Advertisement
Published in:
2009 | OriginalPaper | Chapter
Globally Optimal Least Squares Solutions for Quasiconvex 1D Vision Problems
Authors : Carl Olsson, Martin Byröd, Fredrik Kahl
Published in: Image Analysis
Publisher: Springer Berlin Heidelberg
Activate our intelligent search to find suitable subject content or patents.
Select sections of text to find matching patents with Artificial Intelligence. powered by
Select sections of text to find additional relevant content using AI-assisted search. powered by
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 an 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 on 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.