Two-Grid Preconditioned Solver for Bundle Adjustment

Siddhant Katyan, Shrutimoy Das, Pawan Kumar

Abstract:

We present the design and implementation of Two-Grid Preconditioned Bundle Adjustment (TPBA), a robust and efficient technique for solving the non-linear least squares problem that arises in bundle adjustment. Bundle adjustment (BA) methods for multi-view reconstruction formulate the BA problem as a non-linear least squares problem which is solved by some variant of the traditional LevenbergMarquardt (LM) algorithm. Most of the computation in LM goes into repeatedly solving the normal equations that arise as a result of linearizing the objective function. To solve these system of equations we use the Generalized Minimal Residual (GMRES) method, which is preconditioned using
a deflated algebraic two-grid method. To the best of our knowledge this is the first time that a deflated algebraic twogrid preconditioner has been used along with GMRES, for solving a problem in the computer vision domain. We show that the proposed method is several times faster than the direct method and block Jacobi preconditioned GMRES.