Recognition of projectively transformed planar gures. XI. A new methods for detecting projectively-invariant points of an oval

© 2017 P. P. Nikolayev

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

Received 14 Feb 2017

On the basis of numerical simulations performed, we state and discuss approaches and procedures for projectively- invariant description of ovals, which use our previously developed theory and technique of ht-contours in the problem of nding eight invariant points on a gure contour, given that the curve shows either axial or radial implicit symmetry. It is demonstrated that a similar octet of stable contour points can be obtained by introducing subsidiary structures of ht-polar lines and notes of the developed theory, including those for curves showing no symmetry features and being de ned along with an a priori selected point on the plane of the gure (either inside or outside of its contour). The detected octet, {Ci}, allows computing a compact descriptor of the oval shape on the wurf plane. This descriptor can be used for low-costidenti cation of a curve with respect to the projective equivalence class. Using the examples of ovals of two types of symmetry, we consider some new iterative schemes for detecting their basic elements (the positions of the centers or the axes), the adequate localization of which ensures computation of {Ci}. The key stages of curve recognition procedures (successively engaged schemes of analysis, search, and representation) do not exceed the o(n) threshold of the algorithm complexity, which shows high potentials of their use in systems of automatic analysis of object geometry. We outline the aspects of the suggested theory, further development of which might turn the developed heuristic methods into universal schemes for description of smooth planar curves.

Key words: projective invariant, wurf mapping, symmetry elements, ht-contour, descriptor octet {Ci}, theorems on the number and the properties of invariant points of an oval

Cite: Nikolayev P. P.. Raspoznavanie proektivno preobrazovannykh ploskikh figur. xi. novye metody poiska proektivno invariantnykh tochek ovala [Recognition of projectively transformed planar gures. xi. a new methods for detecting projectively-invariant points of an oval]. Sensornye sistemy [Sensory systems]. 2017. V. 31(4). P. 343-362 (in Russian).

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