A. V. Savchik P. P. Nikolaev Projective correspondence method for an oval with two fixed points
A. V. Savchik P. P. Nikolaev Projective correspondence method for an oval with two fixed points


In this paper, we study projective invariants for general configuration of an oval and two fixed points on its contour. We prove that there are at least two ways to extend such a configuration to an oval with three fixed points, which has a projectively invariant property of Cevians intersection. The proof is based on the construction of ellipses tangent to the oval at three points: inscribed and outscribed. An algorithm for the projective comparison of two ovals of a general type with computational complexity O(n2log(n)) is presented. The algorithm is based on the full search of the fixed points. The specified construction is used is an intermediate step.


projective geometry, projective invariants, inellipse, inscribed and outscribed ellipses.

pp. 60-67 


1. Shemiakina J.A. 2017. Ispol'zovanie tochek i prjamyh dlja vychislenija proektivnogo preobrazovanija po dvum izobrazhenijam ploskogo ob'ekta [The Usage of Points and Lines for the Calculation of Projective Transformation by Two Images of One Plane Object] Informacionnye tehnologii i vychislitel'nye sistemy [Information Technologies and Computing Systems]. (3) P. 79-91.
2. Novikov A.I., Sablina V.A., Nikiforov M.B., Loginov A.A. 2015. The contour analysis and image-superimposition problem in computer vision systems. Pattern recognition and image analysis. 25(1): 73–80.
3. Nikolaev P.P. 2015. Raspoznavanie proektivno preobrazovannyh ploskih figur. I. Analiz i invriantnoe otobrazheniesostavnyh ovalov [Recognition of Projectively Transformed Planar Figures. I: Analysis and Invariant Mapping of Segmented Ovals]. Sensornye sistemy [Sensory Systems]. 25(2): 118–137.
4. Nikolaev P.P. 2015. Raspoznavanie proektivno preobrazovannyh ploskih figur. VIII. O vychislenii ansamblya rotacionnoj korrespondencii ovalov s simmetriej vrashcheniya [Recognition of projectively transformed planar figures. VIII. On computation of the ensemble of correspondence for “rotationally symmetric” ovals]. Sensornye sistemy [Sensory Systems]. 29(1): 28–55.
5. Seliverstov A.V. 2016. O simmetrii proektivnyh krivyh [On symmetry of projective curves] Vestnik TVGU. Seriya: Prikladnaya Matematika [Herald of Tver State University. Series: Applied Mathematics]. (3): 59–66.
6. Nikolaev P.P. 2015. Raspoznavanie proektivno preobrazovannyh ploskih figur. IX. Metody opisaniya ovalov s fiksirovannoj tochkoj na konture [Recognition of projectively transformed planar fi gures. IX. Methods for description of ovals with a fi xed point on the contour]. Sensornye sistemy [Sensory Systems] 29(3): 213–244.
7. Savchik A.V., Nikolaev P.P. 2016. Teorema o peresechenii T- i H-polyar [The Theorem of T- and H- Polars Intersections Count]. Informacionnye processy [Information Processes]. 2016. 16(4): 430–443. Available at: (accessed August 31, 2017).
8. Nikolaev P.P. 2017. Raspoznavanie proektivno preobrazovannyh ploskih figur. X. Metody poiska okteta invariantnyh tochek kontura ovala - itog vklyucheniya razvitoj teorii v skhemy ego opisaniya [Recognition of projectively transformed planar figures. X. Methods for finding an octet of invariant points of an oval contour - the result of introducing a developed theory into the schemes of oval description]. Sensornye sistemy [Sensory Systems]. 31(3): 202–226.
9. Anil Maheshwari, Jörg-Rüdiger Sack, Kaveh Shahbaz, Hamid Zarrabi-Zadeh. 2011. Improved Algorithms for Partial Curve Matching. Algorithms – ESA 2011: 19th Annual European Symposium, Saarbrucken, Germany, September 5-9, 2011. Proceedings Ed. By Camil Demetrescu, Magnus M. Halldorsson. Springer Berlin Heidelberg. 518–529. Available at:


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