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.

将模型拟合到受噪声和离群值污染的数据是计算机视觉中的常见任务，通常可以通过最大化离群值来解决。大多数现有方法不能保证全局最优，这是由于在inlier最大化中广泛使用的两种技术：随机抽样以生成候选模型，以及对残差的硬阈值以对inner和离群值进行分类。在本文中，我们提出了一种确定性全局最优线性模型拟合方法，该方法将负高斯函数用作残差上的软损失函数，并将模型拟合公式化为最小化高斯函数之和。我们导出凸二次函数作为目标函数的下界函数，以便可以通过分支定界算法将其全局最小化。