Moment and Hypergeometric Filters for High Precision Computation ofFocus, Stereo and Optical Flow

  • Authors:

  • Yalin Xiong;Steven A. Shafer

  • Affiliations:

  • The Robotics Institute, Carnegie Mellon University, Pittsburgh, PA 15213-3890, USA/ E-mail: yx@cs.cmu.edu, sas@cs.cmu.edu;The Robotics Institute, Carnegie Mellon University, Pittsburgh, PA 15213-3890, USA/ E-mail: yx@cs.cmu.edu, sas@cs.cmu.edu

  • Venue:
  • International Journal of Computer Vision
  • Year:
  • 1997

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Abstract

Many low level visual computation problems such as focus, stereo,optical flow, etc., can be formulated as problems ofextracting one or moreparameters of a non-stationary transformation betweentwo images. Finite-width windows are widely used in various algorithmsto extract spatially local information from images. While the choice of window width has a very profound impacton the quality of algorithmic results, there has been noquantitative way to measure or eliminate the negative effects offinite-width windows. To address this problem and the foreshorteningproblem caused by non-stationarity, we introduce two novelsets of filters: “moment” filters and“hypergeometric” filters. The recursive properties ofthese filters allow the effects of finite-width windows andforeshortening to be explicitly analyzed and eliminated.We apply the moment filter approach to the focusand stereo problems, in which one parameter is extracted at everypixel location. We apply the hypergeometric approach to the opticalflow problem, in which two parameters are extracted. We demonstratethat algorithms based on moment filters and hypergeometric filtersachieve much higher precision than other state-of-art techniques.