Optimization by Gaussian Smoothing

Optimization Landscape from the Paper "Seeing through the Blur"

About the Method
A well-known heuristic for optimization of non-convex objective functions is coarse-to-fine continuation method. Specifically, this method drastically smoothes the objective in hope of making it convex and hence easy to solve. Then, it follows the path of that minimizer all the way while graually deforming the objective back to the original. This heuristic has empirically shown to attain reasonable solution in some challenging non-convex optimization tasks, including but not limited to signal alignment. The goal of this project is to provide a deeper theoretical understanding about this heuristic, and also to present guidelines on how to efficiently utilize this method in specific application domains.
Related Papers
  • Basic Definitions and Asymptotic Convexity Conditions:
    "Gaussian Smoothing and Asymptotic Convexity"
    Hossein Mobahi, Yi Ma, Technical Report UILU-ENG-12-2201 (DC-254), UIUC, March 2012 [PDF]. [BibTeX]

  • Application of Gaussian Smoothing to Image Alignment through Blur Operators
    "Seeing through the Blur"
    Hossein Mobahi, C. Lawrence Zitnick, Yi Ma, Int. Conf. on Computer Vision and Pattern Recognition (CVPR 2012). Paper [PDF], Poster [PDF], Bibliography [BibTeX].

  • Code
  • Matlab code for reproducing results of the paper "Seeing through the Blur". [alignhomo.m].