GORFLM: Globally Optimal Robust Fitting for Linear Model
Abstract Fitting a model to data contaminated by noise and outliers is a common task in computer vision, and it is often solved by maximizing inlier set. Most existing methods cannot guarantee global optimality, due to the two techniques widely utilized in inlier maximization: randomized sampling to generate candidate models and a hard threshold on residuals to classify inliers and outliers. In this paper, we propose a deterministic globally optimal linear model fitting method, in which we use the negative Gaussian function as a soft loss function over the residual and formulate model fitting as minimizing the sum of the Gaussian functions. We derive a convex quadratic function as the lower bound function of the objective function so that it can be globally minimized by a branch and bound algorithm. Experiments showed that the proposed method outperformed the state of the art methods on several typical CV problems, especially when there are multiple models with different noise levels and large number of data points.
Signal Process. Image Commun.