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Volume 36 #1

Contents

  1. An overview of the visual acuity assessment. 2. Theoretical and clinical requirements to the optotypes and chart designs
  2. Assessment of peripheral visual acuity in various conditions of testing
  3. The expression and function of components of signaling cascades of taste, olfactory, and phototransduction in mammalian pancreas beta-cells
  4. Recognition of projectively transformed planar figures. XVI The octet of projectively stable vertices of the oval and new methods for its reference description using the octet
  5. Heteroscedasticity correction to improve tomographic reconstruction with an algebraic approach

Recognition of projectively transformed planar figures. XVI The octet of projectively stable vertices of the oval and new methods for its reference description using the octet

© 2022 P. P. Nikolaeva,b

aInstitute for Information Transmission Problems “Kharkevich Institute” RAS 127994 Moscow, Bolshoy Karetny per., 19, Russia
bSmart Engines Service LLC 117312 Moscow, Prospect 60-Letiya Oktyabrya, 9, Russia

Received 25 Aug 2021

I propose the idea of the existence of an octet of projectively invariant vertices of an oval (o), which are obtained under the condition of the numerical localization of an external straight line, HL (“horizon line”), which is fixed at the stage of optical registration of the figure o or is calculated in the presence of central symmetry properties of the curve by fast algorithms searching for the center that determines the position of HL. The proposed idea is then illustrated by model experiments. According to the theorem on an arbitrary external line, L, composed with o, the line L always contains at least two pairs of stable points (called dual points – DP), and each DP defines an invariant quartet of vertices on o, as a result of successful positional estimation of which the contour appears to have a set of eight ordered vertices, and it is expedient to use this set for a projectively-invariant description of o. Two hypotheses for HL are expressed and investigated in simulations: about the projective relationship between the positions of two DP pairs and about the possibility, for an axially symmetric o, to estimate the position of its inherent HL on the basis of some projective features revealed for DP. Two novel methods for finding the center of o with hidden radial symmetry are also described. Finally, I have proposed and tested in numerical experiments a pair of new methods for using the octet of stable contour points, found for o (either symmetric or not), for a projectively-invariant description of o.

Key words: oval, center and axis of symmetry, Plucker pole and polar curve, dual pairs, harmonic wurf, wurf function, descriptor, descriptor template, Lamé curve

DOI: 10.31857/S023500922201005X

Cite: Nikolaev P. P. Raspoznavanie proektivno preobrazovannykh ploskikh figur. xvi. oktet proektivno stabilnykh vershin ovala i novye metody etalonnogo ego opisaniya, ispolzuyushchie oktet [Recognition of projectively transformed planar figures. xvi the octet of projectively stable vertices of the oval and new methods for its reference description using the octet]. Sensornye sistemy [Sensory systems]. 2022. V. 36(1). P. 61–89 (in Russian). doi: 10.31857/S023500922201005X

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