• 2021 (Vol.35)

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

© 2017 P. P. Nikolayev

Institute for Information Transmission Problems “Kharkevich Institute” RAS, 127994 Moscow, Bolshoy Karetny per., 19

Received 10 Jan 2017

On the basis of model numerical realizations, we propose and discuss the ideas and procedures of projectively-invariant description of ovals, which use our previously developed theory for nding eight projectively-stable points on a gure contour, given that one invariant point has been found earlier (inside the oval or on its contour, regardless of the presence or absence of features of its implicit symmetry). This makes it possible to use this octet for standard description of the curve as a compact descriptor of shape in technical schemes of planar gure classi cation on the basis of the criterion of their projective equivalence. Using the example of a radially symmetric oval, new features of the triad of external invariant points have been described (these points are called elliptical; their positions are determined by the marked internal point of the gure). This triad provides calculating the invariant octet of the oval contour. For an non-symmetric oval with a selected point on its contour, we propose a procedure for fast (o(n) asymptotics) detection of the stable internal point, the coordinates of which determine the descriptor octet sought for. We also consider and discuss some numerical schemes capable of forming such an octet on a curve showing either axial or rotational symmetry. The overall result of the work is the description of the concept of using the mentioned theoretical propositions in the problem of recognition of ovals.

Key words: oval, invariant, projective transformation, wurf mapping, track of elliptical points, cyclic descriptor graph, theorems on the number of invariant points of an oval

Cite: Nikolayev P. P. Raspoznavanie proektivno preobrazovannykh ploskikh figur. x. metody poiska okteta invariantnykh tochek kontura ovala – itog vklyucheniya razvitoi 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]. 2017. V. 31(3). P. 202-226 (in Russian).


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