文件名称：Supervised Descent Method and its Applications to Face Alignment
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更新时间：2017-02-03 13:15:20
Supervised Descent Method
Many computer vision problems (e.g., camera calibration, image alignment, structure from motion) are solved through a nonlinear optimization method. It is generally accepted that 2 nd 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, 2 nd order descent methods have two main drawbacks: (1) The function might not be analytically differentiable and numerical approximations are impractical. (2) The Hessian might be large and not positive definite. To address these issues, this paper proposes a Supervised Descent Method (SDM) for minimizing a Non-linear Least Squares (NLS) function. During training, the SDM learns a sequence of descent directions that minimizes the mean of NLS functions sampled at different points. In testing, SDM minimizes the NLS objective using the learned descent directions without computing the Jacobian nor the Hessian. We illustrate the benefits of our approach in synthetic and real examples, and show how SDM achieves state-ofthe-art performance in the problem of facial feature detection. The code is available at www.humansensing.cs. cmu.edu/intraface. 1. Introduction Mathematical optimization has a fundamental impact in solving many problems in computer vision. This fact is apparent by having a quick look into any major conference in computer vision, where a significant number of papers use optimization techniques. Many important problems in computer vision such as structure from motion, image alignment, optical flow, or camera calibration can be posed as solving a nonlinear optimization problem. There are a large number of different approaches to solve these continuous nonlinear optimization problems based on first and second order methods, such as gradient descent [1] for dimensionality reduction, Gauss-Newton for image alignment [22, 5, 14] or Levenberg-Marquardt for structure from motion [8]. “I am hungry. Where is the apple? Gotta do Gradient descent”