Global supervised descent method

Mathematical optimization plays a fundamental role in solving many problems in computer vision (e.g., camera calibration, image alignment, structure from motion). 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. Recently, Supervised Descent Method (SDM), a method that learns the “weighted averaged gradients” in a supervised manner has been proposed to solve these issues. However, SDM is a local algorithm and it is likely to average conflicting gradient directions. This paper proposes Global SDM (GSDM), an extension of SDM that divides the search space into regions of similar gradient directions. GSDM provides a better and more efficient strategy to minimize non-linear least squares functions in computer vision problems. We illustrate the effectiveness of GSDM in two problems: non-rigid image alignment and extrinsic camera calibration.