Maximum Consensus Parameter Estimation by Reweighted $\ell_1$ Methods
This work addresses the need for efficient and accurate robust parameter estimation in computer vision, offering a practical solution that improves upon slow global optimizers and approximate randomized methods, though it is incremental as it builds on iterative reweighted techniques.
The paper tackles the maximum consensus (MaxCon) problem for robust parameter estimation in computer vision by proposing an iterative reweighted algorithm based on a smooth surrogate function, which is shown to be very efficient and often yields the global solution, making it an attractive alternative to existing randomized and global methods.
Robust parameter estimation in computer vision is frequently accomplished by solving the maximum consensus (MaxCon) problem. Widely used randomized methods for MaxCon, however, can only produce {random} approximate solutions, while global methods are too slow to exercise on realistic problem sizes. Here we analyse MaxCon as iterative reweighted algorithms on the data residuals. We propose a smooth surrogate function, the minimization of which leads to an extremely simple iteratively reweighted algorithm for MaxCon. We show that our algorithm is very efficient and in many cases, yields the global solution. This makes it an attractive alternative for randomized methods and global optimizers. The convergence analysis of our method and its fundamental differences from the other iteratively reweighted methods are also presented.