Direct Computation of Qualitative 3-D Shape and Motion Invariants

Daphna Weinshall*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


Structure from motion often refers to the computation of 3-D structure from a matched sequence of images. However, a depth map of a surface is difficult to compute and may not be a good representation for storage and recognition. Given matched images, this correspondence will show that the sign of the normal curvature in a given direction at a given point in the image can be computed from a simple difference of slopes of line segments in one image. Using this result, local surface patches can be classified as convex, concave, cylindrical, hyperbolic (saddle point) or planar. At the same time, the translational component of the optical flow is obtained, from which the focus of expansion can be computed.

Original languageAmerican English
Pages (from-to)1236-1240
Number of pages5
JournalIEEE Transactions on Pattern Analysis and Machine Intelligence
Issue number12
StatePublished - Dec 1991
Externally publishedYes


  • Focus of expansion
  • Gaussian curvature
  • motion
  • qualitative
  • structure from motion
  • surface classification
  • vision


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