Volume 38 #2

Contents

1. The characteristic features of the auditory neurons responses in terrestrial vertebrates to species-specific communication calls (analytical review)
2. Clinical physiology of the central parts of the visual system
3. Insect ocelli: ecology, physiology, and morphology of the accessory visual system
4. Identification of speaker gender by voice characteristics under background of multi-talker noise
5. Recognition of projectively transformed planar figures. XVII. Using plucker’s reciprocity theorem to describe ovals with an external fixed point

An approach to a projectively invariant description of a family of ovals (o) in scenes where the figure o is given in a composition with an external point, P, fixed in its plane is considered, and in cases where o has hidden symmetries (central or axial), the position of P is not specified in the form of an additional condition defining the scene, but can be calculated through the symmetry parameters. The invariant description, as a general universal method for numerical processing of compositions like “o + ext-P”, is proposed to be implemented in the form of Wurf mappings.The method uses the apparatus of dual pairs (DP) and wurf functions,previously developed and described by us, which are a product of decomposition of statements of the reciprocity theorem proposed by J. Plьcker to describe the properties of quadratic curves (conics).Illustrated examples of special cases of the “o + ext-P”composition are considered and discussed, actually completing the topic of studying the scenes like “an oval and a linear element of the plane”, which are classified according to the types of symmetry of o.

Key words: oval, center and axis of symmetry, Plücker pole and polar curve, dual pair, harmonic wurf, planar wurf, wurf function, descriptor, Lamй curve

DOI: 10.31857/S0235009224020059  EDN: DDKZPO

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