Many computer vision problems are formulated as the optimization of a cost function. This approach faces two main challenges: designing a cost function with a local optimum at an acceptable solution, and developing an efficient numerical method to search for this optimum. While designing such functions is feasible in the noiseless case, the stability and location of local optima are mostly unknown under noise, occlusion, or missing data. In practice, this can result in undesirable local optima or not having a local optimum in the expected place. On the other hand, numerical optimization algorithms in high-dimensional spaces are typically local and often rely on expensive first or second order information to guide the search. To overcome these limitations, we propose Discriminative Optimization (DO), a method that learns search directions from data without the need of a cost function. DO explicitly learns a sequence of updates in the search space that leads to stationary points that correspond to the desired solutions. We provide a formal analysis of DO and illustrate its benefits in the problem of 3D registration, camera pose estimation, and image denoising. We show that DO outperformed or matched state-of-the-art algorithms in terms of accuracy, robustness, and computational efficiency.

中文翻译：

---

判别优化：计算机视觉的理论和应用

许多计算机视觉问题被表述为成本函数的优化。这种方法面临两个主要挑战：设计具有可接受最优解的局部最优成本函数，并开发一种有效的数值方法来寻找最优值。尽管在无噪声的情况下设计此类功能是可行的，但是在噪声，遮挡或丢失数据的情况下，局部最优的稳定性和位置通常是未知的。实际上，这可能导致不希望的局部最优或在预期位置没有局部最优。另一方面，高维空间中的数值优化算法通常是局部的，通常依赖于昂贵的一阶或二阶信息来指导搜索。为了克服这些限制，我们提出了判别优化（DO），一种无需费用函数即可从数据中学习搜索方向的方法。DO明确学习搜索空间中的一系列更新，这些更新导致对应于所需解的固定点。我们提供了DO的形式分析，并说明了其在3D配准，相机姿态估计和图像降噪方面的优势。我们显示出DO在准确性，鲁棒性和计算效率方面优于或匹配最新的算法。