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

Roger Y. Tsai, Thomas S. Huang

Research output: Contribution to journalArticlepeer-review


Two main results are established in this paper. First, we show that seven point 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. Second, 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 (SVD) of a 3 × 3 matrix containing the essential parameters.

Original languageEnglish (US)
Pages (from-to)13-27
Number of pages15
JournalIEEE transactions on pattern analysis and machine intelligence
Issue number1
StatePublished - Jan 1984
Externally publishedYes


  • Dynamic scene analysis
  • Index Terms
  • image sequence analysis
  • motion estimation
  • motion stereo
  • optical flow

ASJC Scopus subject areas

  • Software
  • Computer Vision and Pattern Recognition
  • Computational Theory and Mathematics
  • Artificial Intelligence
  • Applied Mathematics


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