On the Projective Equivalence of Rational Algebraic Curves


Gözütok U., Çoban H. A. , Sağıroğlu Y.

18th International Geometry Symposium, 12 - 13 July 2021, vol.1, pp.66

  • Publication Type: Conference Paper / Summary Text
  • Volume: 1
  • Page Numbers: pp.66

Abstract

Detecting equivalences of curves is widely studied in the literature, as it directly contributes to fields such as computer vision, computer graphics and pattern recognition. However, it is difficult to find enough studies when the subject is projective equivalences. Recently Hauer and Jüttler published a study [1] in which the projective equivalences of curves were studied comprehensively. In their paper, the authors proposed two methods, which they called the direct method and the reduced method. In this talk, we discuss the answer to the question "Is it possible to solve the problem of detecting projective equivalences of curves with the arguments of differential geometry?". In the light of the results we have obtained, it will be possible to say that the answer to this question is positive, with fast and effective algorithms created by using differential invariants.