TY - GEN

T1 - Globally Optimal Least Squares Solutions for Quasiconvex 1D Vision Problems

AU - Olsson, Carl

AU - Byröd, Martin

AU - Kahl, Fredrik

PY - 2009

Y1 - 2009

N2 - Solutions to non-linear least squares problems play an essential role in structure and motion problems in computer vision. The predominant approach for solving these problems is a Newton like scheme which uses the: hessian of the function to iteratively find a, local solution. Although fast, this strategy inevitably leeds to issues with poor local minima, and missed global minima. In this paper rather than trying to develop all algorithm that is guaranteed to always work, we show that it is often possible to verify that a local solution is in fact; also global. We present a simple test that verifies optimality of a solution using only a few linear programs. We show oil both synthetic and real data that for the vast majority of cases we are able to verify optimality. Further more we show even if the above test fails it is still often possible to verify that the local solution is global with high probability.

AB - Solutions to non-linear least squares problems play an essential role in structure and motion problems in computer vision. The predominant approach for solving these problems is a Newton like scheme which uses the: hessian of the function to iteratively find a, local solution. Although fast, this strategy inevitably leeds to issues with poor local minima, and missed global minima. In this paper rather than trying to develop all algorithm that is guaranteed to always work, we show that it is often possible to verify that a local solution is in fact; also global. We present a simple test that verifies optimality of a solution using only a few linear programs. We show oil both synthetic and real data that for the vast majority of cases we are able to verify optimality. Further more we show even if the above test fails it is still often possible to verify that the local solution is global with high probability.

M3 - Paper in conference proceeding

VL - 5575

SP - 686

EP - 695

BT - Image Analysis, Proceedings

PB - Springer

T2 - 16th Scandinavian Conference on Image Analysis

Y2 - 15 June 2009 through 18 June 2009

ER -