Using Symbolic Computation to Find Algebraic Invariants

Research output: Contribution to journalArticlepeer-review


Implicit polynomials have proved themselves as having excellent representation power for complicated objects, and there is growing use of them in computer vision, graphics, and CAD. A must for every system that tries to recognize objects based on their representation by implicit polynomials are invariants, which are quantities assigned to polynomials that do not change under coordinate transformations. In the recognition system developed at the Laboratory for Engineering Man-Machine Studies in Brown University (LEMS), it became necessary to use invariants which are explicit and simple functions of the polynomial coefficients. A method to find such invariants is described and the new invariants presented. This work addresses only the problem of finding the invariants; their stability is studied in another paper.

Original languageEnglish
Pages (from-to)1143-1149
Number of pages7
JournalIEEE Transactions on Pattern Analysis and Machine Intelligence
Issue number11
StatePublished - Nov 1994
Externally publishedYes

Bibliographical note

Funding Information:
Manuscript received September 11, 1992; revised January 24, 1994. Supported in part by NSF Grant #IRI-8715774 and NSF-DAIWA Grant #IRI-8905436. Recommended for acceptance by Associate Editor R. Nevatia. The author is with the Laboratory for Engineering Man/Machine Systems, Division of Engineering, Brown University, Providence, RI 02912 USA, e-mail: IEEE Log Number 9405787.

ASJC Scopus subject areas

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


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