Proceedings: GI 2000

A Fast, Space-Efficient Algorithm for the Approximation of Images by an Optimal Sum of Gaussians

Jeffrey Childs , Cheng-Chang Lu , Jerry Potter

Proceedings of Graphics Interface 2000: Montréal, Québec, Canada, 15 - 17 May 2000, 153-162

DOI 10.20380/GI2000.21

  • BibTeXex

    @inproceedings{Childs-gi2000,
     title = {A Fast, Space-Efficient Algorithm for the Approximation of Images by an Optimal Sum of Gaussians},
     author = {Jeffrey Childs and Cheng-Chang Lu and Jerry Potter},
     booktitle = {Proceedings of the Graphics Interface 2000 Conference, May 15-17, 2000, Montr{'{e}}al, Qu{'{e}}bec, Canada},
     year = {2000},
     month = {May},
     pages = {153--162},
     url = {http://graphicsinterface.org/wp-content/uploads/gi2000-21.pdf}
    }
    

Abstract

Gaussian decomposition of images leads to many promising applications in computer graphics. Gaussian representations can be used for image smoothing, motion analysis, and feature selection for image recognition. Furthermore, image construction from a Gaussian representation is fast, since the Gaussians only need to be added together. The most optimal algorithms [3, 6, 7] minimize the number of Gaussians needed for decomposition, but they involve nonlinear least-squares approximations, e.g. the use of the Marquardt algorithm [10]. This presents a problem, since, in the Marquardt algorithm, enormous amounts of computations are required and the resulting matrices use a lot of space. In this work, a method is offered, which we call the Quickstep method, that substantially reduces the number of computations and the amount of space used. Unlike the Marquardt algorithm, each iteration has linear time complexity in the number of variables and no Jacobian or Hessian matrices are formed. Yet, Quickstep produces optimal results, similar to those produced by the Marquardt algorithm.