求解计算机视觉中非线性最小二乘问题的监督下降法
Supervised Descent Method for Solving Nonlinear Least Squares Problems in Computer Vision
摘要：
许多计算机视觉问题（例如，摄像机校准、图像对准、运动恢复结构运动恢复结构）。一般认为二阶下降法是求解一般光滑函数的非线性优化问题的最稳健、最快速、最可靠的方法。然而，在计算机视觉的背景下，二阶下降方法具有两个主要缺点：（1）函数可能不是解析可微的并且数值近似是不切实际的，以及（2）Hessian可能很大并且不是正定的。为了解决这些问题，本文提出了通用的下降图，这是平均的“下降方向”和重新调整的因素，在监督的方式学习。使用一般下降映射，我们得到了一个实用的算法-监督下降法（SDM）-最小化非线性最小二乘（NLS）问题。在训练过程中，SDM学习一系列适当的映射，使NLS最小化。在测试中，SDM使用学习的下降映射最小化NLS目标，而不计算雅可比矩阵或海森矩阵。我们证明的条件下，SDM是保证收敛。我们说明了SDM的有效性和准确性在三个计算机视觉问题：刚性图像对齐，非刚性图像对齐，三维姿态估计。特别是，我们将展示SDM如何在面部特征检测问题中实现最先进的性能。该守则已在www.humansensing.cs.cmu.edu/intraface上公布。
英文摘要：
Many computer vision problems (e.g., camera calibration, image alignment, structure from motion) are solved with nonlinear optimization methods. It is generally accepted that second order descent methods are the most robust, fast, and reliable approaches for nonlinear optimization of a general smooth function. However, in the context of computer vision, second order descent methods have two main drawbacks: (1) the function might not be analytically differentiable and numerical approximations are impractical, and (2) the Hessian may be large and not positive definite. To address these issues, this paper proposes generic descent maps, which are average "descent directions" and rescaling factors learned in a supervised fashion. Using generic descent maps, we derive a practical algorithm - Supervised Descent Method (SDM) - for minimizing Nonlinear Least Squares (NLS) problems. During training, SDM learns a sequence of decent maps that minimize the NLS. In testing, SDM minimizes the NLS objective using the learned descent maps without computing the Jacobian or the Hessian. We prove the conditions under which the SDM is guaranteed to converge. We illustrate the effectiveness and accuracy of SDM in three computer vision problems: rigid image alignment, non-rigid image alignment, and 3D pose estimation. In particular, we show how SDM achieves state-of-the-art performance in the problem of facial feature detection. The code has been made available at www.humansensing.cs.cmu.edu/intraface.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
