PATTERN RECOGNITION

Projective correspondence method for an oval with two fixed points

A. V. Savchik, P. P. Nikolaev

Visual Systems Lab (№11), Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Moscow, Russia

Abstract: 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 $O(n^2\log(n))$ is presented. The algorithm is based on the full search of the fixed points. The specified construction is used is an intermediate step.

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

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