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We have shown how Supervised Descent Method outperforms state-of-the-art approaches in facial feature detection and tracking in challenging databases

Supervised Descent Method and Its Applications to Face Alignment

CVPR, no. 1 (2013): 532-539

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摘要

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 2nd order descent methods are the most robust, fast and reliable approaches for nonlinear optimization of a general smooth function. However, in the context of c...更多

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简介
  • Mathematical optimization has a fundamental impact in solving many problems in computer vision.
  • 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].
重点内容
  • Mathematical optimization has a fundamental impact in solving many problems in computer vision
  • The Supervised Descent Method learns a sequence of descent directions that minimizes the mean of Non-linear Least Squares functions sampled at different points
  • This paper presents Supervised Descent Method, a method for solving Non-linear Least Squares problems
  • Supervised Descent Method learns in a supervised manner generic descent directions, and is able to overcome many drawbacks of second order optimization schemes, such as nondifferentiability and expensive computation of the Jacobians and Hessians
  • We have shown how Supervised Descent Method outperforms state-of-the-art approaches in facial feature detection and tracking in challenging databases
  • Eq 3 allows to establish a direct connection with existing Parameterized Appearance Models for face alignment, and apply existing algorithms for minimizing it such as Gauss-Newton
方法
  • The first experiment compares the SDM with the Newton method in four analytic functions.
  • The authors tested the performance of the SDM in the problem of facial feature detection in two standard databases.
  • SDM on analytic scalar functions.
  • This experiment compares the performance in speed and accuracy of the SDM against the Newton’s method on four analytic functions.
结果
  • The authors show how SDM improves state-of-the-art performance for facial feature detection in two “face in the wild” databases [26, 4] and demonstrate extremely good performance tracking faces in the YouTube celebrity database [20].
  • The standard deviations of the scaling and translational perturbation were set to 0.05 and 10, respectively
  • It indicates that in two consecutive frames the probability of a tracked face shifting more than 20 pixels or scaling more than 10% is less than 5%.
  • The authors have shown how SDM outperforms state-of-the-art approaches in facial feature detection and tracking in challenging databases
结论
  • SDM learns in a supervised manner generic descent directions, and is able to overcome many drawbacks of second order optimization schemes, such as nondifferentiability and expensive computation of the Jacobians and Hessians.
  • It is extremely fast and accurate.
  • Eq 3 allows to establish a direct connection with existing PAMs for face alignment, and apply existing algorithms for minimizing it such as Gauss-Newton
表格
  • Table1: Experimental setup for the SDM on analytic functions
Download tables as Excel
基金
  • This work is partially supported by the National Science Foundation (NSF) under the grant RI-1116583 and CPS0931999
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