007

N2 - 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 branching dimensions, independent of the number of views. Experimental evidence of the accuracy, speed and scalability of our algorithm is presented on synthetic and real data. MATLAB code for the implementation is made available to the community.

AB - 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 branching dimensions, independent of the number of views. Experimental evidence of the accuracy, speed and scalability of our algorithm is presented on synthetic and real data. MATLAB code for the implementation is made available to the community.

UR - http://www.scopus.com/inward/record.url?scp=50649097716&partnerID=8YFLogxK

U2 - 10.1109/ICCV.2007.4409114

DO - 10.1109/ICCV.2007.4409114

M3 - Paper

AN - SCOPUS:50649097716

T2 - 2007 IEEE 11th International Conference on Computer Vision, ICCV

Y2 - 14 October 2007 through 21 October 2007

ER -