Lie Groups and Lie Algebras in Video Tracking.

Abstract

When a three-dimensional dynamic scene is projected to a two-dimensional image plane, a complex class of motions are observed, which may be approximated by translation and linear transformation. In this report, we show how such motion may be resolved into principal components and measured from 2-dimensional data. Lie theoretic techniques are used to obtain a motion model, and to incorporate generalized velocity measurements in a closed loop feedback tracker. Stability of numerical calculations is enhanced by a method based on an application of Stoke's Theorem to certain differential 2-forms. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Oct 26, 1981
Accession Number
ADA107858

Entities

People

  • Thomas G. Newman

Organizations

  • Texas Tech University

Tags

Communities of Interest

  • Weapons Technologies

DTIC Thesaurus Topics

  • Algebra
  • Algorithms
  • Analytic Functions
  • Computer Programs
  • Coordinate Systems
  • Differential Equations
  • Dynamic Range
  • Equations
  • Lie Groups
  • Mathematics
  • Military Research
  • Procedures (Computers)
  • Simulations
  • Stratified Fluids
  • Targets
  • Three Dimensional
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Control Systems Engineering.
  • Human-Computer Interaction (HCI).