Uniqueness and Estimation of Three-Dimensional Motion Parameters of Rigid Objects with Curved Surfaces

Abstract

The authors show that seven pilot correspondences are sufficient to uniquely determine from two perspective views the three-dimensional motion parameters (within a scale factor for the translations) of a rigid object with curved surfaces. The seven points should not be traversed by two planes with one plane containing the origin, nor by a cone containing the origin. A set of essential parameters are introduced which uniquely determine the motion parameters up to a scale factor for the translations, and can be estimated by solving a set of linear equations which are derived from the correspondences of eight image points. The actual motion parameters can subsequently be determined by computing the singular value decomposition of a 3x3 matrix containing the essential parameters. No nonlinear equations need be solved.

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Document Details

Document Type
Technical Report
Publication Date
Oct 30, 1981
Accession Number
ADA125825

Entities

People

  • R. Y. Tsai
  • T. S. Huang

Organizations

  • University of Illinois Urbana–Champaign

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Air Force
  • Cameras
  • Cartography
  • Computations
  • Computer Programming
  • Computer Vision
  • Coordinate Systems
  • Decomposition
  • Electrical Engineering
  • Equations
  • Geometry
  • Illinois
  • Image Processing
  • Lie Groups
  • Sequence Analysis
  • Sequences
  • Three Dimensional

Readers

  • Calculus or Mathematical Analysis
  • Computer Vision.